Librations and Obliquity of Mercury from the BepiColombo radio-science and camera experiments

A major goal of the BepiColombo mission to Mercury is the determination of the structure and state of Mercury's interior. Here the BepiColombo rotation experiment has been simulated in order to assess the ability to attain the mission goals and to help lay out a series of constraints on the experiment's possible progress. In the rotation experiment pairs of images of identical surface regions taken at different epochs are used to retrieve information on Mercury's rotation and orientation. The idea is that from observations of the same patch of Mercury's surface at two different solar longitudes of Mercury the orientation of Mercury can be determined, and therefore also the obliquity and rotation variations with respect to the uniform rotation. The estimation of the libration amplitude and obliquity through pattern matching of observed surface landmarks is challenging. The main problem arises from the difficulty to observe the same landmark on the planetary surface repeatedly over the MPO mission lifetime, due to the combination of Mercury's 3:2 spin-orbit resonance, the absence of a drift of the MPO polar orbital plane and the need to combine data from different instruments with their own measurement restrictions. By assuming that Mercury occupies a Cassini state and that the spacecraft operates nominally we show that under worst case assumptions the annual libration amplitude and obliquity can be measured with a precision of respectively 1.4 arcseconds (as) and 1.0 as over the nominal BepiColombo MPO lifetime with about 25 landmarks for rather stringent illumination restrictions. The outcome of the experiment cannot be easily improved by simply relaxing the observational constraints, or increasing the data volume.Comment: 30 pages, 6 figures, 2 table

Theoretical models of planetary system formation. II. Post-formation evolution

We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. We use the symplectic integrator SyMBA to numerically integrate the orbits of planets for 100 Ma, using populations from previous studies as initial conditions.We show that within the populations studied, mass and semi-major axis distributions experience only minor changes from post-formation evolution. We also show that, depending upon their initial distribution, planetary eccentricities can statistically increase or decrease as a result of gravitational interactions. We find that planetary masses and orbital spacings provided by planet formation models do not result in eccentricity distributions comparable to observed exoplanet eccentricities, requiring other phenomena such as e.g. stellar fly-bys to account for observed eccentricities

An efficient simulation algorithm for the generalized von Mises distribution of order two

In this article we propose an exact efficient simulation algorithm for the generalized von Mises circular distribution of order two. It is an acceptance-rejection algorithm with a piecewise linear envelope based on the local extrema and the inflexion points of the generalized von Mises density of order two. We show that these points can be obtained from the roots of polynomials and degrees four and eight, which can be easily obtained by the methods of Ferrari and Weierstrass. A comparative study with the von Neumann acceptance-rejection, with the ratio-of-uniforms and with a Markov chain Monte Carlo algorithms shows that this new method is generally the most efficien

Theoretical models of planetary system formation: mass vs semi-major axis

Planet formation models have been developed during the last years in order to try to reproduce the observations of both the solar system, and the extrasolar planets. Some of these models have partially succeeded, focussing however on massive planets, and for the sake of simplicity excluding planets belonging to planetary systems. However, more and more planets are now found in planetary systems. This tendency, which is a result of both radial velocity, transit and direct imaging surveys, seems to be even more pronounced for low mass planets. These new observations require the improvement of planet formation models, including new physics, and considering the formation of systems. In a recent series of papers, we have presented some improvements in the physics of our models, focussing in particular on the internal structure of forming planets, and on the computation of the excitation state of planetesimals, and their resulting accretion rate. In this paper, we focus on the concurrent effect of the formation of more than one planet in the same protoplanetary disc, and show the effect, in terms of global architecture and composition of this multiplicity. We use a N-body calculation including collision detection to compute the orbital evolution of a planetary system. Moreover, we describe the effect of competition for accretion of gas and solids, as well as the effect of gravitational interactions between planets. We show that the masses and semi-major axis of planets are modified by both the effect of competition and gravitational interactions. We also present the effect of the assumed number of forming planets in the same system (a free parameter of the model), as well as the effect of the inclination and eccentricity damping.Comment: accepted in Astronomy and Astrophysic

"Euboean" Pottery from Early Iron Age Eretria in the Light of the Neutron Activation Analysis

We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly in space and links formed independently between pairs of nodes with probability given by a specified function (the "pair connection function") of their mutual distance. We consider the general case where randomness arises in node positions as well as pairwise connections (i.e., for a given pair distance, the corresponding edge state is a random variable). Classical random geometric graph and exponential graph models can be recovered in certain limits. We derive a simple bound for the entropy of a spatial network ensemble and calculate the conditional entropy of an ensemble given the node location distribution for hard and soft (probabilistic) pair connection functions. Under this formalism, we derive the connection function that yields maximum entropy under general constraints. Finally, we apply our analytical framework to study two practical examples: ad hoc wireless networks and the US flight network. Through the study of these examples, we illustrate that both exhibit properties that are indicative of nearly maximally entropic ensembles.Comment: 7 pages, 4 figure

Personennachlässe im digitalen Zeitalter sichern.: Was braucht es von Seiten der Archive?

Spezialarchive wie das Archiv für Zeitgeschichte (AfZ), die Nachlässe von Privatpersonen sammeln, sind mit dem Übergang ins digitale Zeitalter vor grosse Herausforderungen gestellt. Wie alle Institutionen, die Quellen – und damit je länger je mehr auch digitale Quellen – sichern, müssen sie sich intensiv damit beschäftigen, wie diese Quellen übernommen, aufbereitet und langzeitarchiviert werden können, damit sie Nutzern und Nutzerinnen auch in Zukunft als authentische Dokumente zur Verfügung stehen.Die vorliegende Arbeit versucht, anhand der aktuellen Forschungsliteratur, einer eigenen bei einigen exemplarisch ausgewählten Archiven durchgeführten Umfrage sowie anhand von bereits vorhandener Praxiserfahrung im AfZ und weiteren Archiven zu klären, welche Vorgehensweisen bei der Sicherung von digitalen Nachlässen und Personenarchiven verfolgt werden können bzw. in der Praxis bereits als Konzepte existieren oder gar schon Teil des laufenden Archivbetriebs sind. Das Augenmerk liegt dabei auf der strategisch-organisatorischen Ebene, weniger auf technischen Fragen. Die Phase der Bestandsbildung – also die vorarchivische Phase – wird als zentraler Ansatzpunkt für Massnahmen identifiziert, um eine spätere geordnete und möglichst vollständige Übernahme von Personenarchiven in die Archivinstitution zu gewährleisten. Die Frage, wie Bestandsbildner betreut und begleitet werden sollen sowie diejenige nach der Bewertung von digitalen Unterlagen und dem Verhältnis dieser beiden Fragen zueinander, stehen im Zentrum.Die Arbeit schliesst mit einem vorläufigen Fazit und Empfehlungen für das AfZ

Predictive value of midsagittal tissue bridges on functional recovery after spinal cord injury

Background: The majority of patients with spinal cord injury (SCI) have anatomically incomplete lesions and present with preserved tissue bridges, yet their outcomes vary. Objective: To assess the predictive value of the anatomical location (ventral/dorsal) and width of preserved midsagittal tissue bridges for American Spinal Injury Association (ASIA) Impairment Scale (AIS) grade conversion and SCI patient stratification into recovery-specific subgroups. Methods: This retrospective longitudinal study includes 70 patients (56 men, age: 52.36 ± 18.58 years) with subacute (ie, 1 month) SCI (45 tetraplegics, 25 paraplegics), 1-month neuroimaging data, and 1-month and 12-month clinical data. One-month midsagittal T2-weighted scans were used to determine the location and width of tissue bridges. Their associations with functional outcomes were assessed using partial correlation and unbiased recursive partitioning conditional inference tree (URP-CTREE). Results: Fifty-seven (81.4%) of 70 patients had tissue bridges (2.53 ± 2.04 mm) at 1-month post-SCI. Larger ventral (P = .001, r = 0.511) and dorsal (P < .001, r = 0.546) tissue bridges were associated with higher AIS conversion rates 12 months post-SCI (n = 39). URP-CTREE analysis identified 1-month ventral tissue bridges as predictors of 12-month total motor scores (0.4 mm cutoff, P = .008), recovery of upper extremity motor scores at 12 months (1.82 mm cutoff, P = .002), 12-month pin-prick scores (1.4 mm cutoff, P = .018), and dorsal tissue bridges at 1 month as predictors of 12-month Spinal Cord Independence Measure scores (0.5 mm cutoff, P = .003). Conclusions: Midsagittal tissue bridges add predictive value to baseline clinical measures for post-SCI recovery. Based on tissue bridges' width, patients can be classified into subgroups of clinical recovery profiles. Midsagittal tissue bridges provide means to optimize patient stratification in clinical trials

Tissue bridges predict neuropathic pain emergence after spinal cord injury

Objective To assess associations between preserved spinal cord tissue quantified by the width of ventral and dorsal tissue bridges and neuropathic pain development after spinal cord injury. Methods This retrospective longitudinal study includes 44 patients (35 men; mean (SD) age, 50.05 (18.88) years) with subacute (ie, 1 month) spinal cord injury (25 patients with neuropathic pain, 19 pain-free patients) and neuroimaging data who had a follow-up clinical assessment at 12 months. Widths of tissue bridges were calculated from midsagittal T2-weighted images and compared across groups. Regression analyses were used to identify relationships between these neuroimaging measures and previously assessed pain intensity and pin-prick score. Results Pin-prick score of the 25 patients with neuropathic pain increased from 1 to 12 months (Δmean=10.08, 95% CI 2.66 to 17.50, p=0.010), while it stayed similar in pain-free patients (Δmean=2.74, 95% CI −7.36 to 12.84, p=0.576). They also had larger ventral tissue bridges (Δmedian=0.80, 95% CI 0.20 to 1.71, p=0.008) at 1 month when compared with pain-free patients. Conditional inference tree analysis revealed that ventral tissue bridges’ width (≤2.1 or >2.1 mm) at 1 month is the strongest predictor for 12 months neuropathic pain intensity (1.90±2.26 and 3.83±1.19, p=0.042) and 12 months pin-prick score (63.84±28.26 and 92.67±19.43, p=0.025). Interpretation Larger width of ventral tissue bridges—a proxy for spinothalamic tract function—at 1 month post-spinal cord injury is associated with the emergence and maintenance of neuropathic pain and increased pin-prick sensation. Spared ventral tissue bridges could serve as neuroimaging biomarkers of neuropathic pain and might be used for prediction and monitoring of pain outcomes and stratification of patients in interventional trials