Apparent Fractality Emerging from Models of Random Distributions

The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using analytical and numerical calculations it is shown that in the regime of low volume fraction occupied by the spheres, apparent fractal behavior is observed for a range of scales between physically relevant cut-offs. The width of this range, typically spanning between one and two orders of magnitude, is in very good agreement with the typical range observed in experimental measurements of fractals. The dimensions are not universal and depend on density. These observations are applicable to spatial, temporal and spectral random structures. Polydispersivity in sphere radii and impenetrability of the spheres (resulting in short range correlations) are also introduced and are found to have little effect on the scaling properties. We thus propose that apparent fractal behavior observed experimentally over a limited range may often have its origin in underlying randomness.Comment: 19 pages, 12 figures. More info available at http://www.fh.huji.ac.il/~dani

Exploring the Bimodal Solar System via Sample Return from the Main Asteroid Belt: The Case for Revisiting Ceres

Abstract: Sample return from a main-belt asteroid has not yet been attempted, but appears technologically feasible. While the cost implications are significant, the scientific case for such a mission appears overwhelming. As suggested by the “Grand Tack” model, the structure of the main belt was likely forged during the earliest stages of Solar System evolution in response to migration of the giant planets. Returning samples from the main belt has the potential to test such planet migration models and the related geochemical and isotopic concept of a bimodal Solar System. Isotopic studies demonstrate distinct compositional differences between samples believed to be derived from the outer Solar System (CC or carbonaceous chondrite group) and those that are thought to be derived from the inner Solar System (NC or non-carbonaceous group). These two groups are separated on relevant isotopic variation diagrams by a clear compositional gap. The interface between these two regions appears to be broadly coincident with the present location of the asteroid belt, which contains material derived from both groups. The Hayabusa mission to near-Earth asteroid (NEA) (25143) Itokawa has shown what can be learned from a sample-return mission to an asteroid, even with a very small amount of sample. One scenario for main-belt sample return involves a spacecraft launching a projectile that strikes an object and flying through the debris cloud, which would potentially allow multiple bodies to be sampled if a number of projectiles are used on different asteroids. Another scenario is the more traditional method of landing on an asteroid to obtain the sample. A significant range of main-belt asteroids are available as targets for a sample-return mission and such a mission would represent a first step in mineralogically and isotopically mapping the asteroid belt. We argue that a sample-return mission to the asteroid belt does not necessarily have to return material from both the NC and CC groups to viably test the bimodal Solar System paradigm, as material from the NC group is already abundantly available for study. Instead, there is overwhelming evidence that we have a very incomplete suite of CC-related samples. Based on our analysis, we advocate a dedicated sample-return mission to the dwarf planet (1) Ceres as the best means of further exploring inherent Solar System variation. Ceres is an ice-rich world that may be a displaced trans-Neptunian object. We almost certainly do not have any meteorites that closely resemble material that would be brought back from Ceres. The rich heritage of data acquired by the Dawn mission makes a sample-return mission from Ceres logistically feasible at a realistic cost. No other potential main-belt target is capable of providing as much insight into the early Solar System as Ceres. Such a mission should be given the highest priority by the international scientific community

Sequence‐to‐sequence alignment using a pendulum

Analysing two or more video sequences of dynamic scenes typically requires time synchronisation between sequences, where this alignment is not always possible using hardware. A particular method will most likely process the entire, frequently lengthy, imaged material, requiring additional processing which normally serves for synchronisation only. Software‐based synchronisation methods impose, in basically all cases, certain assumptions about an imaged three‐dimensional (3D) scene and are suited for the already imaged video material in the past. The authors argue that there are applications where the unsynchronised video sequences have not yet been taken. The time‐efficient solution uses a pendulum consisting of a small ball, attached to a 50 cm string and suspended from a pivot so that it can swing freely. The authors estimate the time instant when the ball swings through the equilibrium position. The difference in these times for two cameras yields a subframe time difference between cameras. The proposed method yields subframe differences, statistically no different from ground truth data. 3D reconstruction results for synchronised data clearly outperform those which are unsynchronised. The proposed method relaxes any restrictions and assumptions about the 3D scene that will be imaged later on, yet it allows accurate subframe synchronisation in less than a second

Association of asymptomatic spinal cord lesions and atrophy with disability 5 years after a clinically isolated syndrome

Background: Spinal cord pathology is an important substrate for long-term disability in multiple sclerosis (MS). Objective: To investigate longitudinal changes in spinal cord lesions and atrophy in patients with a non spinal clinically isolated syndrome (CIS), and how they relate to the development of disability. Methods: In all, 131 patients with a non-spinal CIS had brain and spinal cord imaging at the time of CIS and approximately 5 years later (median: 5.2 years, range: 3.0-7.9 years). Brain magnetic resonance imaging (MRI) measures consisted of T2-hyperintense and T1-hypointense lesion loads plus brain atrophy. Spinal cord MRI measures consisted of lesion number and the upper cervical cord cross-sectional area (UCCA). Disability was measured using the Expanded Disability Status Scale (EDSS). Multiple linear regression was used to identify independent predictors of disability after 5 years. Results: During follow-up, 93 (71%) patients were diagnosed with MS. Baseline spinal cord lesion number, change in cord lesion number and change in UCCA were independently associated with EDSS (R-2=0.53) at follow-up. Including brain T2 lesion load and brain atrophy only modestly increased the predictive power of the model (R-2=0.64). Conclusion: Asymptomatic spinal cord lesions and spinal cord atrophy contribute to the development of MS-related disability over the first 5 years after a non-spinal CI