Shadowing Lemma and Chaotic Orbit Determination

Orbit determination is possible for a chaotic orbit of a dynamical system, given a finite set of observations, provided the initial conditions are at the central time. In a simple discrete model, the standard map, we tackle the problem of chaotic orbit determination when observations extend beyond the predictability horizon. If the orbit is hyperbolic, a shadowing orbit is computed by the least squares orbit determination. We test both the convergence of the orbit determination iterative procedure and the behaviour of the uncertainties as a function of the maximum number $n$ of map iterations observed. When the initial conditions belong to a chaotic orbit, the orbit determination is made impossible by numerical instability beyond a computability horizon, which can be approximately predicted by a simple formula. Moreover, the uncertainty of the results is sharply increased if a dynamical parameter is added to the initial conditions as parameter to be estimated. The uncertainty of the dynamical parameter decreases like $n^a$ with $a<0$ but not large (of the order of unity). If only the initial conditions are estimated, their uncertainty decreases exponentially with $n$. If they belong to a non-chaotic orbit the computational horizon is much larger, if it exists at all, and the decrease of the uncertainty is polynomial in all parameters, like $n^a$ with $a\simeq 1/2$. The Shadowing Lemma does not dictate what the asymptotic behaviour of the uncertainties should be. These phenomena have significant implications, which remain to be studied, in practical problems of orbit determination involving chaos, such as the chaotic rotation state of a celestial body and a chaotic orbit of a planet-crossing asteroid undergoing many close approaches

Asteroid family ages

A new family classification, based on a catalog of proper elements with $\sim 384,000$ numbered asteroids and on new methods is available. For the $45$ dynamical families with $>250$ members identified in this classification, we present an attempt to obtain statistically significant ages: we succeeded in computing ages for $37$ collisional families. We used a rigorous method, including a least squares fit of the two sides of a V-shape plot in the proper semimajor axis, inverse diameter plane to determine the corresponding slopes, an advanced error model for the uncertainties of asteroid diameters, an iterative outlier rejection scheme and quality control. The best available Yarkovsky measurement was used to estimate a calibration of the Yarkovsky effect for each family. The results are presented separately for the families originated in fragmentation or cratering events, for the young, compact families and for the truncated, one-sided families. For all the computed ages the corresponding uncertainties are provided. We found 2 cases where two separate dynamical families form together a single V-shape with compatible slopes, thus indicating a single collisional event. We have also found 3 examples of dynamical families containing multiple collisional families, plus a dubious case. We have found 2 cases of families containing a conspicuous subfamily, such that it is possible to measure the slope of a distinct V-shape, thus the age of the secondary collision. We also provide data on the central gaps appearing in some families. The ages computed in this paper are obtained with a single and uniform methodology, thus the ages of different families can be compared, providing a first example of collisional chronology of the asteroid main belt

Testing rTMS-Induced Neuroplasticity: A Single Case Study of Focal Hand Dystonia

Focal hand dystonia in musicians is a neurological motor disorder in which aberrant plasticity is caused by excessive repetitive use. This work's purposes were to induce plasticity changes in a dystonic musician through five daily thirty-minute sessions of 1\u2009Hz repetitive transcranial magnetic stimulation (rTMS) applied to the left M1 by using neuronavigated stimulation and to reliably measure the effect of these changes. To this aim, the relationship between neuroplasticity changes and motor recovery was investigated using fine-grained kinematic analysis. Our results suggest a statistically significant improvement in motor coordination both in a task resembling the dystonic-inducing symptoms and in a reach-to-grasp task. This single case study supports the safe and effective use of noninvasive brain stimulation in neurologic patients and highlights the importance of evaluating outcomes in measurable ways. This issue is a key aspect to focus on to classify the clinical expression of dystonia. These preliminary results promote the adoption of kinematic analysis as a valuable diagnostic tool

Sensation seeking, non-contextual decision making, and driving abilities as measured through a moped simulator.

The general aim of the present study was to explore the relations between driving style (assessed through a moped riding simulator) and psychological variables such as sensation seeking and decision making. Because the influences of sensation seeking and decision making on driving styles have been studied separately in the literature, we have tried to investigate their mutual relations so as to include them in a more integrated framework. Participants rode the Honda Riding Trainer (HRT) simulator, filled in the Sensation Seeking Scale V (SSS V), and performed the Iowa Gambling Task (IGT). A cluster analysis of the HRT riding indexes identified three groups: Prudent, Imprudent, and Insecure riders. First, the results showed that Insecure males seek thrills and adventure less than both Prudent males and Insecure females, whereas Prudent females are less disinhibited than both Prudent males and Insecure females. Moreover, concerning the relations among SSS, decision making as measured by the IGT, and riding performance, high thrill and adventure seekers performed worse in the simulator only if they were also bad decision makers, indicating that these two traits jointly contribute to the quality of riding performance. From an applied perspective, these results also provide useful information for the development of protocols for assessing driving abilities among novice road users. Indeed, the relation between risk proneness and riding style may allow for the identification of road-user populations who require specific training

Teaching Against Hierarchies: An Anarchist Approach

The state of California spends more on prisons than on colleges and universities, and the fact that these two budgetary figures are often compared shows the relationship between the two state institutions. Our classrooms, starting from a very early stage, not only prepare children to be productive members of the consumer economy but educate them for complacency in the face of state violence and mass incarceration. In attempting to move away from hierarchical models of education, this article looks at the feminist pedagogical theory of bell hooks and antiauthoritarian and anarchist theorists such as Jacques Rancière and Derrick Jensen in order to begin investigating alternatives to current education systems. It also identifies major problems in attempting to construct antihierarchical classrooms within a larger society that is still suffering from oppression and structural inequality, and claims that, if not paired with direct action, any attempt for revolutionizing education will meet up against repressive state institutions