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

Asteroid families classification: exploiting very large data sets

The number of asteroids with accurately determined orbits increases fast. The catalogs of asteroid physical observations have also increased, although the number of objects is still smaller than in the orbital catalogs. We developed a new approach to the asteroid family classification by combining the Hierarchical Clustering Method (HCM) with a method to add new members to existing families. This procedure makes use of the much larger amount of information contained in the proper elements catalogs, with respect to classifications using also physical observations for a smaller number of asteroids. Our work is based on the large catalog of the high accuracy synthetic proper elements (available from AstDyS). We first identify a number of core families; to these we attribute the next layer of smaller objects. Then, we remove all the family members from the catalog, and reapply the HCM to the rest. This gives both halo families which extend the core families and new independent families, consisting mainly of small asteroids. These two cases are discriminated by another step of attribution of new members and by merging intersecting families. By using information from absolute magnitudes, we take advantage of the larger size range in some families to analyze their shape in the proper semimajor axis vs. inverse diameter plane. This leads to a new method to estimate the family age (or ages). The results from the previous steps are then analyzed, using also auxiliary information on physical properties including WISE albedos and SDSS color indexes. This allows to solve some difficult cases of families overlapping in the proper elements space but generated by different collisional events. We analyze some examples of cratering families (Massalia, Vesta, Eunomia) which show internal structures, interpreted as multiple collisions. We also discuss why Ceres has no family

On the use of generic types for smart contracts

This paper shows that generic types (generics) are useful for writing more abstract and more general smart contracts, but this comes with some security risks, reporting a concrete security issue found while using generics for writing smart contracts that implement shared entities for the Hotmoka blockchain. That issue can be used to steal the remuneration of validator nodes. This paper proposes a patch based on appropriate code rewriting. Namely, smart contracts are pieces of code that are deployed and executed in the context of a blockchain infrastructure in order to automatically enforce some effects when particular events occur. The writing of smart contracts is a complex and critical activity that can benefit from the use of high-level features of programming languages, and generics is one of them. In many programming languages, such as Java, generics are implemented by erasure, i.e. replaced by their upper bound type during compilation into bytecode. This is safe at source level, since the compiler takes care of checking that types are correct, before erasure. However, the erased types of the generated bytecode are consequently weaker. In a permissionless blockchain, where every user can call the bytecode of smart contracts installed by other users, these weaker types pose a risk of attack

The Shape of Water: How Tai Chi and Mental Imagery Effect the Kinematics of a Reach-to-Grasp Movement

The aim of the present study was to investigate the effect of Tai Chi (TC) and mental imagery (MI) on motor performance. MI is the ability of representing different types of images and it can be improved through constant practice (e.g., of TC). The majority of previous literature has mainly investigated the impact of this mental factor by means of qualitative indexes, whereas studies considering more rigorous measures such as kinematic parameters are rare. In this vein, little is known about how MI can affect reach-to-grasp, one of the most studied models in kinematic research. The present study attempts to fill that gap by investigating the relationship between MI and motor performance in TC, a practice that largely promotes the adoption of mental training. One TC master, four instructors, ten apprentices and fifteen untrained participants were requested to reach toward and grasp an object while mentally representing one out of five different images related to water with an increasing degree of dynamicity and expansion (i.e., still water, flowing water, wave, whirlpool, and opening water flower). Kinematic profiles of movements were recorded by means of six infra-red cameras using a 3-D motion analysis system. We tested whether: (i) focusing on MI during the task would help in optimizing motor efficiency, and (ii) expertise in TC would be reflected in higher flexibility during the task. The results indicate that kinematics is highly sensitive to MI and TC practice. In particular, our main finding suggests a statistically significant general improvement in motor efficiency for the TC group and a beneficial effect for all the participants when focusing on the most expansive image (i.e., opening water flower). Moreover, regression analysis indicates that MI and TC practice make online control more flexible in an experience-based way. These results have important implications for the use of mental imagery and TC in the retraining of motor function in people with physical disabilities

Sex differences in body ownership in adults with autism spectrum disorder

A strong male prevalence has been observed in autism spectrum disorder (ASD) since its definition, but the behavioral manifestations of sex disparity have yet to be clarified. Here, we investigate sex differences in the perception of the Numbness Illusion (NI), a procedure based on a tactile conflict, in adults with ASD and with typical development. We aim to assess if women and men with ASD perceive NI-dependent body ownership differently and whether sex differences emerge in individuals with typical development. To elicit the NI, participants pressed their right-hand palm against the confederate\u2019s hand and stroked with the thumb and the index finger of their left hand the joined index fingers in a synchronous or asynchronous way. Results reveal that women with ASD present a reversed and atypical pattern for the NI compared to men with ASD and a group of matched controls. In particular, women with ASD report a stronger illusion than men with ASD, that is more evident in the asynchronous conditions. In the asynchronous condition, women in the ASD group report stronger NI as compared to women and men in the Control group, whereas men with ASD only to men in the Control group. In the typical sample, the NI emerges only in the synchronous condition and no sex difference is observed. We discuss our results in terms of potential advantage of women in sociality and sensory information processing that might lead women with ASD to use different modalities to solve the illusion compared to men with ASD. In sum, these outcomes describe sex differences in individuals with ASD in the domain of illusory perception. This may be used in the future to support the characterization of the female phenotype of autism

Mixture polarization in inter-rater agreement analysis: a Bayesian nonparametric index

In several observational contexts where different raters evaluate a set of items, it is common to assume that all raters draw their scores from the same underlying distribution. However, a plenty of scientific works have evidenced the relevance of individual variability in different type of rating tasks. To address this issue the intra-class correlation coefficient (ICC) has been used as a measure of variability among raters within the Hierarchical Linear Models approach. A common distributional assumption in this setting is to specify hierarchical effects as independent and identically distributed from a normal with the mean parameter fixed to zero and unknown variance. The present work aims to overcome this strong assumption in the inter-rater agreement estimation by placing a Dirichlet Process Mixture over the hierarchical effects' prior distribution. A new nonparametric index $\lambda$ is proposed to quantify raters polarization in presence of group heterogeneity. The model is applied on a set of simulated experiments and real world data. Possible future directions are discussed