Stochastic Perturbations of Periodic Orbits with Sliding

Vector fields that are discontinuous on codimension-one surfaces are known as Filippov systems and can have attracting periodic orbits involving segments that are contained on a discontinuity surface of the vector field. In this paper we consider the addition of small noise to a general Filippov system and study the resulting stochastic dynamics near such a periodic orbit. Since a straight-forward asymptotic expansion in terms of the noise amplitude is not possible due to the presence of discontinuity surfaces, in order to quantitatively determine the basic statistical properties of the dynamics, we treat different parts of the periodic orbit separately. Dynamics distant from discontinuity surfaces is analyzed by the use of a series expansion of the transitional probability density function. Stochastically perturbed sliding motion is analyzed through stochastic averaging methods. The influence of noise on points at which the periodic orbit escapes a discontinuity surface is determined by zooming into the transition point. We combine the results to quantitatively determine the effect of noise on the oscillation time for a three-dimensional canonical model of relay control. For some parameter values of this model, small noise induces a significantly large reduction in the average oscillation time. By interpreting our results geometrically, we are able to identify four features of the relay control system that contribute to this phenomenon.Comment: 44 pages, 9 figures, submitted to: J Nonlin. Sc

New methodology for assessing the probability of contaminating Mars

Methodology is proposed to assess the probability that the planet Mars will be contaminated by terrestrial microorganisms aboard a spacecraft. The present NASA methods are extended to permit utilization of detailed information on microbial characteristics, the lethality of release and transport mechanisms, and of other information about the Martian environment. Different types of microbial release are distinguished, and for each release mechanism a probability of growth is computed. Using this new methodology, an assessment was carried out for the 1975 Viking landings on Mars. The resulting probability of contamination for each Viking lander is 6 x 10 to the -6 power, and is amenable to revision as additional information becomes available

Probabilistic models of planetary contamination

Likely fundamental inadequacies in the model of planetary contamination advanced by Sagan and Coleman are discussed. It is shown that a relatively minor modification of the basic Sagan-Coleman formula yields approximations that are generally adequate with data in the range of interest. This approximation formula differs from the original Sagan-Coleman version only through an initial conditioning on landing outcome. It always yields an upper (conservative) bound for the total probability of contamination, this appealing feature is lost if the conditioning on landing outcome is deleted

Geographic analysis of multiple sensor data from the NASA/USGS earth resources program

Qualitative and quantitative analyses were made of multi-sensor data acquired during aircraft missions. While the principal analysis effort was concentrated on imagery taken over test sites in Southern California, data were also studied from records acquired on missions over test sites at Phoenix, Chicago, Asheville, and New Orleans. The objectives of the analyses were: (1) to determine the capabilities of ten remote sensors in identifying the elements of information necessary in conducting geographic investigations in land use analysis, urban problems, surface energy budget, and soil moisture; (2) to determine the feasibility of using these sensors for these purposes at orbital altitudes; and (3) to collate and analyze ground and air data previously collected and assemble it in a format useful in the accomplishment of cost effectiveness studies

Assessment of the probability of contaminating Mars

New methodology is proposed to assess the probability that the planet Mars will by biologically contaminated by terrestrial microorganisms aboard a spacecraft. Present NASA methods are based on the Sagan-Coleman formula, which states that the probability of contamination is the product of the expected microbial release and a probability of growth. The proposed new methodology extends the Sagan-Coleman approach to permit utilization of detailed information on microbial characteristics, the lethality of release and transport mechanisms, and of other information about the Martian environment. Three different types of microbial release are distinguished in the model for assessing the probability of contamination. The number of viable microbes released by each mechanism depends on the bio-burden in various locations on the spacecraft and on whether the spacecraft landing is accomplished according to plan. For each of the three release mechanisms a probability of growth is computed, using a model for transport into an environment suited to microbial growth

Analysis of multiply spliced transcripts in lymphoid tissue reservoirs of rhesus macaques infected with RT-SHIV during HAART.

Highly active antiretroviral therapy (HAART) can reduce levels of human immunodeficiency virus type 1 (HIV-1) to undetectable levels in infected individuals, but the virus is not eradicated. The mechanisms of viral persistence during HAART are poorly defined, but some reservoirs have been identified, such as latently infected resting memory CD4⁺ T cells. During latency, in addition to blocks at the initiation and elongation steps of viral transcription, there is a block in the export of viral RNA (vRNA), leading to the accumulation of multiply-spliced transcripts in the nucleus. Two of the genes encoded by the multiply-spliced transcripts are Tat and Rev, which are essential early in the viral replication cycle and might indicate the state of infection in a given population of cells. Here, the levels of multiply-spliced transcripts were compared to the levels of gag-containing RNA in tissue samples from RT-SHIV-infected rhesus macaques treated with HAART. Splice site sequence variation was identified during development of a TaqMan PCR assay. Multiply-spliced transcripts were detected in gastrointestinal and lymphatic tissues, but not the thymus. Levels of multiply-spliced transcripts were lower than levels of gag RNA, and both correlated with plasma virus loads. The ratio of multiply-spliced to gag RNA was greatest in the gastrointestinal samples from macaques with plasma virus loads <50 vRNA copies per mL at necropsy. Levels of gag RNA and multiply-spliced mRNA in tissues from RT-SHIV-infected macaques correlate with plasma virus load

Historical-institutionalist perspectives on the development of the EU budget system

The EU budget has only recently started to feature in theories of European integration. Studies typically adopt a historical-institutionalist framework, exploring notions such as path dependency. They have, however, generally been rather aggregated, or coarse-grained, in their approach. The EU budget has thus been treated as a single entity rather than a series of inter-linked institutions. This paper seeks to address these lacunae by adopting a fine-grained approach. This enables us to emphasize the connections that exist between EU budgetary institutions, in both time and space. We show that the initial set of budgetary institutions was unable, over time, to achieve consistently their treaty-based objectives. In response, rather than reform these institutions at potentially high political cost, additional institutions were layered on top of the extant structures. We thus demonstrate how some EU budgetary institutions have remained unchanged, whilst others have been added or changed over time

Observations of red-giant variable stars by Aboriginal Australians

Aboriginal Australians carefully observe the properties and positions of stars, including both overt and subtle changes in their brightness, for subsistence and social application. These observations are encoded in oral tradition. I examine two Aboriginal oral traditions from South Australia that describe the periodic changing brightness in three pulsating, red-giant variable stars: Betelgeuse (Alpha Orionis), Aldebaran (Alpha Tauri), and Antares (Alpha Scorpii). The Australian Aboriginal accounts stand as the only known descriptions of pulsating variable stars in any Indigenous oral tradition in the world. Researchers examining these oral traditions over the last century, including anthropologists and astronomers, missed the description of these stars as being variable in nature as the ethnographic record contained several misidentifications of stars and celestial objects. Arguably, ethnographers working on Indigenous Knowledge Systems should have academic training in both the natural and social sciences.Comment: The Australian Journal of Anthropology (2018

The radio lighthouse CU Virginis: the spindown of a single main sequence star

The fast rotating star CU Virginis is a magnetic chemically peculiar star with an oblique dipolar magnetic field. The continuum radio emission has been interpreted as gyrosyncrotron emission arising from a thin magnetospheric layer. Previous radio observations at 1.4 GHz showed that a 100% circular polarized and highly directive emission component overlaps to the continuum emission two times per rotation, when the magnetic axis lies in the plane of the sky. This sort of radio lighthouse has been proposed to be due to cyclotron maser emission generated above the magnetic pole and propagating perpendicularly to the magnetic axis. Observations carried out with the Australia Telescope Compact Array at 1.4 and 2.5 GHz one year after this discovery show that this radio emission is still present, meaning that the phenomenon responsible for this process is steady on a timescale of years. The emitted radiation spans at least 1 GHz, being observed from 1.4 to 2.5 GHz. On the light of recent results on the physics of the magnetosphere of this star, the possibility of plasma radiation is ruled out. The characteristics of this radio lighthouse provides us a good marker of the rotation period, since the peaks are visible at particular rotational phases. After one year, they show a delay of about 15 minutes. This is interpreted as a new abrupt spinning down of the star. Among several possibilities, a quick emptying of the equatorial magnetic belt after reaching the maximum density can account for the magnitude of the breaking. The study of the coherent emission in stars like CU Vir, as well as in pre main sequence stars, can give important insight into the angular momentum evolution in young stars. This is a promising field of investigation that high sensitivity radio interferometers such as SKA can exploit.Comment: Accepted to MNRAS, 8 pages, 7 figures, updated versio

Perceived importance of components of asynchronous music in circuit training

This study examined regular exercisers’ perceptions of specific components of music during circuit training. Twenty-four men (38.8 years, s = 11.8 years) and 31 women (32.4 years, s = 9.6 years) completed two questionnaires immediately after a circuit training class. Participants rated the importance of 13 components of music (rhythm, melody, etc.) in relation to exercise enjoyment, and each completed the Affect Intensity Measure (Larsen, 1984) to measure emotional reactivity. Independent t tests were used to evaluate gender differences in perceptions of musical importance. Pearson correlations were computed to evaluate the relationships between affect intensity, age and importance of musical components. Consistent with previous research and theoretical predictions, rhythm response components (rhythm, tempo, beat) were rated as most important. Women rated the importance of melody significantly higher than did men, while men gave more importance to music associated with sport. Affect intensity was found to be positively and significantly related to the perceived importance of melody, lyrical content, musical style, personal associations and emotional content. Results suggest that exercise leaders need to be sensitive to personal factors when choosing music to accompany exercise. Qualitative research that focuses on the personal meaning of music is encouraged