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Brain oscillations exhibit long-range temporal correlations (LRTCs), which reflect the regularity of their fluctuations: low values representing more random (decorrelated) while high values more persistent (correlated) dynamics. LRTCs constitute supporting evidence that the brain operates near criticality, a state where neuronal activities are balanced between order and randomness. Here, healthy adults used closed-loop brain training (neurofeedback, NFB) to reduce the amplitude of alpha oscillations, producing a significant increase in spontaneous LRTCs post-training. This effect was reproduced in patients with post-traumatic stress disorder, where abnormally random dynamics were reversed by NFB, correlating with significant improvements in hyperarousal. Notably, regions manifesting abnormally low LRTCs (i.e., excessive randomness) normalized toward healthy population levels, consistent with theoretical predictions about self-organized criticality. Hence, when exposed to appropriate training, spontaneous cortical activity reveals a residual capacity for "self-tuning" its own temporal complexity, despite manifesting the abnormal dynamics seen in individuals with psychiatric disorder. Lastly, we observed an inverse-U relationship between strength of LRTC and oscillation amplitude, suggesting a breakdown of long-range dependence at high/low synchronization extremes, in line with recent computational models. Together, our findings offer a broader mechanistic framework for motivating research and clinical applications of NFB, encompassing disorders with perturbed LRTCs.

Realistic path planning applications often require optimizing with respect to several criteria simultaneously. Here we introduce an efficient algorithm for bi-criteria path planning on graphs. Our approach is based on augmenting the state space to keep track of the "budget" remaining to satisfy the constraints on secondary cost. The resulting augmented graph is acyclic and the primary cost can be then minimized by a simple upward sweep through budget levels. The efficiency and accuracy of our algorithm is tested on Probabilistic Roadmap graphs to minimize the distance of travel subject to a constraint on the overall threat exposure of the robot. We also present the results from field experiments illustrating the use of this approach on realistic robotic systems., Comment: 19 pages, 12 figures; submitted for publication to IEEE Transactions on Automation Science and Engineering

Warm jupiters are an unexpected population of extrasolar planets that are too near to their host to have formed in situ, but distant enough to retain a significant eccentricity in the face of tidal damping. These planets are curiously absent around stars larger than two solar radii. We hypothesize that the warm jupiters are migrating due to Kozai-Lidov oscillations, which leads to transient episodes of high eccentricity and a consequent tidal decay. As their host evolves, such planets would be rapidly dragged in or engulfed at minimum periapse, leading to a rapid depletion of the population with increasing stellar radius, as is observed. Using numerical simulations, we determine the relationship between periapse distance and orbital migration rate for planets 0.1 to 10 Jupiter masses and with orbital periods between 10 and 100 days. We find that Kozai-Lidov oscillations effectively result in planetary removal early in the evolution of the host star, possibly accounting for the observed deficit. While the observed eccentricity distribution is inconsistent with the simulated distribution for an oscillating and migrating warm jupiter population, observational biases may explain the discrepancy., Comment: 16 pages, 18 figures; to appear in Monthly Notices of the Royal Astronomical Society

We present Hubble Space Telescope observations of the upper part (T_eff> 10 000 K) of the white dwarf cooling sequence in the globular cluster 47 Tucanae and measure a luminosity function of hot white dwarfs. Comparison with previous determinations from large scale field surveys indicates that the previously determined plateau at high effective temperatures is likely a selection effect, as no such feature is seen in this sample. Comparison with theoretical models suggests that the current estimates of white dwarf neutrino emission (primarily by the plasmon channel) are accurate, and variations are restricted to no more than a factor of two globally, at 95% confidence. We use these constraints to place limits on various proposed exotic emission mechanisms, including a non-zero neutrino magnetic moment, formation of axions, and emission of Kaluza-Klein modes into extra dimensions., Comment: 13 pages, 12 figures, to appear in the Astrophysical Journal

A significant fraction of white dwarfs (WDs) are observed to be polluted with metals despite high surface gravities and short settling times. The current theoretical model for this pollution is accretion of rocky bodies delivered to the WD through perturbations by orbiting planets. Using N-body simulations, we examine the possibility of a single planet as the source of pollution. We determine the stability of test particles on circular orbits in systems with a single planet located at 4 au for a range of masses and eccentricities, comparing the fractions that are ejected and accreted. In particular, we compare the instabilities that develop before and after the star loses mass to form a WD, a process which causes orbiting bodies to migrate outward. We determine that a planet must be eccentric (e > 0.02) to deliver significant (> 0.5 per cent) amounts of material to the host and that the amount increases with the planetary eccentricity. This result is robust with respect to the initial eccentricities of the particles for planetary eccentricity above ~0.4 and for randomly-distributed particle long. of pericentre. We also find that the efficiency of pollution is enhanced as planetary mass is reduced. We demonstrate that a 0.03 M_Jup planet with substantial eccentricity (e > 0.4) can account for the observed levels of pollution for initial disc masses of order 1 M_Earth. Such discs are within the range estimated for initial planetesimals discs and below that estimated for the solar system. However, their survival to the WD stage is uncertain as estimates for the collisional evolution of planetesimal discs suggest they should be ground down below the required levels on Gyr timescales. Thus, planetary scattering by eccentric, sub-Jovian planets can explain the observed levels of WD pollution, but only if current estimates of the collisional erosion of planetesimal discs are in error., Comment: 18 pages, 19 figures, accepted to MNRAS

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks.

The magnetic field of the solar corona has a large-scale dipole character, which maps into the bipolar field in the solar wind. Using standard representations of the coronal field, we show that high-energy ions can be trapped stably in these large-scale closed fields. The drift shells that describe the conservation of the third adiabatic invariant may have complicated geometries. Particles trapped in these zones would resemble the Van Allen Belts and could have detectable consequences. We discuss potential sources of trapped particles.

We describe a reverse integration approach for the exploration of low-dimensional effective potential landscapes. Coarse reverse integration initialized on a ring of coarse states enables efficient "navigation" on the landscape terrain: escape from local effective potential wells, detection of saddle points, and identification of significant transition paths between wells. We consider several distinct ring evolution modes: backward stepping in time, solution arc--length, and effective potential. The performance of these approaches is illustrated for a deterministic problem where the energy landscape is known explicitly. Reverse ring integration is then applied to "noisy" problems where the ring integration routine serves as an outer "wrapper" around a forward-in-time inner simulator. Three versions of such inner simulators are considered: a system of stochastic differential equations, a Gillespie--type stochastic simulator, and a molecular dynamics simulator. In these "equation-free" computational illustrations, estimation techniques are applied to the results of short bursts of "inner" simulation to obtain the unavailable (in closed form) quantities (local drift and diffusion coefficient estimates) required for reverse ring integration; this naturally leads to approximations of the effective landscape., Comment: article submitted to J Chem Phys

We study a stochastic nonlocal PDE, arising in the context of modelling spatially distributed neural activity, which is capable of sustaining stationary and moving spatially-localized ``activity bumps''. This system is known to undergo a pitchfork bifurcation in bump speed as a parameter (the strength of adaptation) is changed; yet increasing the noise intensity effectively slowed the motion of the bump. Here we revisit the system from the point of view of describing the high-dimensional stochastic dynamics in terms of the effective dynamics of a single scalar "coarse" variable. We show that such a reduced description in the form of an effective Langevin equation characterized by a double-well potential is quantitatively successful. The effective potential can be extracted using short, appropriately-initialized bursts of direct simulation. We demonstrate this approach in terms of (a) an experience-based "intelligent" choice of the coarse observable and (b) an observable obtained through data-mining direct simulation results, using a diffusion map approach., Comment: Corrected aknowledgements

Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these complex systems and (b) characterizing the dynamics of the observables. In a previous paper [13], we assumed that good observables were known a priori, and presented an equation-free approach to approximate coarse-grained quantities (i.e, effective drift and diffusion coefficients) that characterize the long-time behavior of the observables. Here we use diffusion maps [9] to extract appropriate observables ("reduction coordinates") in an automated fashion; these involve the leading eigenvectors of a weighted Laplacian on a graph constructed from network simulation data. We present lifting and restriction procedures for translating between physical variables and these data-based observables. These procedures allow us to perform equation-free coarse-grained, computations characterizing the long-term dynamics through the design and processing of short bursts of stochastic simulation initialized at appropriate values of the data-based observables., Comment: 26 pages, 9 figures