Robust high-dimensional precision matrix estimation

The dependency structure of multivariate data can be analyzed using the covariance matrix $\Sigma$. In many fields the precision matrix $\Sigma^{-1}$ is even more informative. As the sample covariance estimator is singular in high-dimensions, it cannot be used to obtain a precision matrix estimator. A popular high-dimensional estimator is the graphical lasso, but it lacks robustness. We consider the high-dimensional independent contamination model. Here, even a small percentage of contaminated cells in the data matrix may lead to a high percentage of contaminated rows. Downweighting entire observations, which is done by traditional robust procedures, would then results in a loss of information. In this paper, we formally prove that replacing the sample covariance matrix in the graphical lasso with an elementwise robust covariance matrix leads to an elementwise robust, sparse precision matrix estimator computable in high-dimensions. Examples of such elementwise robust covariance estimators are given. The final precision matrix estimator is positive definite, has a high breakdown point under elementwise contamination and can be computed fast

Poly-essential and general Hyperelastic World (brane) models

This article provides a unified treatment of an extensive category of non-linear classical field models whereby the universe is represented (perhaps as a brane in a higher dimensional background) in terms of a structure of a mathematically convenient type describable as hyperelastic, for which a complete set of equations of motion is provided just by the energy-momentum conservation law. Particular cases include those of a perfect fluid in quintessential backgrounds of various kinds, as well as models of the elastic solid kind that has been proposed to account for cosmic acceleration. It is shown how an appropriately generalised Hadamard operator can be used to construct a symplectic structure that controles the evolution of small perturbations, and that provides a characteristic equation governing the propagation of weak discontinuities of diverse (extrinsic and extrinsic) kinds. The special case of a poly-essential model - the k-essential analogue of an ordinary polytropic fluid - is examined and shown to be well behaved (like the fluid) only if the pressure to density ratio $w$ is positive.Comment: 16 pages Latex, Contrib. to 10th Peyresq Pysics Meeting, June 2005: Micro and Macro Structures of Spacetim

Close encounters of a rotating star with planets in parabolic orbits of varying inclination and the formation of Hot Jupiters

(abbreviated) We extend the theory of close encounters of a planet on a parabolic orbit with a star to include the effects of tides induced on the central rotating star. Orbits with arbitrary inclination to the stellar rotation axis are considered. We obtain results both from an analytic treatment and numerical one that are in satisfactory agreement. These results are applied to the initial phase of the tidal circularisation problem. We find that both tides induced in the star and planet can lead to a significant decrease of the orbital semi-major axis for orbits having periastron distances smaller than 5-6 stellar radii (corresponding to periods $\sim 4-5$ days after the circularisation has been completed) with tides in the star being much stronger for retrograde orbits compared to prograde orbits. We use the simple Skumanich law for the stellar rotation with its rotational period equal to one month at the age of 5Gyr. The strength of tidal interactions is characterised by circularisation time scale, $t_{ev}$ defined as a time scale of evolution of the planet's semi-major axis due to tides considered as a function of orbital period $P_{obs}$ after the process of tidal circularisation has been completed. We find that the ratio of the initial circularisation time scales corresponding to prograde and retrograde orbits is of order 1.5-2 for a planet of one Jupiter mass and $P_{obs}\sim$ four days. It grows with the mass of the planet, being of order five for a five Jupiter mass planet with the same $P_{orb}$. Thus, the effect of stellar rotation may provide a bias in the formation of planetary systems having planets on close orbits around their host stars, as a consequence of planet-planet scattering, favouring systems with retrograde orbits. The results may also be applied to the problem of tidal capture of stars in young stellar clusters.Comment: to be published in Celestial Mechanics and Dynamical Astronom

Crowdfunding biodiversity conservation

Raising funds is critical for conserving biodiversity and hence so too is scrutinizing emerging financial mechanisms that might help achieve this goal. In this context, anecdotal evidence indicates crowdfunding is being used to support a variety of activities needed for biodiversity conservation, yet its magnitude and allocation remain largely unknown. We conducted a global analysis to help address this knowledge gap, based on empirical data from conservation‐focused projects extracted from crowdfunding platforms. For each project, we determined the funds raised, date, country of implementation, proponent characteristics, activity type, biodiversity realm, and target taxa. We identified 72 relevant platforms and 577 conservation‐focused projects that have raised US$4 790 634 since 2009. Whilst proponents were based in 38 countries, projects were delivered across 80 countries, indicating a potential mechanism of resource mobilization. Proponents were from non‐governmental organizations (35%), universities (30%), or were freelancers (26%). Most projects were for research (40%), persuasion (31%), and on‐ground actions (21%). Projects have focused primarily on species (57.7%) and terrestrial ecosystems (20.3%), and less on marine (8.8%) and freshwater ecosystems (3.6%). Projects have focused on 208 species, including a disproportionate number of threatened bird and mammal species. Crowdfunding for biodiversity conservation has now become a global phenomenon and presents signals for potential expansion, despite possible pitfalls. Opportunities arise from its spatial amplifying effect, steady increase over time, inclusion of Cinderella species, adoption by multiple actors, and funding of a range of activities beyond research. Our study paves the way for further research on key questions, such as campaign success rates, effectiveness, and drivers of adoption. Even though the capital input of crowdfunding so far has been modest compared to other conservation finance mechanisms, its contribution goes beyond funding research and providing capital. Embraced with due care, crowdfunding could potentially become an increasingly important financial mechanism for biodiversity conservation

Electronic transport through ballistic chaotic cavities: reflection symmetry, direct processes, and symmetry breaking

We extend previous studies on transport through ballistic chaotic cavities with spatial left-right (LR) reflection symmetry to include the presence of direct processes. We first analyze fully LR-symmetric systems in the presence of direct processes and compare the distribution w(T) of the transmission coefficient T with that for an asymmetric cavity with the same "optical" S matrix. We then study the problem of "external mixing" of the symmetry caused by an asymmetric coupling of the cavity to the outside. We first consider the case where symmetry breaking arises because two symmetrically positioned waveguides are coupled to the cavity by means of asymmetric tunnel barriers. Although this system is asymmetric with respect to the LR operation, it has a striking memory of the symmetry of the cavity it was constructed from. Secondly, we break LR symmetry in the absence of direct proceses by asymmetrically positioning the two waveguides and compare the results with those for the completely asymmetric case.Comment: 15 pages, 8 Postscript figures, submitted to Phys. Rev.

Local time and the pricing of time-dependent barrier options

A time-dependent double-barrier option is a derivative security that delivers the terminal value $\phi(S_T)$ at expiry $T$ if neither of the continuous time-dependent barriers b_\pm:[0,T]\to \RR_+ have been hit during the time interval $[0,T]$. Using a probabilistic approach we obtain a decomposition of the barrier option price into the corresponding European option price minus the barrier premium for a wide class of payoff functions $\phi$, barrier functions $b_\pm$ and linear diffusions $(S_t)_{t\in[0,T]}$. We show that the barrier premium can be expressed as a sum of integrals along the barriers $b_\pm$ of the option's deltas \Delta_\pm:[0,T]\to\RR at the barriers and that the pair of functions $(\Delta_+,\Delta_-)$ solves a system of Volterra integral equations of the first kind. We find a semi-analytic solution for this system in the case of constant double barriers and briefly discus a numerical algorithm for the time-dependent case.Comment: 32 pages, to appear in Finance and Stochastic

Suppression of inhomogeneous broadening in rf spectroscopy of optically trapped atoms

We present a novel method for reducing the inhomogeneous frequency broadening in the hyperfine splitting of the ground state of optically trapped atoms. This reduction is achieved by the addition of a weak light field, spatially mode-matched with the trapping field and whose frequency is tuned in-between the two hyperfine levels. We experimentally demonstrate the new scheme with Rb 85 atoms, and report a 50-fold narrowing of the rf spectrum

Magnetic Field Effects on the Far-Infrared Absorption in Mn_12-acetate

We report the far-infrared spectra of the molecular nanomagnet Mn_12-acetate (Mn_12) as a function of temperature (5-300 K) and magnetic field (0-17 T). The large number of observed vibrational modes is related to the low symmetry of the molecule, and they are grouped together in clusters. Analysis of the mode character based on molecular dynamics simulations and model compound studies shows that all vibrations are complex; motion from a majority of atoms in the molecule contribute to most modes. Three features involving intramolecular vibrations of the Mn_12 molecule centered at 284, 306 and 409 cm-1 show changes with applied magnetic field. The structure near 284 cm$^{-1}$ displays the largest deviation with field and is mainly intensity related. A comparison between the temperature dependent absorption difference spectra, the gradual low-temperature cluster framework distortion as assessed by neutron diffraction data, and field dependent absorption difference spectra suggests that this mode may involve Mn motion in the crown.Comment: 5 pages, 4 figures, PRB accepte

Antiproton-deuteron annihilation at low energies

Recent experimental studies of the antiproton-deuteron system at low energies have shown that the imaginary part of the antiproton-deuteron scattering length is smaller than the antiproton-proton one. Two- and three-body systems with strong annihilation are investigated and a mechanism explaining this unexpected relation between the imaginary parts of the scattering lengths is proposed.Comment: 6 pages, 3 figures, to be published in The European Physical Journal

Subthreshold dynamics of the neural membrane potential driven by stochastic synaptic input

In the cerebral cortex, neurons are subject to a continuous bombardment of synaptic inputs originating from the network's background activity. This leads to ongoing, mostly subthreshold membrane dynamics that depends on the statistics of the background activity and of the synapses made on a neuron. Subthreshold membrane polarization is, in turn, a potent modulator of neural responses. The present paper analyzes the subthreshold dynamics of the neural membrane potential driven by synaptic inputs of stationary statistics. Synaptic inputs are considered in linear interaction. The analysis identifies regimes of input statistics which give rise to stationary, fluctuating, oscillatory, and unstable dynamics. In particular, I show that (i) mere noise inputs can drive the membrane potential into sustained, quasiperiodic oscillations (noise-driven oscillations), in the absence of a stimulus-derived, intraneural, or network pacemaker; (ii) adding hyperpolarizing to depolarizing synaptic input can increase neural activity (hyperpolarization-induced activity), in the absence of hyperpolarization-activated currents