FINE: Fisher Information Non-parametric Embedding

We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward Euclidean representation exists. Typically, these tasks are performed by first reducing the high-dimensional data to some lower dimensional Euclidean space, as many manifold learning methods have been developed for this task. In many practical problems however, the assumption of a Euclidean manifold cannot be justified. In these cases, a more appropriate assumption would be that the data lies on a statistical manifold, or a manifold of probability density functions (PDFs). In this paper we propose using the properties of information geometry in order to define similarities between data sets using the Fisher information metric. We will show this metric can be approximated using entirely non-parametric methods, as the parameterization of the manifold is generally unknown. Furthermore, by using multi-dimensional scaling methods, we are able to embed the corresponding PDFs into a low-dimensional Euclidean space. This not only allows for classification of the data, but also visualization of the manifold. As a whole, we refer to our framework as Fisher Information Non-parametric Embedding (FINE), and illustrate its uses on a variety of practical problems, including bio-medical applications and document classification.Comment: 30 pages, 21 figure

Survival-Time Distribution for Inelastic Collapse

In a recent publication [PRL {\bf 81}, 1142 (1998)] it was argued that a randomly forced particle which collides inelastically with a boundary can undergo inelastic collapse and come to rest in a finite time. Here we discuss the survival probability for the inelastic collapse transition. It is found that the collapse-time distribution behaves asymptotically as a power-law in time, and that the exponent governing this decay is non-universal. An approximate calculation of the collapse-time exponent confirms this behaviour and shows how inelastic collapse can be viewed as a generalised persistence phenomenon.Comment: 4 pages, RevTe

Magnetic levitation stabilized by streaming fluid flows

We demonstrate that the ubiquitous laboratory magnetic stirrer provides a simple passive method of magnetic levitation, in which the so-called “flea” levitates indefinitely. We study the onset of levitation and quantify the flea’s motion (a combination of vertical oscillation, spinning and “waggling”), finding excellent agreement with a mechanical analytical model. The waggling motion drives recirculating flow, producing a centripetal reaction force that stabilized the flea. Our findings have implications for the locomotion of artificial swimmers and the development of bidirectional microfluidic pumps, and they provide an alternative to sophisticated commercial levitators

Lattice-gas Monte Carlo study of adsorption in pores

A lattice gas model of adsorption inside cylindrical pores is evaluated with Monte Carlo simulations. The model incorporates two kinds of site: (a line of) ``axial'' sites and surrounding ``cylindrical shell'' sites, in ratio 1:7. The adsorption isotherms are calculated in either the grand canonical or canonical ensembles. At low temperature, there occur quasi-transitions that would be genuine thermodynamic transitions in mean-field theory. Comparison between the exact and mean-field theory results for the heat capacity and adsorption isotherms are provided

Ground state non-universality in the random field Ising model

Two attractive and often used ideas, namely universality and the concept of a zero temperature fixed point, are violated in the infinite-range random-field Ising model. In the ground state we show that the exponents can depend continuously on the disorder and so are non-universal. However, we also show that at finite temperature the thermal order parameter exponent one half is restored so that temperature is a relevant variable. The broader implications of these results are discussed.Comment: 4 pages 2 figures, corrected prefactors caused by a missing factor of two in Eq. 2., added a paragraph in conclusions for clarit

Effects of Pore Walls and Randomness on Phase Transitions in Porous Media

We study spin models within the mean field approximation to elucidate the topology of the phase diagrams of systems modeling the liquid-vapor transition and the separation of He$^3$--He$^4$ mixtures in periodic porous media. These topologies are found to be identical to those of the corresponding random field and random anisotropy spin systems with a bimodal distribution of the randomness. Our results suggest that the presence of walls (periodic or otherwise) are a key factor determining the nature of the phase diagram in porous media.Comment: REVTeX, 11 eps figures, to appear in Phys. Rev.

Tensionless structure of glassy phase

We study a class of homogeneous finite-dimensional Ising models which were recently shown to exhibit glassy properties. Monte Carlo simulations of a particular three-dimensional model in this class show that the glassy phase obtained under slow cooling is dominated by large scale excitations whose energy $E_l$ scales with their size $l$ as $E_l\sim l^{\Theta}$ with $\Theta\sim 1.33(5)$. Simulations suggest that in another model of this class, namely the four-spin model, energy is concentrated mainly in linear defects making also in this case domain walls tensionless. Two-dimensinal variants of these models are trivial and energy of excitations scales with the exponent $\Theta=1.05(5)$.Comment: 5 page

Nonequilibrium phase transitions in models of adsorption and desorption

The nonequilibrium phase transition in a system of diffusing, coagulating particles in the presence of a steady input and evaporation of particles is studied. The system undergoes a transition from a phase in which the average number of particles is finite to one in which it grows linearly in time. The exponents characterizing the mass distribution near the critical point are calculated in all dimensions.Comment: 10 pages, 2 figures (To appear in Phys. Rev. E

The nature of transition circumstellar disks. I. The ophiuchus molecular cloud

We have obtained millimeter-wavelength photometry, high-resolution optical spectroscopy, and adaptive optics near-infrared imaging for a sample of 26 Spitzer-selected transition circumstellar disks. All of our targets are located in the Ophiuchus molecular cloud (d ∼ 125pc) and have spectral energy distributions (SEDs) suggesting the presence of inner opacity holes. We use these ground-based data to estimate the disk mass, multiplicity, and accretion rate for each object in our sample in order to investigate the mechanisms potentially responsible for their inner holes. We find that transition disks are a heterogeneous group of objects, with disk masses ranging from JUP and accretion rates ranging from JUP) and negligible accretion (<10-11 M ⊙yr-1), and are thus consistent with photoevaporating (or photoevaporated) disks. Four of these nine non-accreting objects have fractional disk luminosities <10-3 and could already be in a debris disk stage. Seventeen of our transition disks are accreting. Thirteen of these accreting objects are consistent with grain growth. The remaining four accreting objects have SEDs suggesting the presence of sharp inner holes, and thus are excellent candidates for harboring giant planets.Facultad de Ciencias Astronómicas y Geofísica

Rayleigh loops in the random-field Ising model on the Bethe lattice

We analyze the demagnetization properties of the random-field Ising model on the Bethe lattice focusing on the beahvior near the disorder induced phase transition. We derive an exact recursion relation for the magnetization and integrate it numerically. Our analysis shows that demagnetization is possible only in the continous high disorder phase, where at low field the loops are described by the Rayleigh law. In the low disorder phase, the saturation loop displays a discontinuity which is reflected by a non vanishing magnetization m_\infty after a series of nested loops. In this case, at low fields the loops are not symmetric and the Rayleigh law does not hold.Comment: 8pages, 6 figure