High-Dimensional Inference with the generalized Hopfield Model: Principal Component Analysis and Corrections

We consider the problem of inferring the interactions between a set of N binary variables from the knowledge of their frequencies and pairwise correlations. The inference framework is based on the Hopfield model, a special case of the Ising model where the interaction matrix is defined through a set of patterns in the variable space, and is of rank much smaller than N. We show that Maximum Lik elihood inference is deeply related to Principal Component Analysis when the amp litude of the pattern components, xi, is negligible compared to N^1/2. Using techniques from statistical mechanics, we calculate the corrections to the patterns to the first order in xi/N^1/2. We stress that it is important to generalize the Hopfield model and include both attractive and repulsive patterns, to correctly infer networks with sparse and strong interactions. We present a simple geometrical criterion to decide how many attractive and repulsive patterns should be considered as a function of the sampling noise. We moreover discuss how many sampled configurations are required for a good inference, as a function of the system size, N and of the amplitude, xi. The inference approach is illustrated on synthetic and biological data.Comment: Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2011) to appea

Viscous diffusion and photoevaporation of stellar disks

The evolution of a stellar disk under the influence of viscous evolution, photoevaporation from the central source, and photoevaporation by external stars is studied. We take the typical parameters of TTSs and the Trapezium Cluster conditions. The photoionizing flux from the central source is assumed to arise both from the quiescent star and accretion shocks at the base of stellar magnetospheric columns, along which material from the disk accretes. The accretion flux is calculated self-consistently from the accretion mass loss rate. We find that the disk cannot be entirely removed using only viscous evolution and photoionization from the disk-star accretion shock. However, when FUV photoevaporation by external massive stars is included the disk is removed in 10^6 -10^7yr; and when EUV photoevaporation by external massive stars is included the disk is removed in 10^5 - 10^6yr. An intriguing feature of photoevaporation by the central star is the formation of a gap in the disk at late stages of the disk evolution. As the gap starts forming, viscous spreading and photoevaporation work in resonance. There is no gap formation for disks nearby external massive stars because the outer annuli are quickly removed by the dominant EUV flux. On the other hand, at larger, more typical distances (d>>0.03pc) from the external stars the flux is FUV dominated. As a consequence, the disk is efficiently evaporated at two different locations; forming a gap during the last stages of the disk evolution.Comment: 27 pages, 11 figures, accepted for publication in Ap

A Critique of Current Magnetic-Accretion Models for Classical T-Tauri Stars

Current magnetic-accretion models for classical T-Tauri stars rely on a strong, dipolar magnetic field of stellar origin to funnel the disk material onto the star, and assume a steady-state. In this paper, I critically examine the physical basis of these models in light of the observational evidence and our knowledge of magnetic fields in low-mass stars, and find it lacking. I also argue that magnetic accretion onto these stars is inherently a time-dependent problem, and that a steady-state is not warranted. Finally, directions for future work towards fully-consistent models are pointed out.Comment: 2 figure

The cool wake around 4C 34.16 as seen by XMM-Newton

We present XMM-Newton observations of the wake-radiogalaxy system 4C34.16, which shows a cool and dense wake trailing behind 4C34.16's host galaxy. A comparison with numerical simulations is enlightening, as they demonstrate that the wake is produced mainly by ram pressure stripping during the galactic motion though the surrounding cluster. The mass of the wake is a substantial fraction of the mass of an elliptical galaxy's X-ray halo. This observational fact supports a wake formation scenario similar to the one demonstrated numerically by Acreman et al (2003): the host galaxy of 4C34.16 has fallen into its cluster, and is currently crossing its central regions. A substantial fraction of its X-ray halo has been stripped by ram pressure, and remains behind to form the galaxy wake.Comment: 9 pages, 6 figures, accepted for publication in MNRA

Hitting Time of Quantum Walks with Perturbation

The hitting time is the required minimum time for a Markov chain-based walk (classical or quantum) to reach a target state in the state space. We investigate the effect of the perturbation on the hitting time of a quantum walk. We obtain an upper bound for the perturbed quantum walk hitting time by applying Szegedy's work and the perturbation bounds with Weyl's perturbation theorem on classical matrix. Based on the definition of quantum hitting time given in MNRS algorithm, we further compute the delayed perturbed hitting time (DPHT) and delayed perturbed quantum hitting time (DPQHT). We show that the upper bound for DPQHT is actually greater than the difference between the square root of the upper bound for a perturbed random walk and the square root of the lower bound for a random walk.Comment: 9 page

Towards a Holistic View of the Heating and Cooling of the Intracluster Medium

(Abridged) X-ray clusters are conventionally divided into two classes: "cool core" (CC) clusters and "non-cool core" (NCC) clusters. Yet relatively little attention has been given to the origins of this dichotomy and, in particular, to the energetics and thermal histories of the two classes. We develop a model for the entropy profiles of clusters starting from the configuration established by gravitational shock heating and radiative cooling. At large radii, gravitational heating accounts for the observed profiles and their scalings well. However, at small and intermediate radii, radiative cooling and gravitational heating cannot be combined to explain the observed profiles of either type of cluster. The inferred entropy profiles of NCC clusters require that material is preheated prior to cluster collapse in order to explain the absence of low entropy (cool) material in these systems. We show that a similar modification is also required in CC clusters in order to match their properties at intermediate radii. In CC clusters, this modification is unstable, and an additional process is required to prevent cooling below a temperature of a few keV. We show that this can be achieved by adding a self-consistent AGN feedback loop in which the lowest-entropy, most rapidly cooling material is heated so that it rises buoyantly to mix with material at larger radii. The resulting model does not require fine tuning and is in excellent agreement with a wide variety of observational data. Some of the other implications of this model are briefly discussed.Comment: 27 pages, 13 figures, MNRAS accepted. Discussion of cluster heating energetics extended, results unchange

Conceptual design of a nonscaling fixed field alternating gradient accelerator for protons and carbon ions for charged particle therapy

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.The conceptual design for a nonscaling fixed field alternating gradient accelerator suitable for charged particle therapy (the use of protons and other light ions to treat some forms of cancer) is described.EPSR

Clonal interference and Muller's ratchet in spatial habitats

Competition between independently arising beneficial mutations is enhanced in spatial populations due to the linear rather than exponential growth of clones. Recent theoretical studies have pointed out that the resulting fitness dynamics is analogous to a surface growth process, where new layers nucleate and spread stochastically, leading to the build up of scale-invariant roughness. This scenario differs qualitatively from the standard view of adaptation in that the speed of adaptation becomes independent of population size while the fitness variance does not. Here we exploit recent progress in the understanding of surface growth processes to obtain precise predictions for the universal, non-Gaussian shape of the fitness distribution for one-dimensional habitats, which are verified by simulations. When the mutations are deleterious rather than beneficial the problem becomes a spatial version of Muller's ratchet. In contrast to the case of well-mixed populations, the rate of fitness decline remains finite even in the limit of an infinite habitat, provided the ratio $U_d/s^2$ between the deleterious mutation rate and the square of the (negative) selection coefficient is sufficiently large. Using again an analogy to surface growth models we show that the transition between the stationary and the moving state of the ratchet is governed by directed percolation

An ALMA Search for Substructure, Fragmentation, and Hidden Protostars in Starless Cores in Chamaeleon I

We present an Atacama Large Millimeter/submillimeter Array (ALMA) 106 GHz (Band 3) continuum survey of the complete population of dense cores in the Chamaeleon I molecular cloud. We detect a total of 24 continuum sources in 19 different target fields. All previously known Class 0 and Class I protostars in Chamaeleon I are detected, whereas all of the 56 starless cores in our sample are undetected. We show that the Spitzer+Herschel census of protostars in Chamaeleon I is complete, with the rate at which protostellar cores have been misclassified as starless cores calculated as <1/56, or < 2%. We use synthetic observations to show that starless cores collapsing following the turbulent fragmentation scenario are detectable by our ALMA observations when their central densities exceed ~10^8 cm^-3, with the exact density dependent on the viewing geometry. Bonnor-Ebert spheres, on the other hand, remain undetected to central densities at least as high as 10^10 cm^-3. Our starless core non-detections are used to infer that either the star formation rate is declining in Chamaeleon I and most of the starless cores are not collapsing, matching the findings of previous studies, or that the evolution of starless cores are more accurately described by models that develop less substructure than predicted by the turbulent fragmentation scenario, such as Bonnor-Ebert spheres. We outline future work necessary to distinguish between these two possibilities.Comment: Accepted by Ap

Minimax estimation of the Wigner function in quantum homodyne tomography with ideal detectors

We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared pulses. The state is represented through the Wigner function, a ``quasi-probability density'' on $\mathbb{R}^{2}$ which may take negative values and must respect intrinsic positivity constraints imposed by quantum physics. The data consists of $n$ i.i.d. observations from a probability density equal to the Radon transform of the Wigner function. We construct an estimator for the Wigner function, and prove that it is minimax efficient for the pointwise risk over a class of infinitely differentiable functions. A similar result was previously derived by Cavalier in the context of positron emission tomography. Our work extends this result to the space of smooth Wigner functions, which is the relevant parameter space for quantum homodyne tomography.Comment: 15 page