Categorification of persistent homology

We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving distance, which we show generalizes the previously-studied bottleneck distance. To illustrate the utility of this approach, we greatly generalize previous stability results for persistence, extended persistence, and kernel, image and cokernel persistence. We give a natural construction of a category of interleavings of these diagrams, and show that if the target category is abelian, so is this category of interleavings.Comment: 27 pages, v3: minor changes, to appear in Discrete & Computational Geometr

Whither Correlated Electron Theory?

This is the text of the 'Theory' opening talk at the 2001 Strongly Correlated Electron Systems conference. It contains opinions about some of the outstanding scientific challenges facing the theory side of the correlated electrons field.Comment: 7 pages. No figures. To appear in Physica

Microwave conductivity of a d-wave superconductor disordered by extended impurities: a real-space renormalization group approach

Using a real-space renormalization group (RSRG) technique, we compute the microwave conductivity of a d-wave superconductor disordered by extended impurities. To do this, we invoke a semiclassical approximation which naturally accesses the Andreev bound states localized near each impurity. Tunneling corrections (which are captured using the RSRG) lead to a delocalization of these quasiparticles and an associated contribution to the microwave conductivity.Comment: 8 pages, 4 figures. 2 figures added to previous versio

ESR, ENDOR and TRIPLE resonance studies of the primary donor radical cation P960+ in the photosynthetic bacterium Rhodopseudomonas viridis

The light-induced radical cation of the primary electron donor P960+• in photosynthetic reaction centers from Rhodopseudomonas viridis has been investigated by ESR, ENDOR and TRIPLE techniques. Both the comparison with the cation radical of monomeric bacteriochlorophyll b (BChl b) and with molecular-orbital calculations performed on P960+• using the results of an X-ray structure analysis, consistently show an asymmetric distribution of the unpaired electron over the two BChl b molecules which constitute P960+•. The possible relevance of this result for the primary electron transfer step in the reaction center is briefly discussed

Random Mass Dirac Fermions in Doped Spin-Peierls and Spin-Ladder systems: One-Particle Properties and Boundary Effects

Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized by a gap in the spin-excitation spectrum, which can be modeled at low energies by that of Dirac fermions with a mass. In the presence of disorder these systems can still be described by a Dirac fermion model, but with a random mass. Some peculiar properties, like the Dyson singularity in the density of states, are well known and attributed to creation of low-energy states due to the disorder. We take one step further and study single-particle correlations by means of Berezinskii's diagram technique. We find that, at low energy $\epsilon$, the single-particle Green function decays in real space like $G(x,\epsilon) \propto (1/x)^{3/2}$. It follows that at these energies the correlations in the disordered system are strong -- even stronger than in the pure system without the gap. Additionally, we study the effects of boundaries on the local density of states. We find that the latter is logarithmically (in the energy) enhanced close to the boundary. This enhancement decays into the bulk as $1/\sqrt{x}$ and the density of states saturates to its bulk value on the scale $L_\epsilon \propto \ln^2 (1/\epsilon)$. This scale is different from the Thouless localization length $\lambda_\epsilon\propto\ln (1/\epsilon)$. We also discuss some implications of these results for the spin systems and their relation to the investigations based on real-space renormalization group approach.Comment: 26 pages, LaTex, 9 PS figures include

Experiments on subcooled flow boiling in I.C. engine-like conditions at low flow velocities

[EN] Subcooled boiling flow is specially attractive for engine cooling system design, as no essential changes in its architecture are required while it is still possible to take advantage of the highest rates of heat transfer associated with nucleate boiling, mostly at high engine loads. In this paper, experiments on subcooled boiling flow in representative temperature conditions were conducted with a usual engine coolant in the low velocity range, for which little information is available, even if it may be relevant when advanced thermal management strategies are used. The results were analyzed by comparison with a reference Chen-type model which provided reasonable results for relatively low wall temperatures, but with noticeable discrepancies at higher wall temperatures. Analysis of the deviations observed indicated a significant influence of the Prandtl number on the suppression factor, and the inclusion into the model of a first estimate of this effect produced a noticeable improvement in its results, thus suggesting that one such modified additive model may be useful for practical engine cooling applications. (C) 2013 Elsevier Inc. All rights reserved.This work has been supported by Ministerio de Ciencia e Innovacion through Grant TRA2010-16205. O. Cornejo is indebted to Senacyt Panama for their support.Torregrosa, AJ.; Broatch, A.; Olmeda, P.; Cornejo, O. (2014). Experiments on subcooled flow boiling in I.C. engine-like conditions at low flow velocities. Experimental Thermal and Fluid Science. 52:347-354. https://doi.org/10.1016/j.expthermflusci.2013.10.004S3473545

Measuring Black Hole Spin using X-ray Reflection Spectroscopy

I review the current status of X-ray reflection (a.k.a. broad iron line) based black hole spin measurements. This is a powerful technique that allows us to measure robust black hole spins across the mass range, from the stellar-mass black holes in X-ray binaries to the supermassive black holes in active galactic nuclei. After describing the basic assumptions of this approach, I lay out the detailed methodology focusing on "best practices" that have been found necessary to obtain robust results. Reflecting my own biases, this review is slanted towards a discussion of supermassive black hole (SMBH) spin in active galactic nuclei (AGN). Pulling together all of the available XMM-Newton and Suzaku results from the literature that satisfy objective quality control criteria, it is clear that a large fraction of SMBHs are rapidly-spinning, although there are tentative hints of a more slowly spinning population at high (M>5*10^7Msun) and low (M<2*10^6Msun) mass. I also engage in a brief review of the spins of stellar-mass black holes in X-ray binaries. In general, reflection-based and continuum-fitting based spin measures are in agreement, although there remain two objects (GROJ1655-40 and 4U1543-475) for which that is not true. I end this review by discussing the exciting frontier of relativistic reverberation, particularly the discovery of broad iron line reverberation in XMM-Newton data for the Seyfert galaxies NGC4151, NGC7314 and MCG-5-23-16. As well as confirming the basic paradigm of relativistic disk reflection, this detection of reverberation demonstrates that future large-area X-ray observatories such as LOFT will make tremendous progress in studies of strong gravity using relativistic reverberation in AGN.Comment: 19 pages. To appear in proceedings of the ISSI-Bern workshop on "The Physics of Accretion onto Black Holes" (8-12 Oct 2012). Revised version adds a missing source to Table 1 and Fig.6 (IRAS13224-3809) and corrects the referencing of the discovery of soft lags in 1H0707-495 (which were in fact first reported in Fabian et al. 2009

Implicit weight bias in children age 9 to 11 years

OBJECTIVES: Assess implicit weight bias in children 9 to 11 years old. METHODS: Implicit weight bias was measured in children ages 9 to 11 (N = 114) by using the Affect Misattribution Procedure. Participants were shown a test image of a child for 350 milliseconds followed by a meaningless fractal (200 milliseconds), and then they were asked to rate the fractal image as "good" or "bad." We used 9 image pairs matched on age, race, sex, and activity but differing by weight of the child. Implicit bias was the difference between positive ratings for fractals preceded by an image of a healthy-weight child and positive ratings for fractals preceded by an image of an overweight child. RESULTS: On average, 64% of fractals shown after pictures of healthy-weight children were rated as "good, " compared with 59% of those shown after pictures of overweight children, reflecting an overall implicit bias rate of 5.4% against overweight children (P < .001). Healthy-weight participants showed greater implicit bias than over-and underweight participants (7.9%, 1.4%, and 0.3% respectively; P = .049). CONCLUSIONS: Implicit bias toward overweight individuals is evident in children aged 9 to 11 years with a magnitude of implicit bias (5.4%) similar to that in studies of implicit racial bias among adults