Primer for the algebraic geometry of sandpiles

The Abelian Sandpile Model (ASM) is a game played on a graph realizing the dynamics implicit in the discrete Laplacian matrix of the graph. The purpose of this primer is to apply the theory of lattice ideals from algebraic geometry to the Laplacian matrix, drawing out connections with the ASM. An extended summary of the ASM and of the required algebraic geometry is provided. New results include a characterization of graphs whose Laplacian lattice ideals are complete intersection ideals; a new construction of arithmetically Gorenstein ideals; a generalization to directed multigraphs of a duality theorem between elements of the sandpile group of a graph and the graph's superstable configurations (parking functions); and a characterization of the top Betti number of the minimal free resolution of the Laplacian lattice ideal as the number of elements of the sandpile group of least degree. A characterization of all the Betti numbers is conjectured.Comment: 45 pages, 14 figures. v2: corrected typo

Transformative ethics consultation : a supplement to ethics facilitation for emotionally charged health care value conflicts

An emotionally difficult case of withdrawing artificial food and water from a patient in persistent vegetative state prompts consideration of the role of empathy and emotion in health care ethics consultation. Rather than viewing ethics consultation purely in terms of consultant-initiated ethical and largely cognitive analysis followed by interpersonal facilitation of consensus, this dissertation seeks a process to address emotion early and to cultivate empathy as-a collective responsibility among patients, surrogates, and clinicians. Moral decision-making and thus ethics consultation must integrate the emotional and cognitive processing of value perceptions and judgments. Promoting integration during ethics consultation encourages participants to adopt a moral orientation of respect and concern that facilitates consensus-building in emotionally charged value conflicts. Phenomenologists Jurgen Habermas and Arne Vetlesen describe this process as overcoming one\u27s own perspective in order to understand the interests and perspective of one\u27s fellows. By adapting this phenomenological sequence to ethics consultation, the dissertation culminates in the presentation of a two-step process, transformative ethics consultation (TEC). If consultants identify an emotional tension early, TEC can serve as a supplement to the identification and analysis of the value conflict or uncertainty. The first step of TEC allows consultation parties to explore, express, and have their emotions validated by the consultant as an initial empathy-building phase. The second step attempts to extend empathy to all parties in such a way that each party understands the other. Extending empathy thus encourages shared moral ownership of the problem and the process for its resolution. To illustrate the two steps of TEC in action, I analyze the case that sparked the dissertation and present another to supplement the argument. In the final chapter, I address two potential challenges to TEC—that it is equivalent to bioethics mediation and thus open to the pitfalls of bioethics mediation as a stand-alone consultation modality. I rebut both of these challenges. I overcome the first by arguing for a new understanding of impartiality in ethics consultation that comports with the spirit of ethics facilitation. I defend against the second by suggesting that TEC skills can be easily adapted for use outside of or after ethics consultation as a means to ameliorate the moral distress associated with emotionally charged value conflicts

Masterworks III

Program listing performers and works performe

A Magnetohydrodynamic Model of the M87 Jet I: Superluminal Knot Ejections from HST-1 as Trails of Quad Relativistic MHD Shocks

This is the first in a series of papers that introduces a new paradigm for understanding the jet in M87: a collimated relativistic flow in which strong magnetic fields play a dominant dynamical role. Here wefocus on the flow downstream of HST-1 - an essentially stationary flaring feature that ejects trails of superluminal components. We propose that these components are quad relativistic magnetohydrodynamic shock fronts (forward/reverse fast and slow modes) in a narrow jet with a helically twisted magnetic structure. And we demonstrate the properties of such shocks with simple one-dimensional numerical simulations. Quasi-periodic ejections of similar component trails may be responsible for the M87 jet substructures observed further downstream on 100 - 1,000 pc scales. This new paradigm requires the assimilation of some new concepts into the astrophysical jet community, particularly the behavior of slow/fast-mode waves/shocks and of current-driven helical kink instabilities. However, the prospects of these ideas applying to a large number of other jet systems may make this worth the effort.Comment: 7 pages, 4 figures, Accepted for Publication in Ap

Small Molecule LC-MS/MS Fragmentation Data Analysis and Application to Siderophore Identification

Rapid developments in tandem liquid chromatography-mass spectrometry (LC-MS/MS) have created wide interest in applications for the analysis of small molecule mixtures. MS/MS spectra can contain rich structural information, but because of the structural diversity of small molecules and different data acquisition methods, analysis algorithms and workflows frequently need to be tailored to individual research questions. This chapter shows how MATLAB can be used for LC-MS/MS-based structural characterization of small molecules. Starting with the import of raw data, ways for visualization and the creation of graphical user interfaces (GUIs) for individual applications are demonstrated. A selection of frequently used algorithms for pre-processing and data analysis is reviewed in context of their MATLAB implementation. The approaches are then tailored and applied to the analysis of iron-binding peptides (peptidic siderophores) by high-resolution LC-MS/MS. The method uses a database with siderophore structures to exploit prior knowledge about siderophore structural diversity for the interpretation of MS/MS spectra from known and new siderophores

New Constraints on Quantum Gravity from X-ray and Gamma-Ray Observations

One aspect of the quantum nature of spacetime is its "foaminess" at very small scales. Many models for spacetime foam are defined by the accumulation power $\alpha$, which parameterizes the rate at which Planck-scale spatial uncertainties (and thephase shifts they produce) may accumulate over large path-lengths. Here $\alpha$ is defined by theexpression for the path-length fluctuations, $\delta \ell$, of a source at distance $\ell$, wherein $\delta \ell \simeq \ell^{1 - \alpha} \ell_P^{\alpha}$, with $\ell_P$ being the Planck length. We reassess previous proposals to use astronomical observations ofdistant quasars and AGN to test models of spacetime foam. We show explicitly how wavefront distortions on small scales cause the image intensity to decay to the point where distant objects become undetectable when the path-length fluctuations become comparable to the wavelength of the radiation. We use X-ray observations from {\em Chandra} to set the constraint $\alpha \gtrsim 0.58$, which rules out the random walk model (with $\alpha = 1/2$). Much firmer constraints canbe set utilizing detections of quasars at GeV energies with {\em Fermi}, and at TeV energies with ground-based Cherenkovtelescopes: $\alpha \gtrsim 0.67$ and $\alpha \gtrsim 0.72$, respectively. These limits on $\alpha$ seem to rule out $\alpha = 2/3$, the model of some physical interest.Comment: 11 pages, 9 figures, ApJ, in pres