Quantum statistics on graphs

Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph, concentrating on the simplest case of abelian statistics for two particles. In spite of the fact that graphs are locally one-dimensional, anyon statistics emerge in a generalized form. A given graph may support a family of independent anyon phases associated with topologically inequivalent exchange processes. In addition, for sufficiently complex graphs, there appear new discrete-valued phases. Our analysis is simplified by considering combinatorial rather than metric graphs -- equivalently, a many-particle tight-binding model. The results demonstrate that graphs provide an arena in which to study new manifestations of quantum statistics. Possible applications include topological quantum computing, topological insulators, the fractional quantum Hall effect, superconductivity and molecular physics.Comment: 21 pages, 6 figure

The Shape of Pulverized Bituminous Vitrinite Coal Particles

The shape of pulverized bituminous coal particles (vitrinites) was determined by optical and laser light scattering. Vitrain samples were collected from obvious tree remains located in the ceilings of two Appalachian coal mines. Wet sieving produced narrow size cuts. The particles were determined to be oblong or blocky in shape, with average length-to-width ratio of 1.7 and sphericity of 0.78. They were analogous in shape to a square ended, rectangular house brick . The two bituminous coals and different size cuts of each coal had essentially the same shape parameters. Characteristic heating times and terminal velocities were higher by 22 and 20%, respectively compared to spherical particles

On the Expansions in Spin Foam Cosmology

We discuss the expansions used in spin foam cosmology. We point out that already at the one vertex level arbitrarily complicated amplitudes contribute, and discuss the geometric asymptotics of the five simplest ones. We discuss what type of consistency conditions would be required to control the expansion. We show that the factorisation of the amplitude originally considered is best interpreted in topological terms. We then consider the next higher term in the graph expansion. We demonstrate the tension between the truncation to small graphs and going to the homogeneous sector, and conclude that it is necessary to truncate the dynamics as well.Comment: 17 pages, 4 figures, published versio

Differences in client and therapist views of the working alliance in drug treatment

Background - There is growing evidence that the therapeutic alliance is one of the most consistent predictors of retention and outcomes in drug treatment. Recent psychotherapy research has indicated that there is a lack of agreement between client, therapist and observer ratings of the therapeutic alliance; however, the clinical implications of this lack of consensus have not been explored. Aims - The aims of the study are to (1) explore the extent to which, in drug treatment, clients and counsellors agree in their perceptions of their alliance, and (2) investigate whether the degree of disagreement between clients and counsellors is related to retention in treatment. Methods - The study recruited 187 clients starting residential rehabilitation treatment for drug misuse in three UK services. Client and counsellor ratings of the therapeutic alliance (using the WAI-S) were obtained during weeks 1-12. Retention was in this study defined as remaining in treatment for at least 12 weeks. Results - Client and counsellor ratings of the alliance were only weakly related (correlations ranging from r = 0.07 to 0.42) and tended to become more dissimilar over the first 12 weeks in treatment. However, whether or not clients and counsellors agreed on the quality of their relationship did not influence whether clients were retained in treatment. Conclusions - The low consensus between client and counsellor views of the alliance found in this and other studies highlights the need for drug counsellors to attend closely to their clients' perceptions of the alliance and to seek regular feedback from clients regarding their feelings about their therapeutic relationship

Homotopy Theory of Strong and Weak Topological Insulators

We use homotopy theory to extend the notion of strong and weak topological insulators to the non-stable regime (low numbers of occupied/empty energy bands). We show that for strong topological insulators in d spatial dimensions to be "truly d-dimensional", i.e. not realizable by stacking lower-dimensional insulators, a more restrictive definition of "strong" is required. However, this does not exclude weak topological insulators from being "truly d-dimensional", which we demonstrate by an example. Additionally, we prove some useful technical results, including the homotopy theoretic derivation of the factorization of invariants over the torus into invariants over spheres in the stable regime, as well as the rigorous justification of replacing $T^d$ by $S^d$ and $T^{d_k}\times S^{d_x}$ by $S^{d_k+d_x}$ as is common in the current literature.Comment: 11 pages, 3 figure

Technical Note: Molecular characterization of aerosol-derived water soluble organic carbon using ultrahigh resolution electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry

Despite the acknowledged relevance of aerosol-derived water-soluble organic carbon (WSOC) to climate and biogeochemical cycling, characterization of aerosol WSOC has been limited. Electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI FT-ICR MS) was utilized in this study to provide detailed molecular level characterization of the high molecular weight (HMW; m/z>223) component of aerosol-derived WSOC collected from rural sites in Virginia and New York, USA. More than 3000 peaks were detected by ESI FT-ICR MS within a m/z range of 223–600 for each sample. Approximately 86% (Virginia) and 78% (New York) of these peaks were assigned molecular formulas using only carbon (C), hydrogen (H), oxygen (O), nitrogen (N), and sulfur (S) as elemental constituents. H/C and O/C molar ratios were plotted on van Krevelen diagrams and indicated a strong contribution of lignin-like and lipid-like compounds to the aerosol-derived WSOC samples. Approximately 1–4% of the peaks in the aerosol-derived WSOC mass spectra were classified as black carbon (BC) on the basis of double bond equivalents calculated from the assigned molecular formulas. In addition, several high-magnitude peaks in the mass spectra of samples from both sites corresponded to molecular formulas proposed in previous secondary organic aerosol (SOA) laboratory investigations indicating that SOAs are important constituents of the WSOC. Overall, ESI FT-ICR MS provides a level of resolution adequate for detailed compositional and source information of the HMW constituents of aerosol-derived WSOC

Type I D-branes in an H-flux and twisted KO-theory

Witten has argued that charges of Type I D-branes in the presence of an H-flux, take values in twisted KO-theory. We begin with the study of real bundle gerbes and their holonomy. We then introduce the notion of real bundle gerbe KO-theory which we establish is a geometric realization of twisted KO-theory. We examine the relation with twisted K-theory, the Chern character and provide some examples. We conclude with some open problems.Comment: 23 pages, Latex2e, 2 new references adde

The Theory of the Interleaving Distance on Multidimensional Persistence Modules

In 2009, Chazal et al. introduced $\epsilon$-interleavings of persistence modules. $\epsilon$-interleavings induce a pseudometric $d_I$ on (isomorphism classes of) persistence modules, the interleaving distance. The definitions of $\epsilon$-interleavings and $d_I$ generalize readily to multidimensional persistence modules. In this paper, we develop the theory of multidimensional interleavings, with a view towards applications to topological data analysis. We present four main results. First, we show that on 1-D persistence modules, $d_I$ is equal to the bottleneck distance $d_B$. This result, which first appeared in an earlier preprint of this paper, has since appeared in several other places, and is now known as the isometry theorem. Second, we present a characterization of the $\epsilon$-interleaving relation on multidimensional persistence modules. This expresses transparently the sense in which two $\epsilon$-interleaved modules are algebraically similar. Third, using this characterization, we show that when we define our persistence modules over a prime field, $d_I$ satisfies a universality property. This universality result is the central result of the paper. It says that $d_I$ satisfies a stability property generalizing one which $d_B$ is known to satisfy, and that in addition, if $d$ is any other pseudometric on multidimensional persistence modules satisfying the same stability property, then $d\leq d_I$. We also show that a variant of this universality result holds for $d_B$, over arbitrary fields. Finally, we show that $d_I$ restricts to a metric on isomorphism classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in Foundations of Computational Mathematics. 36 page

The development of coal-based technologies for Department of Defense facilities. Volume 1, Technical report. Semiannual technical progress report, September 28, 1994--March 27, 1995

This program is being conducted as a cooperative agreement between the Consortium for Coal Water Mixture Technology and the U.S. Department of Energy. Activities this reporting period are summarized by phase. Phase I is nearly completed. During this reporting period, coal beneficiation/preparation studies, engineering designs and economics for retrofitting the Crane, Indiana boiler to fire coal-based fuels, and a 1,000-hour demonstration of dry, micronized coal were completed. In addition, a demonstration-scale micronized-coal water mixture (MCWM) preparation circuit was constructed and a 1,000-hour demonstration firing MCWM began. Work in Phase II focused on emissions reductions, coal beneficiation/preparation studies, and economic analyses of coal use. Emissions reductions investigations involved literature surveys of NO{sub x}, SO{sub 2}, trace metals, volatile organic compounds, and fine particulate matter capture. In addition, vendors and engineering firms were contacted to identify the appropriate emissions technologies for the installation of commercial NO{sub x} and SO{sub 2} removal systems on the demonstration boiler. Information from the literature surveys and engineering firms will be used to identify, design, and install a control system(s). Work continued on the refinement and optimization of coal grinding and MCWM preparation procedures, and on the development of advanced processes for beneficiating high ash, high sulfur coals. Work also continued on determining the basic cost estimation of boiler retrofits, and evaluating environmental, regulatory, and regional economic impacts. In addition, the feasibility of technology adoption, and the public`s perception of the benefits and costs of coal usage was studied. A coal market analysis was completed. Work in Phase III focused on coal preparation studies, emissions reductions and economic analyses of coal use

Biolability of Fresh and Photodegraded Pyrogenic Dissolved Organic Matter From Laboratory-Prepared Chars

Pyrogenic dissolved organic matter (pyDOM) is known to be an important biogeochemical constituent of aquatic ecosystems and the carbon cycle. While recent studies have examined how pyDOM production, composition, and photolability varies with parent pyrogenic solid material type, we lack an understanding of potential microbial mineralization and transformation of pyDOM in the biogeosphere. Thus, leachates of oak, charred at 400 °C and 650 °C, as well as their photodegraded counterparts were incubated with a soil‐extracted microbial consortium over 96 days. During the incubation, significantly more carbon was biomineralized from the lower versus higher temperature char leachate (45% vs. 37% lost, respectively). Further, the photodegraded leachates were biomineralized to significantly greater extents than their fresh non‐photodegraded counterparts. Kinetic modeling identified the mineralizable pyDOC fractions to have half‐lives of 9–13 days. Proton nuclear magnetic resonance spectroscopy indicated that the majority of this loss could be attributed to low molecular weight constituents of pyDOM (i.e., simple alcohols and acids). Further, the quantification of benzenepolycarboxylic acid (BPCA) molecular markers indicated that condensed aromatic compounds in pyDOM were biomineralized to much lesser extents (4.4% and 10.1% decrease in yields of ΣBPCA‐C over 66 days from 400 °C and 650 °C oak pyDOM, respectively), but most of this loss could be attributed to the biomineralization of smaller condensed clusters (four aromatic rings or less). These results highlight the contrasting bioavailability of different portions of pyDOM, and the need to examine both to evaluate its role in soil or aquatic heterotrophy and its environmental fate in the hydrogeosphere