On globally non-trivial almost-commutative manifolds

Within the framework of Connes' noncommutative geometry, we define and study globally non-trivial (or topologically non-trivial) almost-commutative manifolds. In particular, we focus on those almost-commutative manifolds that lead to a description of a (classical) gauge theory on the underlying base manifold. Such an almost-commutative manifold is described in terms of a 'principal module', which we build from a principal fibre bundle and a finite spectral triple. We also define the purely algebraic notion of 'gauge modules', and show that this yields a proper subclass of the principal modules. We describe how a principal module leads to the description of a gauge theory, and we provide two basic yet illustrative examples.Comment: 34 pages, minor revision

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

Inverse monoids and immersions of 2-complexes

It is well known that under mild conditions on a connected topological space $\mathcal X$, connected covers of $\mathcal X$ may be classified via conjugacy classes of subgroups of the fundamental group of $\mathcal X$. In this paper, we extend these results to the study of immersions into 2-dimensional CW-complexes. An immersion $f : {\mathcal D} \rightarrow \mathcal C$ between CW-complexes is a cellular map such that each point $y \in {\mathcal D}$ has a neighborhood $U$ that is mapped homeomorphically onto $f(U)$ by $f$. In order to classify immersions into a 2-dimensional CW-complex $\mathcal C$, we need to replace the fundamental group of $\mathcal C$ by an appropriate inverse monoid. We show how conjugacy classes of the closed inverse submonoids of this inverse monoid may be used to classify connected immersions into the complex

Singular sources in gravity and homotopy in the space of connections

Suppose a Lagrangian is constructed from its fields and their derivatives. When the field configuration is a distribution, it is unambiguously defined as the limit of a sequence of smooth fields. The Lagrangian may or may not be a distribution, depending on whether there is some undefined product of distributions. Supposing that the Lagrangian is a distribution, it is unambiguously defined as the limit of a sequence of Lagrangians. But there still remains the question: Is the distributional Lagrangian uniquely defined by the limiting process for the fields themselves? In this paper a general geometrical construction is advanced to address this question. We describe certain types of singularities, not by distribution valued tensors, but by showing that the action functional for the singular fields is (formally) equivalent to another action built out of \emph{smooth} fields. Thus we manage to make the problem of the lack of a derivative disappear from a system which gives differential equations. Certain ideas from homotopy and homology theory turn out to be of central importance in analyzing the problem and clarifying finer aspects of it. The method is applied to general relativity in first order formalism, which gives some interesting insights into distributional geometries in that theory. Then more general gravitational Lagrangians in first order formalism are considered such as Lovelock terms (for which the action principle admits space-times more singular than other higher curvature theories).Comment: 21 pages, 9 figures, RevTe

Production and Composition of Pyrogenic Dissolved Organic Matter From a Logical Series of Laboratory-Generated Chars

Though pyrogenic carbon (pyC) has been assumed to be predominantly stable, degradation and transfers of pyC between various pools have been found to influence its cycling and longevity in the environment. Dissolution via leaching may be the main control on loss processes such as microbial or abiotic oxidation, mineral sorption, or export to aquatic systems. Yet, little is known about the controls on pyrogenic dissolved organic matter (pyDOM) generation or composition. Here, the yield and composition of pyDOM generated through batch leaching of a thermal series of oak and grass biochars, as well as several non-pyrogenic reference materials, was compared to that of their parent solids. Over 17 daily leaching cycles, biochars made from oak at 250–650◦C released decreasing amounts of C on both a weight (16.9–0.3%, respectively) and C yield basis (7.4–0.2% C, respectively). Aryl-C represented an estimated 32–82% of C in the parent solids (identified by 13C-NMR), but only 7–38% in the leachates (identified by 1H-NMR), though both increased with pyrolysis temperature. PyC, often operationally defined as condensed aromatic carbon (ConAC), was quantified using the benzenepolycarboxylic acid (BPCA) method. Tri- and tetra-carboxylated BPCAs were formed from non-pyrogenic reference materials, thus, only penta- and hexa-carboxylated BPCAs were used to derive a BPCA-C to ConAC conversion factor of 7.04. ConAC made up 24–57% of the pyrogenic solid C (excluding the 250◦C biochar), but only about 9–23% of their respective leachates’ DOC, though both proportions generally increased with pyrolysis temperature. Weighted BPCA compound distributions, or the BPCA Aromatic Condensation (BACon) Index, indicate that ConAC cluster size increased in pyrogenic solids but not in leachates. Additional evidence presented suggests that both aromatic cluster size and O-containing functional group contents in the pyrogenic solid control pyC solubility. Overall, pyDOM was found to be compositionally dissimilar from its parent chars and contained a complex mixture of organic compound groups. Thus, it is expected that estimates of dissolved pyC production and export, made only by detection of ConAC, are too low by factors of 4–11

Genome sequence and comparative analysis of a putative entomopathogenic Serratia isolated from Caenorhabditis briggsae

Background: Entomopathogenic associations between nematodes in the genera Steinernema and Heterorhabdus with their cognate bacteria from the bacterial genera Xenorhabdus and Photorhabdus, respectively, are extensively studied for their potential as biological control agents against invasive insect species. These two highly coevolved associations were results of convergent evolution. Given the natural abundance of bacteria, nematodes and insects, it is surprising that only these two associations with no intermediate forms are widely studied in the entomopathogenic context. Discovering analogous systems involving novel bacterial and nematode species would shed light on the evolutionary processes involved in the transition from free living organisms to obligatory partners in entomopathogenicity. Results: We report the complete genome sequence of a new member of the enterobacterial genus Serratia that forms a putative entomopathogenic complex with Caenorhabditis briggsae. Analysis of the 5.04 MB chromosomal genome predicts 4599 protein coding genes, seven sets of ribosomal RNA genes, 84 tRNA genes and a 64.8 KB plasmid encoding 74 genes. Comparative genomic analysis with three of the previously sequenced Serratia species, S. marcescens DB11 and S. proteamaculans 568, and Serratia sp. AS12, revealed that these four representatives of the genus share a core set of ~3100 genes and extensive structural conservation. The newly identified species shares a more recent common ancestor with S. marcescens with 99 % sequence identity in rDNA sequence and orthology across 85.6 % of predicted genes. Of the 39 genes/operons implicated in the virulence, symbiosis, recolonization, immune evasion and bioconversion, 21 (53.8 %) were present in Serratia while 33 (84.6 %) and 35 (89 %) were present in Xenorhabdus and Photorhabdus EPN bacteria respectively. Conclusion: The majority of unique sequences in Serratia sp. SCBI (South African Caenorhabditis briggsae Isolate) are found in ~29 genomic islands of 5 to 65 genes and are enriched in putative functions that are biologically relevant to an entomopathogenic lifestyle, including non-ribosomal peptide synthetases, bacteriocins, fimbrial biogenesis, ushering proteins, toxins, secondary metabolite secretion and multiple drug resistance/efflux systems. By revealing the early stages of adaptation to this lifestyle, the Serratia sp. SCBI genome underscores the fact that in EPN formation the composite end result – killing, bioconversion, cadaver protection and recolonization- can be achieved by dissimilar mechanisms. This genome sequence will enable further study of the evolution of entomopathogenic nematode-bacteria complexes

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

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

Discrete Morse functions for graph configuration spaces

We present an alternative application of discrete Morse theory for two-particle graph configuration spaces. In contrast to previous constructions, which are based on discrete Morse vector fields, our approach is through Morse functions, which have a nice physical interpretation as two-body potentials constructed from one-body potentials. We also give a brief introduction to discrete Morse theory. Our motivation comes from the problem of quantum statistics for particles on networks, for which generalized versions of anyon statistics can appear.Comment: 26 page

Homotopy types of stabilizers and orbits of Morse functions on surfaces

Let $M$ be a smooth compact surface, orientable or not, with boundary or without it, $P$ either the real line $R^1$ or the circle $S^1$, and $Diff(M)$ the group of diffeomorphisms of $M$ acting on $C^{\infty}(M,P)$ by the rule $h\cdot f\mapsto f \circ h^{-1}$, where $h\in Diff(M)$ and $f \in C^{\infty}(M,P)$. Let $f:M \to P$ be a Morse function and $O(f)$ be the orbit of $f$ under this action. We prove that $\pi_k O(f)=\pi_k M$ for $k\geq 3$, and $\pi_2 O(f)=0$ except for few cases. In particular, $O(f)$ is aspherical, provided so is $M$. Moreover, $\pi_1 O(f)$ is an extension of a finitely generated free abelian group with a (finite) subgroup of the group of automorphisms of the Reeb graph of $f$. We also give a complete proof of the fact that the orbit $O(f)$ is tame Frechet submanifold of $C^{\infty}(M,P)$ of finite codimension, and that the projection $Diff(M) \to O(f)$ is a principal locally trivial $S(f)$-fibration.Comment: 49 pages, 8 figures. This version includes the proof of the fact that the orbits of a finite codimension of tame action of tame Lie group on tame Frechet manifold is a tame Frechet manifold itsel