Making Toilets More Affordable for the Poor Through Microfinance

Over a 13-month period, the Water and Sanitation Program (WSP) worked with a number of partners, including the international non-profit Program for Appropriate Technology in Health (PATH) and International Development Enterprises (iDE), to pilot a sanitation financing program to address the challenge of reaching low-income households with improved sanitation solutions. This learning note presents the lessons from this pilot to promote scale-up in Cambodia and to inform similar efforts in other countries

Proper conformal symmetries in SD Einstein spaces

Proper conformal symmetries in self-dual (SD) Einstein spaces are considered. It is shown, that such symmetries are admitted only by the Einstein spaces of the type [N]x[N]. Spaces of the type [N]x[-] are considered in details. Existence of the proper conformal Killing vector implies existence of the isometric, covariantly constant and null Killing vector. It is shown, that there are two classes of [N]x[-]-metrics admitting proper conformal symmetry. They can be distinguished by analysis of the associated anti-self-dual (ASD) null strings. Both classes are analyzed in details. The problem is reduced to single linear PDE. Some general and special solutions of this PDE are presented

Behaviour of Eigenfunction Subsequences for Delta-Perturbed 2D Quantum Systems

We consider a quantum system whose unperturbed form consists of a self-adjoint $-\Delta$ operator on a 2-dimensional compact Riemannian manifold, which may or may not have a boundary. Then as a perturbation, we add a delta potential / point scatterer at some select point $p$. The perturbed self-adjoint operator is constructed rigorously by means of self-adjoint extension theory. We also consider a corresponding classical dynamical system on the cotangent/cosphere bundle, consisting of geodesic flow on the manifold, with specular reflection if there is a boundary. Chapter 2 describes the mathematics of the unperturbed and perturbed quantum systems, as well as outlining the classical dynamical system. Included in the discussion on the delta-perturbed quantum system is consideration concerning the strength of the delta potential. It is reckoned that the delta potential effectively has negative infinitesimal strength. Chapter 3 continues on with investigations from [KMW10], concerned with perturbed eigenfunctions that approximate to a linear combination of only two "surrounding" unperturbed eigenfunctions. In Thm. 4.4 of [KMW10], conditions are derived under which a sequence of perturbed eigenfunctions exhibits this behaviour in the limit. The approximating pair linear combinations belong to a class of quasimodes constructed within [KMW10]. The aim of Chapter 3 in this thesis is to improve on the result in [KMW10]. In Chapter 3, preliminary results are first derived constituting a broad consideration of the question of when a perturbed eigenfunction subsequence approaches linear combinations of only two surrounding unperturbed eigenfunctions. Afterwards, the central result of this Chapter, namely Thm. 3.4.1, is derived, which serves as an improved version of Thm. 4.4 in [KMW10]. The conditions of this theorem are shown to be weaker than those in [KMW10]. At the same time though, the conclusion does not require the approximating pair linear combinations to be quasimodes contained in the domain of the perturbed operator. Cor. 3.5.2 allows for a transparent comparison between the results of this Chapter and [KMW10]. Chapter 4 deals with the construction of non-singular rank-one perturbations for which the eigenvalues and eigenfunctions approximate those of the delta-perturbed operator. This is approached by means of direct analysis of the construction and formulae for the rank-one-perturbed eigenvalues and eigenfunctions, by comparison that of the delta-perturbed eigenvalues and eigenfunctions. Successful results are derived to this end, the central result being Thm. 4.4.19. This provides conditions on a sequence of non-singular rank-one perturbations, under which all eigenvalues and eigenbasis members within an interval converge to those of the delta-perturbed operator. Comparisons have also been drawn with previous literature such as [Zor80], [AK00] and [GN12]. These deal with rank-one perturbations approaching the delta potential within the setting of a whole Euclidean space $\mathbb{R}^n$, for example by strong resolvent convergence, and by limiting behaviour of generalised eigenfunctions associated with energies at every $E\in(0,\infty)$. Furthermore in Chapter 4, the suggestion from Chapter 2 that the delta potential has negative infinitessimal strength is further supported, due to the coefficients of the approximating rank-one perturbations being negative and tending to zero. This phenomenon is also in agreement with formulae from [Zor80], [AK00] and [GN12]. Chapter 5 first reviews the correspondence between certain classical dynamics and equidistribution in position space of almost all unperturbed quantum eigenfunctions, as demonstrated for example in [MR12]. Equidistribution in position space of almost all perturbed eigenfunctions, in the case of the 2D rectangular flat torus, is also reviewed. This result comes from [RU12], which is only stated in terms of the "new" perturbed eigenfunctions, which would only be a subset of the full perturbed eigenbasis. Nevertheless, in this Chapter it is explained how it follows that this position space equidistribution result also applies to a full-density subsequence of the full perturbed eigenbasis. Finally three methods of approach are discussed for attempting to derive this position space equidistribution result in the case of a more general delta-perturbed system whose classical dynamics satisfies the particular key property. [AK00] S. Albeverio and P. Kurasov: Singular Perturbations of Differential Operators. London Math. Soc. Lecture Note Ser. 271. Cambridge University Press (2000). [GN12] P. G. Grinevich and R. G. Novikov: Faddeev eigenfunctions for point potentials in two dimensions. Phys. Lett. A 376, 1102 (2012). [KMW10] J. P. Keating, J. Marklof and B. Winn: Localized eigenfunctions in \v{S}eba billiards. J. Math. Phys. 51, 062101 (2010). [MR12] J. Marklof and Z. Rudnick: Almost all eigenfunctions of a rational polygon are uniformly distributed. J. Spectr. Theory 2, 107 (2012). [RU12] Z. Rudnick and H. Uebersch\"{a}r: Statistics of Wave Functions for a Point Scatterer on the Torus. Commun. Math. Phys. 316, 763 (2012). [Zor80] J. Zorbas: Perturbation of self-adjoint operators by Dirac distributions. J. Math. Phys. 21(4), 840 (1980)

Citation Networks in High Energy Physics

The citation network constituted by the SPIRES data base is investigated empirically. The probability that a given paper in the SPIRES data base has $k$ citations is well described by simple power laws, $P(k) \propto k^{-\alpha}$, with $\alpha \approx 1.2$ for $k$ less than 50 citations and $\alpha \approx 2.3$ for 50 or more citations. Two models are presented that both represent the data well, one which generates power laws and one which generates a stretched exponential. It is not possible to discriminate between these models on the present empirical basis. A consideration of citation distribution by subfield shows that the citation patterns of high energy physics form a remarkably homogeneous network. Further, we utilize the knowledge of the citation distributions to demonstrate the extreme improbability that the citation records of selected individuals and institutions have been obtained by a random draw on the resulting distribution.Comment: 9 pages, 6 figures, 2 table

Acute Hypercapnia/Ischemia Alters the Esterification of Arachidonic Acid and Docosahexaenoic Acid Epoxide Metabolites in Rat Brain Neutral Lipids.

In the brain, approximately 90% of oxylipins are esterified to lipids. However, the significance of this esterification process is not known. In the present study, we (1) validated an aminopropyl solid phase extraction (SPE) method for separating esterified lipids using 100 and 500 mg columns and (2) applied the method to quantify the distribution of esterified oxylipins within phospholipids (PL) and neutral lipids (NL) (i.e. triacylglycerol and cholesteryl ester) in rats subjected to head-focused microwave fixation (controls) or CO2 -induced hypercapnia/ischemia. We hypothesized that oxylipin esterification into these lipid pools will be altered following CO2 -induced hypercapnia/ischemia. Lipids were extracted from control (n = 8) and CO2 -asphyxiated (n = 8) rat brains and separated on aminopropyl cartridges to yield PL and NL. The separated lipid fractions were hydrolyzed, purified with hydrophobic-lipophilic-balanced SPE columns, and analyzed with ultra-high-pressure liquid chromatography coupled to tandem mass spectrometry. Method validation showed that the 500 mg (vs 100 mg) aminopropyl columns yielded acceptable separation and recovery of esterified fatty acid epoxides but not other oxylipins. Two epoxides of arachidonic acid (ARA) were significantly increased, and three epoxides of docosahexaenoic acid (DHA) were significantly decreased in brain NL of CO2 -asphyxiated rats compared to controls subjected to head-focused microwave fixation. PL-bound fatty acid epoxides were highly variable and did not differ significantly between the groups. This study demonstrates that hypercapnia/ischemia alters the concentration of ARA and DHA epoxides within NL, reflecting an active turnover process regulating brain fatty acid epoxide concentrations

Consumption-Based Conservation Targeting: Linking Biodiversity Loss to Upstream Demand through a Global Wildlife Footprint.

Although most conservation efforts address the direct, local causes of biodiversity loss, effective long-term conservation will require complementary efforts to reduce the upstream economic pressures, such as demands for food and forest products, which ultimately drive these downstream losses. Here, we present a wildlife footprint analysis that links global losses of wild birds to consumer purchases across 57 economic sectors in 129 regions. The United States, India, China, and Brazil have the largest regional wildlife footprints, while per-person footprints are highest in Mongolia, Australia, Botswana, and the United Arab Emirates. A US$100 purchase of bovine meat or rice products occupies approximately 0.1 km2 of wild bird ranges, displacing 1-2 individual birds, for 1 year. Globally significant importer regions, including Japan, the United Kingdom, Germany, Italy, and France, have large footprints that drive wildlife losses elsewhere in the world and represent important targets for consumption-focused conservation attention

ENGINEERING OF FUNGAL AROMATIC POLYKETIDE BIOSYNTHESIS AND ELUCIDATION OF CERCOSPORIN BIOSYNTHESIS IN THE PLANT PATHOGEN CERCOSPORA NICOTIANAE

In fungi, the iterative, non-reducing polyketide synthases (NR-PKSs) are responsible for the biosynthesis of aromatic polyketide products. While the modular type I PKSs have been extensively studied for 20 years, the biochemistry of NR-PKS is only now beginning to be elucidated. The NR-PKSs share a common domain architecture that is intrinsically linked to their function. The mode of biosynthesis is analogous to that of fatty acids by animal fatty acid synthases (FAS), but simplified. The three N-terminal domains, the starter unit:acyl-carrier protein transacylase (SAT), ketosynthase (KS) and malonyl acyl transferase (MAT) domains are responsible for the initiation and polyketide elongation phases. The SAT domain selects a precursor or starter unit substrate as an acyl thioester while the MAT domain introduces ketide extender units from malonyl-CoA. The KS works in collaboration with the acyl-carrier protein (ACP) to catalyze the decarboxylative Claisen condensation of these substrates generating a linear, ACP-bound β-ketone intermediate. The C-terminal domains of NR-PKSs control the final stage of biosynthesis, which includes regiospecific aldol cyclizations/aromatizations by the product template (PT) domain and product release by the thioesterase (TE) domain. In this way, the four factors governing chemical diversity in aromatic polyketides are entirely controlled by the enzyme, with the N-terminal half determining starter unit selection and chain length, and the C-terminal half controlling the cyclization pattern and mode of product evolution. Our lab has innovated the use of enzyme deconstruction in NR-PKSs to determine the catalytic program of these enzymes. The enzyme deconstruction approach requires the dissection of an individual NR-PKS into its constituent domains or multidomain fragments. Mono- and multidomain fragments are expressed and purified individually and then recombined in vitro, reconstituting wild-type activity. Using the enzyme deconstruction approach, the catalytic activity of CTB1—the NR-PKS of cercosporin biosynthesis in the fungal plant pathogen Cercospora nicotianae—was determined. The CTB1 TE domain was demonstrated to catalyze an unprecedented enol-lactonization to form the naphthopyrone nor-toralactone—representing an expansion of known TE chemistry. The formation of nor-toralactone was unexpected and in conflict with the accepted cercosporin biosynthetic pathway. Using a combination of gene knockout strains and in vitro enzymology, a new cercosporin biosynthetic pathway was identified. Of particular interest was the activity of an unusual didomain enzyme CTB3. The flavin-dependent monooxygenase domain of CTB3 was identified to catalyze a unique oxidative aromatic ring cleavage—expanding the chemical repertoire of these ubiquitous proteins. Enzyme deconstruction served as the basis of an NR-PKS engineering project in which homologous domains from non-cognate parent NR-PKSs were swapped in vitro to produce non-native polyketide products. Using a systematic approach to domain-swapping, several rules governing rational engineering of NR-PKS were codified. Domain-swapping of deconstructed NR-PKSs facilitated rational engineering of intact, chimeric NR-PKSs. A library of chimeric NR-PKSs was prepared and selected members were assayed for activity. Combining the rules of engineering gleaned from deconstructed NR-PKS domain-swapping and the construction of the chimeric NR-PKS library, an attempt to rationally design a topopyrone synthase was unsuccessfully made. By examining the activities of individual domains and perturbing the composition of NR-PKSs, we have made invaluable insights into the NR-PKS catalytic program—understanding that will underpin future efforts towards rational NR-PKS engineering

Zipf's law and log-normal distributions in measures of scientific output across fields and institutions: 40 years of Slovenia's research as an example

Slovenia's Current Research Information System (SICRIS) currently hosts 86,443 publications with citation data from 8,359 researchers working on the whole plethora of social and natural sciences from 1970 till present. Using these data, we show that the citation distributions derived from individual publications have Zipfian properties in that they can be fitted by a power law $P(x) \sim x^{-\alpha}$, with $\alpha$ between 2.4 and 3.1 depending on the institution and field of research. Distributions of indexes that quantify the success of researchers rather than individual publications, on the other hand, cannot be associated with a power law. We find that for Egghe's g-index and Hirsch's h-index the log-normal form $P(x) \sim \exp[-a\ln x -b(\ln x)^2]$ applies best, with $a$ and $b$ depending moderately on the underlying set of researchers. In special cases, particularly for institutions with a strongly hierarchical constitution and research fields with high self-citation rates, exponential distributions can be observed as well. Both indexes yield distributions with equivalent statistical properties, which is a strong indicator for their consistency and logical connectedness. At the same time, differences in the assessment of citation histories of individual researchers strengthen their importance for properly evaluating the quality and impact of scientific output.Comment: 8 pages, 3 figures; accepted for publication in Journal of Informetrics [supplementary material available at http://www.matjazperc.com/sicris/stats.html