The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

Relaxation methods for solving linear inequality systems: Converging results

The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In [12] an algorithm, called extended relaxation method, that solves the feasibility problem, has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we onsider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.

Double adjunctions

We characterize double adjunctions in terms of presheaves and universal squares, and then apply these characterizations to free monads and Eilenberg-Moore objects in double categories. We improve upon an earlier result of Fiore-Gambino-Kock in [7] to conclude: if a double category with cofolding admits the construction of free monads in its horizontal 2-category, then it also admits the construction of free monads as a double category horizontally and vertically, and also in its vertical 2-category. We also prove that a double category admits Eilenberg-Moore objects if and only if a certain parameterized presheaf is representable. Along the way, we develop parameterized presheaves on double categories and prove a double Yoneda Lemma.

Real-time imaging of regional myocardial function using fast-SENC.

A technique for fast imaging of regional myocardial function using a spiral acquisition in combination with strain-encoded (SENC) magnetic resonance imaging (MRI) is presented in this paper. This technique, which is termed fast-SENC, enables scan durations as short as a single heartbeat. A reduced field of view (FOV) without foldover artifacts was achieved by localized SENC, which selectively excited the region around the heart. The two images required for SENC imaging (low- and high-tuning) were acquired in an interleaved fashion throughout the cardiac cycle to further shorten the scan time. Regional circumferential contraction and longitudinal shortening of both the left ventricle (LV) and right ventricle (RV) were examined in long- and short-axis views, respectively. The in vivo results obtained from five human subjects and five infarcted dogs are presented. The results of the fast-SENC technique in a single heartbeat acquisition were comparable to those obtained by conventional SENC in a long acquisition time. Therefore, fast-SENC may prove useful for imaging during stress or arrhythmia.

Assessing the value of CAN-gene mutations using MALDI-TOF MS.

PURPOSE: To identify cancer-linked genes, Sjöblom et al. and Wood et al. performed a genome-wide mutation screening in human breast and colorectal cancers. 140 CAN-genes were found in breast cancer, which in turn contained overall 334 mutations. These mutations could prove useful for diagnostic and therapeutic purposes. METHODS: We used a MALDI-TOF MS 40-plex assay for testing 40 loci within 21 high-ranking breast cancer CAN-genes. To confirm mutations, we performed single-plex assays and sequencing. RESULTS: In general, the mutation rate of the analyzed loci in our sample cohort was very low. No mutation from the 40 loci analyzed could be found in the 6 cell lines. In tissue samples, a single breast cancer tissue sample showed heterozygosity at locus c.5834G>A within the ZFYVE26 gene (Zinc finger FYVE domain-containing gene 26). CONCLUSIONS: Sjöblom et al./Wood et al. already showed that the vast majority of CAN-genes are mutated at very low frequency. Due to the fact that we only found one mutation in our cohort, we therefore assume that at the selected loci, mutations might be low-frequency events and therefore, more rarely detectable. However, further evaluation of the CAN-gene mutations in larger cohorts should be the aim of further studies.

Paper money and national distress: William Huskisson and the early theories of credit, speculation and crises

This paper examines the explanation of commercial crises offered by William Huskisson in 1810 in the wake of the debate on the Bullion Report. Huskisson argued that the suspension of convertibility made it possible to extend issues of paper currency beyond its proper limits. Such an expansion, being in the interest of all parties concerned, would actually take place and stimulate excessive speculations, which would eventually prove unsustainable and bring generalized ruin and distress. Although some elements of this explanations were not new (having been anticipated by writers sucha as James Currie in 1793, William Roscoe in 1793, William Anderson in 1797 and an anonymous in 1796), Huskisson's explanation is more systematic and better organized, and his emphasis on the endogenous character of the crisis and on the instability of the dynamics of trade and credit makes it an interesting foreshadower of the theories of crises that were advanced half a century later.

Macrophage migration inhibitory factor: a counter-regulator of glucocorticoid action and critical mediator of septic shock.

Recent studies have led to the discovery of a mediator that acts as an endogenous counter-regulator of glucocorticoid action within the immune system. Isolated as a product of anterior pituitary cells, this protein was found to have the sequence of macrophage migration inhibitory factor (MIF), one of the first cytokine activities to be described. Macrophages and T cells release MIF in response both to various inflammatory stimuli and upon incubation with low concentrations of glucocorticoids. The glucocorticoid-induced secretion of MIF is tightly regulated and decreases at high, anti-inflammatory steroid concentrations. Once secreted, MIF "overrides" the anti-inflammatory and immunosuppressive effects of steroids on macrophage and T-cell cytokine production. The physiological role of MIF thus appears to be to counter-balance steroid inhibition of the inflammatory response. Anti-MIF antibodies fully protect animals from experimentally induced gram-negative or gram-positive septic shock, an effect that may be the result of the increased anti-inflammatory effects of glucocorticoids after neutralization of endogenous MIF. Anti-MIF therapeutic strategies are presently under development and may prove to be a means to modulate cytokine production in septic shock as well as in other inflammatory disease states.

Development of an enzyme-linked immunosorbent assay for detection of IgM antibodies to Babesia bigemina in cattle

A crude antigenic preparation of Babesia bigemina was used to develop an ELISA for the detection of IgM antibodies. Optimal dilutions of the antigen, using positive and negative reference sera, were determined by checkerboard titrations. Negative sera from cattle imported from tick-free areas, serum samples collected from infected B. bigemina cattle were used to validate the test. The specificity was 94% and sensitivity of the Elisa 87.5%. Sera from 385 cattle deriving from areas free from tick-borne diseases, which were submitted to a preimmunization process, were screened by this technique. The Elisa detected seroconversion on the 14th day post-inoculation in animals either infested with Boophilus microplus ticks (infected with B. bigemina), or inoculated with B. bigemina infected blood. Antibody titers decreased after day 33; however, all animals remained positive until the end of the experiment (124 days). The ELISA described may prove to be an appropriate serological test for the detection of IgM antibodies against B. bigemina.

Hyperglycemia-induced abnormalities in rat and human corneas: the potential of second harmonic generation microscopy.

BACKGROUND: Second Harmonic Generation (SHG) microscopy recently appeared as an efficient optical imaging technique to probe unstained collagen-rich tissues like cornea. Moreover, corneal remodeling occurs in many diseases and precise characterization requires overcoming the limitations of conventional techniques. In this work, we focus on diabetes, which affects hundreds of million people worldwide and most often leads to diabetic retinopathy, with no early diagnostic tool. This study then aims to establish the potential of SHG microscopy for in situ detection and characterization of hyperglycemia-induced abnormalities in the Descemet's membrane, in the posterior cornea. METHODOLOGY/PRINCIPAL FINDINGS: We studied corneas from age-matched control and Goto-Kakizaki rats, a spontaneous model of type 2 diabetes, and corneas from human donors with type 2 diabetes and without any diabetes. SHG imaging was compared to confocal microscopy, to histology characterization using conventional staining and transmitted light microscopy and to transmission electron microscopy. SHG imaging revealed collagen deposits in the Descemet's membrane of unstained corneas in a unique way compared to these gold standard techniques in ophthalmology. It provided background-free images of the three-dimensional interwoven distribution of the collagen deposits, with improved contrast compared to confocal microscopy. It also provided structural capability in intact corneas because of its high specificity to fibrillar collagen, with substantially larger field of view than transmission electron microscopy. Moreover, in vivo SHG imaging was demonstrated in Goto-Kakizaki rats. CONCLUSIONS/SIGNIFICANCE: Our study shows unambiguously the high potential of SHG microscopy for three-dimensional characterization of structural abnormalities in unstained corneas. Furthermore, our demonstration of in vivo SHG imaging opens the way to long-term dynamical studies. This method should be easily generalized to other structural remodeling of the cornea and SHG microscopy should prove to be invaluable for in vivo corneal pathological studies.

Determination of 13C/12C ratios of endogenous urinary 5-amino-imidazole-4-carboxamide 1-D-ribofuranoside (AICAR)

RATIONALE: AICAR (5-aminoimidazole-4-carboxamide 1β-D-ribofuranoside) is prohibited in sport according to rules established by the World Anti-Doping Agency. Doping control laboratories identify samples where AICAR abuse is suspected by measuring its urinary concentration and comparing the observed level with naturally occurring concentrations. As the inter-individual variance of urinary AICAR concentrations is large, this approach requires a complementary method to unambiguously prove the exogenous origin of AICAR. Therefore, a method for the determination of carbon isotope ratios (CIRs) of urinary AICAR has been developed and validated. METHODS: Concentrated urine samples were fractionated by means of liquid chromatography for analyte cleanup. Derivatization of AICAR yielding the trimethylsilylated analog was necessary to enable CIR determinations by gas chromatography/combustion/isotope ratio mass spectrometry. The method was tested for its repeatability and stability over time and a linear mixing model was applied to test for possible isotopic discrimination. A reference population of n = 63 males and females was investigated to calculate appropriate reference limits to differentiate endogenous from exogenous urinary AICAR. These limits were tested by an AICAR elimination study. RESULTS: The developed method fulfills all the requirements for adequate sports drug testing and was found to be fit for purpose. The investigated reference population showed a larger variability in the CIR of AICAR than of the endogenous steroids. Nevertheless, the calculated thresholds for differences between AICAR and endogenous steroids can be applied straightforwardly to evaluate suspicious doping control samples with the same statistical confidence as established e.g. for testosterone misuse. These thresholds enabled the detection of a single oral AICAR administration for more than 40 h. CONCLUSIONS: Determination of thee CIRs is the method of choice to distinguish between an endogenous and an exogenous source of urinary AICAR. The developed method will enable investigations into doping control samples with elevated urinary concentrations of AICAR and clearly differentiate between naturally produced/elevated and illicitly administered AICAR.

Nonpersistence of resonant caustics in perturbed elliptic billiards

Caustics are curves with the property that a billiard trajectory, once tangent to it, stays tangent after every reflection at the boundary of the billiard table. When the billiard table is an ellipse, any nonsingular billiard trajectory has a caustic, which can be either a confocal ellipse or a confocal hyperbola. Resonant caustics —the ones whose tangent trajectories are closed polygons— are destroyed under generic perturbations of the billiard table. We prove that none of the resonant elliptical caustics persists under a large class of explicit perturbations of the original ellipse. This result follows from a standard Melnikov argument and the analysis of the complex singularities of certain elliptic functions.

Recovering the Elliott invariant from the Cuntz semigroup

Let A be a simple, separable C*-algebra of stable rank one. We prove that the Cuntz semigroup of C (T, A) is determined by its Murray-von Neumann semigroup of projections and a certain semigroup of lower semicontinuous functions (with values in the Cuntz semigroup of A). This result has two consequences. First, specializing to the case that A is simple, finite, separable and Z-stable, this yields a description of the Cuntz semigroup of C (T, A) in terms of the Elliott invariant of A. Second, suitably interpreted, it shows that the Elliott functor and the functor defined by the Cuntz semigroup of the tensor product with the algebra of continuous functions on the circle are naturally equivalent.

Dynamical systems of type (m,n) and their C*-algebras

Given positive integers n and m, we consider dynamical systems in which n copies of a topological space is homeomorphic to m copies of that same space. The universal such system is shown to arise naturally from the study of a C*-algebra we denote by Om;n, which in turn is obtained as a quotient of the well known Leavitt C*-algebra Lm;n, a process meant to transform the generating set of partial isometries of Lm;n into a tame set. Describing Om;n as the crossed-product of the universal (m; n) -dynamical system by a partial action of the free group Fm+n, we show that Om;n is not exact when n and m are both greater than or equal to 2, but the corresponding reduced crossed-product, denoted Or m;n, is shown to be exact and non-nuclear. Still under the assumption that m; n &= 2, we prove that the partial action of Fm+n is topologically free and that Or m;n satisfies property (SP) (small projections). We also show that Or m;n admits no finite dimensional representations. The techniques developed to treat this system include several new results pertaining to the theory of Fell bundles over discrete groups.

Quantitative analysis of image factors in a cultural heritage tourist destination

The tourism consumer’s purchase decision process is, to a great extent, conditioned by the image the tourist has of the different destinations that make up his or her choice set. In a highly competitive international tourist market, those responsible for destinations’ promotion and development policies seek differentiation strategies so that they may position the destinations in the most suitable market segments for their product in order to improve their attractiveness to visitors and increase or consolidate the economic benefits that tourism activity generates in their territory. To this end, the main objective we set ourselves in this paper is the empirical analysis of the factors that determine the image formation of Tarragona city as a cultural heritage destination. Without a doubt, UNESCO’s declaration of Tarragona’s artistic and monumental legacies as World Heritage site in the year 2000 meant important international recognition of the quality of the cultural and patrimonial elements offered by the city to the visitors who choose it as a tourist destination. It also represents a strategic opportunity to boost the city’s promotion of tourism and its consolidation as a unique destination given its cultural and patrimonial characteristics. Our work is based on the use of structured and unstructured techniques to identify the factors that determine Tarragona’s tourist destination image and that have a decisive influence on visitors’ process of choice of destination. In addition to being able to ascertain Tarragona’s global tourist image, we consider that the heterogeneity of its visitors requires a more detailed study that enables us to segment visitor typology. We consider that the information provided by these results may prove of great interest to those responsible for local tourism policy, both when designing products and when promoting the destination.