New prophylactic and therapeutic treatments to combat pathogenic Enterohaemorrhagic Escherichia coli

Bacterial diarrhoeal diseases have significant influence on global human health, and are a leading cause of preventable death in the developing world. Enterohaemorrhagic Escherichia coli (EHEC), pathogenic strains of E. coli that carry potent toxins, have been associated with a high number of large-scale outbreaks caused by contaminated food and water sources. This pathotype produces diarrhoea and haemorrhagic colitis in infected humans, and in some patients leads to the development of haemolytic uremic syndrome (HUS), which can result in mortality and chronic kidney disease. A major obstacle to the treatment of EHEC infections is the increased risk of HUS development that is associated with antibiotic treatment, and rehydration and renal support are often the only options available. New treatments designed to prevent or clear E. coli infections and reduce symptoms of illness would therefore have large public health and economic impacts. The three main aims of this thesis were: to explore mouse models for pre-clinical evaluation in vivo of small compounds that inhibit a major EHEC colonisation factor, to assess the production and role of two proteins considered promising candidates for a broad-spectrum vaccine against pathogenic E. coli, and to investigate a novel compound that has recently been identified as a potential inhibitor of EHEC toxin production. As EHEC cannot be safely tested in humans due to the risk of HUS development, appropriate small animal models are required for in vivo testing of new drugs. A number of different mouse models have been developed to replicate different features of EHEC pathogenesis, several of which we investigated with a focus on colonisation mediated by the Type III Secretion System (T3SS), a needle-like structure that translocates bacterial proteins into host cells, resulting in a tight, intimate attachment between pathogen and host, aiding colonisation of the gastrointestinal tract. As E. coli models were found not to depend significantly on the T3SS for colonisation, the Citrobacter rodentium model, a natural mouse pathogen closely related to E. coli, was deemed the most suitable mouse model currently available for in vivo testing of T3SS-targeting compounds. Two bacterial proteins, EaeH (an outer membrane adhesin) and YghJ (a putative secreted lipoprotein), highly conserved surface-associated proteins recently identified as III protective antigens against E. coli infection of mice, were explored in order to determine their suitability as candidates for a human vaccine against pathogenic E. coli. We focused on the expression and function of these proteins in the EHEC O157:H7 EDL933 strain and the adherent-invasive E. coli (AIEC) LF82 strain. Although expression of EaeH by other E. coli pathotypes has recently been shown to be upregulated upon contact with host intestinal cells, no evidence of this upregulation could be demonstrated in our strains. Additionally, while YghJ was produced by the AIEC strain, it was not secreted by bacteria under conditions that other YghJ-expressing E. coli pathotypes do, despite the AIEC strain carrying all the genes required to encode the secretion system it is associated with. While our findings indicate that a vaccine that raises antibodies against EaeH and YghJ may have limited effect on the EHEC and AIEC strains we used, recent studies into these proteins in different E. coli pathogens have suggested they are still excellent candidates for a broadly effective vaccine against E. coli. Finally, we characterised a small lead compound, identified by high-throughput screening as a possible inhibitor of Shiga toxin expression. Shiga toxin production causes both the symptoms of illness and development of HUS, and thus reduction of toxin production, release, or binding to host receptors could therefore be an effective way to treat infections and decrease the risk of HUS. Inhibition of Shiga toxin production by this compound was confirmed, and was shown to be caused by an inhibitory effect on activation of the bacterial SOS response rather than on the Shiga toxin genes themselves. The bacterial target of this compound was identified as RecA, a major regulator of the SOS response, and we hypothesise that the compound binds covalently to its target, preventing oligomerisation of RecA into an activated filament. Altogether, the results presented here provide an improved understanding of these different approaches to combating EHEC infection, which will aid the development of safe and effective vaccines and anti-virulence treatments against EHEC.

Quantum integrability as a new method for exact results on N=2 supersymmetric gauge theories and black holes

In this thesis I show a triple new connection we found between quantum integrability, N=2 supersymmetric gauge theories and black holes perturbation theory. I use the approach of the ODE/IM correspondence between Ordinary Differential Equations (ODE) and Integrable Models (IM), first to connect basic integrability functions - the Baxter’s Q, T and Y functions - to the gauge theory periods. This fundamental identification allows several new results for both theories, for example: an exact non linear integral equation (Thermodynamic Bethe Ansatz, TBA) for the gauge periods; an interpretation of the integrability functional relations as new exact R-symmetry relations for the periods; new formulas for the local integrals of motion in terms of gauge periods. This I develop in all details at least for the SU(2) gauge theory with Nf=0,1,2 matter flavours. Still through to the ODE/IM correspondence, I connect the mathematically precise definition of quasinormal modes of black holes (having an important role in gravitational waves’ obervations) with quantization conditions on the Q, Y functions. In this way I also give a mathematical explanation of the recently found connection between quasinormal modes and N=2 supersymmetric gauge theories. Moreover, it follows a new simple and effective method to numerically compute the quasinormal modes - the TBA - which I compare with other standard methods. The spacetimes for which I show these in all details are in the simplest Nf=0 case the D3 brane in the Nf=1,2 case a generalization of extremal Reissner-Nordström (charged) black holes. Then I begin treating also the Nf=3,4 theories and argue on how our integrability-gauge-gravity correspondence can generalize to other types of black holes in either asymptotically flat (Nf=3) or Anti-de-Sitter (Nf=4) spacetime. Finally I begin to show the extension to a 4-fold correspondence with also Conformal Field Theory (CFT), through the renowned AdS/CFT correspondence.

Experimental evaluation of the z-resolution in different clinical Digital Breast Tomosynthesis systems using commercial phantoms

Digital Breast Tomosynthesis (DBT) is an advanced mammography technique based on the reconstruction of a pseudo-volumetric image. To date, image quality represents the most deficient section of DBT quality control protocols. In fact, related tests are not yet characterized by either action levels or typical values. This thesis work focuses on the evaluation of one aspect of image quality: the z-resolution. The latter is studied in terms of Artifact Spread Function (ASF), a function that describes the signal spread of a detail along the reconstructed focal planes. To quantify the ASF numerically, its Full Width at Half Maximum (FWHM) is calculated and used as a representative index of z-resolution. Experimental measurements were acquired in 24 DBT systems, of 7 different models, currently in use in 20 hospital facilities in Italy. The analysis, performed on the clinical reconstructed images, of 5 different commercial phantoms, lead to the identification of characteristic FWHM values for each type of DBT system. The ASF clearly showed a dependence on the size of the detail, providing higher FWHM values for larger objects. The z-resolution was found to be positively influenced by the acquisition angle: Fujifilm sistematically showed wider ASF profiles in ST mode (15°) than in HR mode (40°). However, no clear relationship was found between angular range and ASF, among different DBT systems, due to the influence of the peculiarities of each reconstruction algorithm. The experimental approach shown in this thesis work can be proposed as a z-resolution quality control test procedure. Contextually, the values found could be used as a starting point for identifying typical values to be included in the test, in a DBT protocol. Clearly, a statistically significant number of images is needed to do this. The equipment involved in this work is located in hospitals and is not available for research purposes, so only a limited amount of data was acquired and processed.

Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations

A numerical method based on integral equations is proposed and investigated for the Cauchy problem for the Laplace equation in 3-dimensional smooth bounded doubly connected domains. To numerically reconstruct a harmonic function from knowledge of the function and its normal derivative on the outer of two closed boundary surfaces, the harmonic function is represented as a single-layer potential. Matching this representation against the given data, a system of boundary integral equations is obtained to be solved for two unknown densities. This system is rewritten over the unit sphere under the assumption that each of the two boundary surfaces can be mapped smoothly and one-to-one to the unit sphere. For the discretization of this system, Weinert’s method (PhD, Göttingen, 1990) is employed, which generates a Galerkin type procedure for the numerical solution, and the densities in the system of integral equations are expressed in terms of spherical harmonics. Tikhonov regularization is incorporated, and numerical results are included showing the efficiency of the proposed procedure.

Existence Results for Abstract Partial Neutral Integro-differential Equation with Unbounded Delay

In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.

A numerical analysis of generalized Boussinesq-type equation using continuos/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time-dependent varying seabed are included. Thus, high-order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher-order models, an extra O(mu 2n+2) term (n ??? N) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth-order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor-corrector scheme with an initialization given by an explicit RungeKutta method is also used for the time-variable integration. Moreover, a CFL-type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved.

A thermoelastic system of memory type in noncylindrical domains

In this paper, we consider a hyperbolic thermoelastic system of memory type in domains with moving boundary. The problem models vibrations of an elastic bar under thermal effects according to the heat conduction law of Gurtin and Pipkin. Global existence is proved by using the penalty method of Lions. (c) 2007 Elsevier Inc. All rights reserved.

A MODEL OF THE DEUTERON BASED ON A BREIT TYPE EQUATION

A relativistic treatment of the deuteron and its observables based on a two-body Dirac (Breit) equation, with phenomenological interactions, associated to one-boson exchanges with cutoff masses, is presented. The 16-component wave function for the deuteron (J(pi) = 1+) solution contains four independent radial functions which obey a system of four coupled differential equations of first order. This radial system is numerically integrated, from infinity to the origin, by fixing the value of the deuteron binding energy and using appropriate boundary conditions at infinity. Specific examples of mixtures containing scalar, pseudoscalar and vector like terms are discussed in some detail and several observables of the deuteron are calculated. Our treatment differs from more conventional ones in that nonrelativistic reductions of the order c-2 are not used.

Characterizing chaos in a type of fractional duffing's equation

We characterize the chaos in a fractional Duffing’s equation computing the Lyapunov exponents and the dimension of the strange attractor in the effective phase space of the system. We develop a specific analytical method to estimate all Lyapunov exponents and check the results with the fiduciary orbit technique and a time series estimation method.

Integral Transforms Method to Solve a Time-Space Fractional Diffusion Equation

Mathematical Subject Classification 2010: 35R11, 42A38, 26A33, 33E12.

Solvability of an Infinite System of Singular Integral Equations

2000 Mathematics Subject Classification: 45G15, 26A33, 32A55, 46E15.

Application of Volterra Equations to Solve Unit Commitment Problem of Optimised Energy Storage and Generation

Development of reliable methods for optimised energy storage and generation is one of the most imminent challenges in modern power systems. In this paper an adaptive approach to load leveling problem using novel dynamic models based on the Volterra integral equations of the first kind with piecewise continuous kernels. These integral equations efficiently solve such inverse problem taking into account both the time dependent efficiencies and the availability of generation/storage of each energy storage technology. In this analysis a direct numerical method is employed to find the least-cost dispatch of available storages. The proposed collocation type numerical method has second order accuracy and enjoys self-regularization properties, which is associated with confidence levels of system demand. This adaptive approach is suitable for energy storage optimisation in real time. The efficiency of the proposed methodology is demonstrated on the Single Electricity Market of Republic of Ireland and Northern Ireland.

Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert's method [24] is employed, which generates a Galerkin-type procedure for the numerical solution via rewriting the boundary integrals over the unit sphere and expanding the densities in terms of spherical harmonics. Numerical results are included as well.

Predictions of J integral and tensile strength of clay/epoxy nanocomposites material using phase field model

We predict macroscopic fracture related material parameters of fully exfoliated clay/epoxy nano- composites based on their fine scale features. Fracture is modeled by a phase field approach which is implemented as user subroutines UEL and UMAT in the commercial finite element software Abaqus. The phase field model replaces the sharp discontinuities with a scalar damage field representing the diffuse crack topology through controlling the amount of diffusion by a regularization parameter. Two different constitutive models for the matrix and the clay platelets are used; the nonlinear coupled system con- sisting of the equilibrium equation and a diffusion-type equation governing the phase field evolution are solved via a NewtoneRaphson approach. In order to predict the tensile strength and fracture toughness of the clay/epoxy composites we evaluated the J integral for different specimens with varying cracks. The effect of different geometry and material parameters, such as the clay weight ratio (wt.%) and the aspect ratio of clay platelets are studied.

Equivalence between Redfield- and master-equation approaches for a time-dependent quantum system and coherence control

We present a derivation of the Redfield formalism for treating the dissipative dynamics of a time-dependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a time-dependent spin-1/2 system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times T(1) and T(2) (associated with the longitudinal and transverse relaxations, respectively). These characteristic times are shown to be related to the operator-sum representation and the equivalent phenomenological-operator approach. Finally, we present a protocol to circumvent the decoherence processes due to the loss of energy (and thus, associated with T(1)). To this end, we simply associate the time dependence of the quantum system to an easily achieved modulated frequency. A possible implementation of the protocol is also proposed in the context of nuclear magnetic resonance.