Root parametrized differential equations

The present thesis is about the inverse problem in differential Galois Theory. Given a differential field, the inverse  problem asks which linear algebraic groups can be realized as differential Galois groups of Picard-Vessiot extensions of this field.   In this thesis we will concentrate on the realization of the classical groups as differential Galois groups. We introduce a method for a very general realization of these groups. This means that we present for the classical groups of Lie rank $l$ explicit linear differential equations where the coefficients are differential polynomials in $l$ differential indeterminates over an algebraically closed field of constants $C$, i.e. our differential ground field is purely differential transcendental over the constants.   For the groups of type $A_l$, $B_l$, $C_l$, $D_l$ and $G_2$ we managed to do these realizations at the same time in terms of Abhyankar's program 'Nice Equations for Nice Groups'. Here the choice of the defining matrix is important. We found out that an educated choice of $l$ negative roots for the parametrization together with the positive simple roots leads to a nice differential equation and at the same time defines a sufficiently general element of the Lie algebra. Unfortunately for the groups of type $F_4$ and $E_6$ the linear differential equations for such elements are of enormous length. Therefore we keep in the case of $F_4$ and $E_6$ the defining matrix differential equation which has also an easy and nice shape.   The basic idea for the realization is the application of an upper and lower bound criterion for the differential Galois group to our parameter equations and to show that both bounds coincide. An upper and lower bound criterion can be found in literature. Here we will only use the upper bound, since for the application of the lower bound criterion an important condition has to be satisfied. If the differential ground field is $C_1$, e.g., $C(z)$ with standard derivation, this condition is automatically satisfied. Since our differential ground field is purely differential transcendental over $C$, we have no information whether this condition holds or not.   The main part of this thesis is the development of an alternative lower bound criterion and its application. We introduce the specialization bound. It states that the differential Galois group of a specialization of the parameter equation is contained in the differential Galois group of the parameter equation. Thus for its application we need a differential equation over $C(z)$ with given differential Galois group. A modification of a result from Mitschi and Singer yields such an equation over $C(z)$ up to differential conjugation, i.e. up to transformation to the required shape. The transformation of their equation to a specialization of our parameter equation is done for each of the above groups in the respective transformation lemma.

Langmuir turbulence and deeply penetrating jets in an unstratified mixed layer

The influence of surface waves and an applied wind stress is studied in an ensemble of large eddy simulations to investigate the nature of deeply penetrating jets into an unstratified mixed layer. The influence of a steady monochromatic surface wave propagating parallel to the wind direction is parameterized using the wave-filtered Craik-Leibovich equations. Tracer trajectories and instantaneous downwelling velocities reveal classic counterrotating Langmuir rolls. The associated downwelling jets penetrate to depths in excess of the wave's Stokes depth scale, δs. Qualitative evidence suggests the depth of the jets is controlled by the Ekman depth scale. Analysis of turbulent kinetic energy (tke) budgets reveals a dynamical distinction between Langmuir turbulence and shear-driven turbulence. In the former, tke production is dominated by Stokes shear and a vertical flux term transports tke to a depth where it is dissipated. In the latter, tke production is from the mean shear and is locally balanced by dissipation. We define the turbulent Langmuir number Lat = (v*/Us)0.5 (v* is the ocean's friction velocity and Us is the surface Stokes drift velocity) and a turbulent anisotropy coefficient Rt = /( + ). The transition between shear-driven and Langmuir turbulence is investigated by varying external wave parameters δs and Lat and by diagnosing Rt and the Eulerian mean and Stokes shears. When either Lat or δs are sufficiently small the Stokes shear dominates the mean shear and the flow is preconditioned to Langmuir turbulence and the associated deeply penetrating jets.

Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

Puroindoline-b mutations control the lipid binding interactions in mixed puroindoline-a: puroindoline-b systems

The interactions have been investigated of puroindoline-a (Pin-a) and mixed protein systems of Pin-a and wild-type puroindoline-b (Pin-b+) or puroindoline-b mutants (G46S mutation (Pin bH) or W44R mutation (Pin-bS)) with condensed phase monolayers of an anionic phospholipid (L-α-dipalmitoylphosphatidyl-dl-glycerol (DPPG)) at the air/water interface. The interactions of the mixed systems were studied at three different concentration ratios of Pin-a:Pin-b, namely 3:1, 1:1 and 1:3 in order to establish any synergism in relation to lipid binding properties. Surface pressure measurements revealed that Pin-a interaction with DPPG monolayers led to an equilibrium surface pressure increase of 8.7 ± 0.6 mN m-1. This was less than was measured for Pin-a:Pin-b+ (9.6 to 13.4 mN m-1), but was significantly more than was measured for Pin-a:Pin-bH (4.0 to 6.2 mN m-1) or Pin-a:Pin-bS (3.8 to 6.3 mN m-1) over the complete range of concentration ratio. Consequently, surface pressure increases were shown to correlate to endosperm hardness phenotype, with puroindolines present in hard-textured wheat varieties yielding lower equilibrium surface pressure changes. Integrated amide I peak areas from corresponding external reflectance Fourier-transform infrared (ER-FTIR) spectra, used to indicate levels of protein adsorption to the lipid monolayers, showed that differences in adsorbed amount were less significant. The data therefore suggest that Pin-b mutants having single residue substitutions within their tryptophan-rich loop that are expressed in some hard-textured wheat varieties influence the degree of penetration of Pin-a and Pin-b into anionic phospholipid films. These findings highlight the key role of the tryptophan-rich loop in puroindoline-lipid interactions.

Evaluation of NRC, UC Davis and ADAS approaches to estimate the metabolizable energy values of feeds at maintenance energy intake from equations utilizing chemical assays and in vitro determinations

Feed samples received by commercial analytical laboratories are often undefined or mixed varieties of forages, originate from various agronomic or geographical areas of the world, are mixtures (e.g., total mixed rations) and are often described incompletely or not at all. Six unified single equation approaches to predict the metabolizable energy (ME) value of feeds determined in sheep fed at maintenance ME intake were evaluated utilizing 78 individual feeds representing 17 different forages, grains, protein meals and by-product feedstuffs. The predictive approaches evaluated were two each from National Research Council [National Research Council (NRC), Nutrient Requirements of Dairy Cattle, seventh revised ed. National Academy Press, Washington, DC, USA, 2001], University of California at Davis (UC Davis) and ADAS (Stratford, UK). Slopes and intercepts for the two ADAS approaches that utilized in vitro digestibility of organic matter and either measured gross energy (GE), or a prediction of GE from component assays, and one UC Davis approach, based upon in vitro gas production and some component assays, differed from both unity and zero, respectively, while this was not the case for the two NRC and one UC Davis approach. However, within these latter three approaches, the goodness of fit (r(2)) increased from the NRC approach utilizing lignin (0.61) to the NRC approach utilizing 48 h in vitro digestion of neutral detergent fibre (NDF:0.72) and to the UC Davis approach utilizing a 30 h in vitro digestion of NDF (0.84). The reason for the difference between the precision of the NRC procedures was the failure of assayed lignin values to accurately predict 48 h in vitro digestion of NDF. However, differences among the six predictive approaches in the number of supporting assays, and their costs, as well as that the NRC approach is actually three related equations requiring categorical description of feeds (making them unsuitable for mixed feeds) while the ADAS and UC Davis approaches are single equations, suggests that the procedure of choice will vary dependent Upon local conditions, specific objectives and the feedstuffs to be evaluated. In contrast to the evaluation of the procedures among feedstuffs, no procedure was able to consistently discriminate the ME values of individual feeds within feedstuffs determined in vivo, suggesting that the quest for an accurate and precise ME predictive approach among and within feeds, may remain to be identified. (C) 2004 Elsevier B.V. All rights reserved.

Methylene spacer-regulated structural variation in cobalt(II/III) complexes with bridging acetate and Salen- or Salpn-type Schiff-base ligands

Two linear, trinuclear mixed-valence complexes, [Co-II{(mu-L-1)(mu-OAc)Co-III (OAc)}(2)] (1) and [Co-II(mu-L-2) (mu-OAc)Co-III(OAc)}(2)] (2) and two mononuclear Con' complexes [Co-III{L-3)(OAc)] (3), and [Co-III {L-4}(OAc)] (4) were prepared and the molecular structures of 1, 2 and 4 elucidated on the basis of X-ray crystallography [OAc = Acetate ion, H2L1 = H(2)Salen 1,6-bis(2-hydroxyphenyl)-2,5-diazahexa-1,5-diene, H2L2 H2Me2-Salen = 2,7-bis(2-hydroxyphenyl)-2,6-diazaocta-2,6-diene, H2L3 = H(2)Salpn = 1,7-bis(2-hydroxyphenyl)-2,6-diazahepta1,6-diene, H2L4 = H(2)Me(2)Salpn = 2,8-bis(2-hydroxyphenyl)3,7-diazanona-2,7-dienel. In complexes I and 2, the acetate groups show both monodentate and bridging bidentate coordination modes, whereas chelating bidentate acetate is present in 4. The terminal (CoN2O4)-N-III centres in 1 and 2 exhibit uniform facial arrangements of both non-bridged N2O and bridging O-3 donor sets and the Co-II centre is coordinated to six (four phenoxo and two acetato) oxygen atoms of the bridging ligands. The effective magnetic moment at room temperature corresponds to the presence of high-spin Coll in both 1 and 2. The complexes 1 and 2 are thus Co-III(S = 0)Co-II(S = 3/2)-Co-II(S = 0) trimers. Complexes 3 and 4 are monomeric and diamagnetic containing low-spin Co-III(S = 0) with chelating tetradentate Schiff base and bidentate acetate. Calculations based on DFT rationalise the formation of trinuclear or monomiclear complexes. (C) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2008).

Synthesis, structure and solution chemistry of mixed-ligand oxovanadium(IV) and oxovanadium(V) complexes incorporating tridentate ONO donor hydrazone ligands

In the title family, the ONO donor ligands are the acetylhydrazones of salicylaidehyde (H2L1) and 2-hydroxyacetophenone (H2L2) (general abbreviation, H2L). The reaction of bis(acetylacetonato)oxovanadium(IV) with a mixture of tridentate H2L and a bidentate NN donor [e.g., 2,2'-bipyridine(bpy) or 1,10-phenanthroline(phen), hereafter B] ligands in equimolar ratio afforded the tetravalent complexes of the type [(VO)-O-IV(L)(B)]; complexes (1)-(4) whereas, if B is replaced by 8-hydroxyquinoline(Hhq) (which is a bidentate ON donor ligand), the above reaction mixture yielded the pentavalent complexes of the type [(VO)-O-V(L)(hq)]; complexes (5) and (6). Aerial oxygen is most likely the oxidant (for the oxidation of V-IV -> V-V) in the synthesis of pentavalent complexes (5) and (6). [(VO)-O-IV(L)(B)] complexes are one electron paramagnetic and display axial EPR spectra, while the [(VO)-O-V(L)(hq)] complexes are diamagnetic. The X-ray structure of [(VO)-O-V(L-2)(hq)] (6) indicates that H2L2 ligand is bonded with the vanadium meridionally in a tridentate dinegative fashion through its phenolic-O, enolic-O and imine-N atoms. The general bond length order is: oxo < phenolato < enolato. The V-O (enolato) bond is longer than V-O (phenolato) bond by similar to 0.07 angstrom and is identical with V-O (carboxylate) bond. H-1 NMR spectrum of (6) in CDCl3 solution indicates that the binding nature in the solid state is also retained in solution. Complexes (1)(4) display two ligand-field transitions in the visible region near 820 and 480 nm in DMF solution and exhibit irreversible oxidation peak near +0.60 V versus SCE in DMSO solution, while complexes (5) and (6) exhibit only LMCT band near 535 nm and display quasi-reversible one electron reduction peak near -0.10 V versus SCE in CH2Cl2 solution. The VO3+-VO2+ E-1/2 values shift considerably to more negative values when neutral NN donor is replaced by anionic ON donor species and it also provides better VO3+ binding via phenolato oxygen. For a given bidentate ligand, E-1/2 increases in the order: (L-2)(2-) < (L-1)(2-). (c) 2004 Elsevier B.V. All rights reserved.

Synthesis, structure, solution chemistry and the electronic effect of para substituents on the vanadium center in a family of mixed-ligand [(VO)-O-V(ONO)(ON)] compexes

Four tridentate dibasic ONO donor hydrazone ligands derived from the condensation of benzoylhydrazine with either 2-hydroxyacetophenone or its para substituted derivatives (H2L1-4, general abbreviation H2L) have been used as primary ligands and 8-hydroxyquinoline (Hhq, a bidentate monobasic ON donor species) has been used as auxiliary ligand. The reaction of [(VO)-O-IV(acac)21 with H2L in methanol followed by the addition of Hhq in equimolar ratio under aerobic condition afforded the mixed-ligand oxovanadium(V) complexes of the type [(VO)-O-V(L)(hq)] (1-4) in excellent yield. The X-ray structure of the compound [(VO)-O-V(L-4)(hq)] (4) indicates that the H2L4 ligand is bonded with vanadium meridionally in a tridentate dinegative fashion through its deprotonated phenolic-O, deprotonated enolic-O and imine-N atoms. The V-O bond length order is: oxo < phenolato < enolato. H-1 NMR spectra of 4 in CDCl3 solution indicates that it's solid-state structure is retained in solution. Complexes are diamagnetic and exhibit only ligand to metal charge transfer (LMCT) transition band near 530 nm in CH2Cl2 solution in addition to intra-ligand pi-pi* transition band near 335 rim and they display quasi-reversible one electron reduction peak near -0.10 V versus SCE in CH2Cl2 solution. lambda(max) (for LMCT transition) and the reduction peak potential (E-p(c)) values of the complexes are found to be linearly related with the Hammett (sigma) constants of the substituents in the aryloxy ring of the hydrazone ligands. lambda(max) and E-p(c) values show large dependence d lambda(max)/d sigma = 32.54 nm and dE(p)(c)/d sigma = 0.19 V, respectively, on the Hammett constant. (c) 2006 Elsevier B.V. All rights reserved.

Chemistry of mixed-ligand methoxy bonded oxidovanadium(V) complexes with a family of hydrazone ligands containing VO3+ core and their substituent controlled methoxy-bridged dimeric forms

[(VO)-O-IV(acac)(2)] reacts with an equimolar amount of benzoyl hydrazones of 2-hydroxyacetophenone (H2L1), 2-hydroxy-5-methylacetophenone (H2L2) and 5-chloro-2-hydroxyacetophenone (H2L4) in methanol to afford the penta-coordinated mixed-ligand methoxy bonded oxidovanadium(V) complexes [(VO)-O-V(L-1)-(OCHA(3))](1). [(VO)-O-V(L-2)(OCH3)](2), and [(VO)-O-V(L-4)(OCH3)](4), respectively, whereas, the similar reaction with the benzoyl hydrazone of 2-hydroxy-5-methoxyacetophenone (H2L3) producing only the hexa-coordinated dimethoxy-bridged dimeric complex [(VO)-O-V(L-3)(OCH3)](2) (3A). Similar type of hexa-coordinated dimeric analogue of 1 i.e., [(VO)-O-V(L-1)(OCH3)](2) (1A) was obtained from the reaction of [(VO)-O-IV(acac)(2)] with the equimolar amount of H2L1 in presence of half equivalent 4,4'-bipyridine in methanol while the decomposition of [(VO)-O-IV(L-2)(bipy)] complex in methanol afforded the dimeric analogue of 2 i.e., [(VO)-O-V(L-2)(OCH3)](2) (2A). All these dimeric complexes 1A-3A react with an excess amount of imidazole in methanol producing the respective monomeric complex. The X-ray structural analysis of 1-3 and their dimeric analogues 1A-3A indicates that the geometry around the vanadium center in the monomeric form is distorted square-pyramidal while that of their respective dimeric forms is distorted octahedral, where the ligands are bonded to vanadium meridionally in their fully deprotonated enol forms. Due to the formation of bridge, the V-O(methoxy) bond in the dimeric complexes is lengthened to such an extent that it becomes equal in length with the V-O(phenolate) bond in 3A and even longer in 1A and 2A, which is unprecedented. The H-1 NMR spectra of the complexes 1A-3A in CDCl3 solution, indicates that these dimeric complexes are converted appreciably into their respective monomeric form. Complexes are electro-active displaying one quasi-reversible reduction peak near +0.25 V versus SCE in CH2Cl2 solution. The E-1/2 values of the complexes show linear relationship with the Hammett parameter (sigma) of the substituents. All these VO3+-complexes are converted to the corresponding complexes with V2O34+ motif simply on refluxing them in acetone and to the complexes with VO2+ motif on reaction with 2 KOH in methanol. (C) 2008 Elsevier Ltd. All rights reserved.

Effect of forage type and proportion of concentrate in the diet on milk fatty acid composition in cows given sunflower oil and fish oil

Based on the potential benefits of cis-9, trans- 11 conjugated linoleic acid (CLA) for human health there is a need to develop effective strategies for enhancing milk fat CLA concentrations. In this experiment, the effect of forage type and level of concentrate in the diet on milk fatty acid composition was examined in cows given a mixture of fish oil and sunflower oil. Four late lactation Holstein-British Friesian cows were used in a 4 x 4 Latin-square experiment with a 2 x 2 factorial arrangement of treatments and 21-day experimental periods. Treatments consisted of grass (G) or maize (M) silage supplemented with low (L) or high (H) levels of concentrates (65: 35 and 35: 65; forage: concentrate ratio, on a dry matter (DM) basis, respectively) offered as a total mixed ration at a restricted level of intake (20 kg DM per day). Lipid supplements (30 g/kg DM) containing fish oil and sunflower oil (2: 3 w/w) were offered during the last 14 days of each experimental period. Treatments had no effect on total DM intake, milk yield, milk constituent output or milk fat content, but milk protein concentrations were lower (P<0.05) for G than M diets (mean 43.0 and 47.3 g/kg, respectively). Compared with grass silage, milk fat contained higher (P<0.05) amounts Of C-12: 0, C-14: 0, trans C-18:1 and long chain >= C20 (n-3) polyunsaturated fatty acids (PUFA) and lower (P<0.05) levels Of C-18:0 and trans C-18:2 when maize silage was offered. Increases in the proportion of concentrate in the diet elevated (P<0.05) C-18:2 (n-6) and long chain >= C20 (n-3) PUFA content, but reduced (P<0.05) the amount Of C-18:3 (n-3). Concentrations of trans-11 C-18:1 in milk were independent of forage type, but tended (P<0.10) to be lower for high concentrate diets (mean 7.2 and 4.0 g/100 g fatty acids, for L and H respectively). Concentrations of trans-10 C-18:1 were higher (P<0.05) in milk from maize compared with grass silage (mean 10.3 and 4.1 g/100 g fatty acids, respectively) and increased in response to high levels of concentrates in the diet (mean 4.1 and 10.3 g/100 g fatty acids, for L and H, respectively). Forage type had no effect (P>0.05) on total milk conjugated linoleic acid (CLA) (2.7 and 2.8 g/100 g fatty acids, for M and G, respectively) or cis-9, trans-11 CLA content (2.2 and 2.4 g/100 g fatty acids). Feeding high concentrate diets tended (P<0.10) to decrease total CLA (3.3 and 2.2 g/100 g fatty acids, for L and H, respectively) and cis-9, trans-11 CLA (2.9 and 1/7 g/100 g fatty acids) concentrations and increase milk trans-9, cis-11 CLA and trans-10, cis-12 CLA content. In conclusion, the basal diet is an important determinant of milk fatty acid composition when a supplement of fish oil and sunflower oil is given.

An efficient numerical scheme for the Euler equations

A finite difference scheme based on flux difference splitting is presented for the solution of the Euler equations for the compressible flow of an ideal gas. A linearised Riemann problem is defined, and a scheme based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency, leading to arithmetic averaging. This is in contrast to the usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. The scheme is applied to a shock tube problem and a blast wave problem. Each approximate solution compares well with those given by other schemes, and for the shock tube problem is in agreement with the exact solution.

An efficient numerical scheme for the two-dimensional shallow water equations using arithmetic averaging

A finite difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gas dynamics is defined, and a scheme, based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem, and incorporates the technique of operator splitting. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. An extension to the two-dimensional equations with source terms is included. The scheme is applied to the one-dimensional problems of a breaking dam and reflection of a bore, and in each case the approximate solution is compared to the exact solution of ideal fluid flow. The scheme is also applied to a problem of stationary bore generation in a channel of variable cross-section. Finally, the scheme is applied to two other dam-break problems, this time in two dimensions with one having cylindrical symmetry. Each approximate solution compares well with those given by other authors.

Wind-driven mixing below the oceanic mixed layer

This study describes the turbulent processes in the upper ocean boundary layer forced by a constant surface stress in the absence of the Coriolis force using large-eddy simulation. The boundary layer that develops has a two-layer structure, a well-mixed layer above a stratified shear layer. The depth of the mixed layer is approximately constant, whereas the depth of the shear layer increases with time. The turbulent momentum flux varies approximately linearly from the surface to the base of the shear layer. There is a maximum in the production of turbulence through shear at the base of the mixed layer. The magnitude of the shear production increases with time. The increase is mainly a result of the increase in the turbulent momentum flux at the base of the mixed layer due to the increase in the depth of the boundary layer. The length scale for the shear turbulence is the boundary layer depth. A simple scaling is proposed for the magnitude of the shear production that depends on the surface forcing and the average mixed layer current. The scaling can be interpreted in terms of the divergence of a mean kinetic energy flux. A simple bulk model of the boundary layer is developed to obtain equations describing the variation of the mixed layer and boundary layer depths with time. The model shows that the rate at which the boundary layer deepens does not depend on the stratification of the thermocline. The bulk model shows that the variation in the mixed layer depth is small as long as the surface buoyancy flux is small.

Minimum norm regularization of descriptor systems by mixed output feedback

We study the regularization problem for linear, constant coefficient descriptor systems Ex' = Ax+Bu, y1 = Cx, y2 = Γx' by proportional and derivative mixed output feedback. Necessary and sufficient conditions are given, which guarantee that there exist output feedbacks such that the closed-loop system is regular, has index at most one and E+BGΓ has a desired rank, i.e., there is a desired number of differential and algebraic equations. To resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of E is decreased. Numerical procedures are derived to construct the desired feedback gains. These numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way.

Role of NleH, a Type III Secreted Effector from Attaching and Effacing Pathogens, in Colonization of the Bovine, Ovine, and Murine Gut

The human pathogen enterohemorrhagic Escherichia coli (EHEC) O157:H7 colonizes human and animal gut via formation of attaching and effacing lesions. EHEC strains use a type III secretion system to translocate a battery of effector proteins into the mammalian host cell, which subvert diverse signal transduction pathways implicated in actin dynamics, phagocytosis, and innate immunity. The genomes of sequenced EHEC O157: H7 strains contain two copies of the effector protein gene nleH, which share 49% sequence similarity with the gene for the Shigella effector OspG, recently implicated in inhibition of migration of the transcriptional regulator NF-kappa B to the nucleus. In this study we investigated the role of NleH during EHEC O157: H7 infection of calves and lambs. We found that while EHEC Delta nleH colonized the bovine gut more efficiently than the wild-type strain, in lambs the wild-type strain exhibited a competitive advantage over the mutant during mixed infection. Using the mouse pathogen Citrobacter rodentium, which shares many virulence factors with EHEC O157: H7, including NleH, we observed that the wild-type strain exhibited a competitive advantage over the mutant during mixed infection. We found no measurable differences in T-cell infiltration or hyperplasia in colons of mice inoculated with the wild-type or the nleH mutant strain. Using NF-kappa B reporter mice carrying a transgene containing a luciferase reporter driven by three NF-kappa B response elements, we found that NleH causes an increase in NF-kappa B activity in the colonic mucosa. Consistent with this, we found that the nleH mutant triggered a significantly lower tumor necrosis factor alpha response than the wild-type strain.