Marginal Perturbations Research Articles

Integrated metabolomic and transcriptomic analyses of the synergistic effect of polymyxin–rifampicin combination against Pseudomonas aeruginosa

BackgroundUnderstanding the mechanism of antimicrobial action is critical for improving antibiotic therapy. For the first time, we integrated correlative metabolomics and transcriptomics of Pseudomonas aeruginosa to elucidate the mechanism of synergistic killing of polymyxin–rifampicin combination.MethodsLiquid chromatography-mass spectrometry and RNA-seq analyses were conducted to identify the significant changes in the metabolome and transcriptome of P. aeruginosa PAO1 after exposure to polymyxin B (1 mg/L) and rifampicin (2 mg/L) alone, or in combination over 24 h. A genome-scale metabolic network was employed for integrative analysis.ResultsIn the first 4-h treatment, polymyxin B monotherapy induced significant lipid perturbations, predominantly to fatty acids and glycerophospholipids, indicating a substantial disorganization of the bacterial outer membrane. Expression of ParRS, a two-component regulatory system involved in polymyxin resistance, was increased by polymyxin B alone. Rifampicin alone caused marginal metabolic perturbations but significantly affected gene expression at 24 h. The combination decreased the gene expression of quorum sensing regulated virulence factors at 1 h (e.g. key genes involved in phenazine biosynthesis, secretion system and biofilm formation); and increased the expression of peptidoglycan biosynthesis genes at 4 h. Notably, the combination caused substantial accumulation of nucleotides and amino acids that last at least 4 h, indicating that bacterial cells were in a state of metabolic arrest.ConclusionThis study underscores the substantial potential of integrative systems pharmacology to determine mechanisms of synergistic bacterial killing by antibiotic combinations, which will help optimize their use in patients.Graphical

Reprint of: Marginal CFT perturbations at the integer quantum Hall transition

According to recent arguments by the author, the conformal field theory (CFT) describing the scaling limit of the integer quantum Hall plateau transition is a deformed level-4 Wess–Zumino–Novikov–Witten model with Riemannian target space inside a complex Lie supergroup GL. After a summary of that proposal and some of its predictions, the leading irrelevant and relevant perturbations of the proposed CFT are discussed. Argued to be marginal, these result in a non-standard renormalization group (RG) flow near criticality, which calls for modified finite-size scaling analysis and may explain the long-standing inability of numerical work to reach agreement on the values of critical exponents. The technique of operator product expansion is used to compute the RG-beta functions up to cubic order in the couplings. The mean value of the dissipative conductance at the RG-fixed point is calculated for a cylinder geometry with any aspect ratio.

Asymptotics for nonlinear integral equations with a generalized heat kernel using renormalization group technique II: Marginal perturbations and logarithmic corrections to the time decay of solutions

In this paper, we proceed with the analysis started in \cite{bib:braga-mor-souza} and, using the Renormalization Group method, we obtain logarithmic corrections to the decay of solutions for a class of nonlinear integral equations whenever the nonlinearities are classified as marginal in the Renormalization Group sense.

Lattice regularisation and entanglement structure of the Gross-Neveu model

We construct a Hamiltonian lattice regularisation of the N-flavour Gross-Neveu model that manifestly respects the full O(2N) symmetry, preventing the appearance of any unwanted marginal perturbations to the quantum field theory. In the context of this lattice model, the dynamical mass generation is intimately related to the Coleman-Mermin-Wagner and Lieb-Schultz-Mattis theorems. In particular, the model can be interpreted as lying at the first order phase transition line between a trivial and symmetry-protected topological (SPT) phase, which explains the degeneracy of the elementary kink excitations. We show that our Hamiltonian model can be solved analytically in the large N limit, producing the correct expression for the mass gap. Furthermore, we perform extensive numerical matrix product state simulations for N = 2, thereby recovering the emergent Lorentz symmetry and the proper non-perturbative mass gap scaling in the continuum limit. Finally, our simulations also reveal how the continuum limit manifests itself in the entanglement spectrum. As expected from conformal field theory we find two conformal towers, one tower spanned by the linear representations of O(4), corresponding to the trivial phase, and the other by the projective (i.e. spinor) representations, corresponding to the SPT phase.

Marginal CFT perturbations at the integer quantum Hall transition

According to recent arguments by the author, the conformal field theory (CFT) describing the scaling limit of the integer quantum Hall plateau transition is a deformed level-4 Wess–Zumino–Novikov–Witten model with Riemannian target space inside a complex Lie supergroup GL. After a summary of that proposal and some of its predictions, the leading irrelevant and relevant perturbations of the proposed CFT are discussed. Argued to be marginal, these result in a non-standard renormalization group (RG) flow near criticality, which calls for modified finite-size scaling analysis and may explain the long-standing inability of numerical work to reach agreement on the values of critical exponents. The technique of operator product expansion is used to compute the RG-beta functions up to cubic order in the couplings. The mean value of the dissipative conductance at the RG-fixed point is calculated for a cylinder geometry with any aspect ratio.

Effect of pressure on the drag coefficient of individual bubbles in a contaminated polydisperse swarm

This study investigated the effect of pressure on individual bubble drag for a contaminated polydisperse swarm. Bubble size distributions and individual bubble drag coefficients were experimentally determined at four different pressures (0.14, 0.46, 2.00, 4.00 MPa) to establish if there is a relationship between bubble size distribution and individual drag coefficient and quantify the effect of pressure on bubble drag. The analysis is limited to bubbles with diameters between 0.4 and 6 mm. Individual bubble drag coefficients were found to decrease with pressure at constant gas hold-up. This effect is attributed to changes in bubble size distribution driven by pressure. As pressure increased, the bubble size distribution shifted towards smaller sizes. Relatively speaking, these smaller bubbles induce marginal liquid perturbations and could potentially dampen turbulence from other sources, resulting in reduced drag. A new drag model has been proposed to improve CFD simulation of bubble columns at elevated pressures.

Jump Detection and Noise Separation by a Singular Wavelet Method for Predictive Analytics of High-Frequency Data

High-frequency data is a big data in finance in which a large amount of intra-day transactions arriving irregularly in financial markets are recorded. Given the high frequency and irregularity, such data require efficient tools to filter out the noise (i.e. jumps) arising from the anomaly, irregularity, and heterogeneity of financial markets. In this article, we use a recurrently adaptive separation algorithm, which is based on the maximal overlap discrete wavelet transform (MODWT) and that can effectively: (1) identify the time-variant jumps, (2) extract the time-consistent patterns from the noise (jumps), and (3) denoise the marginal perturbations. In addition, the proposed algorithm enables reinforcement learning to optimize a multiple-criteria decision or convex programming when reconstructing the wavelet-denoised data. Using simulated data, we show the proposed approach can perform efficiently in comparison with other conventional methods documented in the literature. We also apply our method in an empirical study by using high-frequency data from the US stock market and confirm that the proposed method can significantly improve the accuracy of predictive analytics models for financial market returns.

Robust genetically optimized skew laminates

The present research work explores genetically optimized skew laminates, whose stacking sequence has been varied to maximize their fundamental frequencies with the help of an efficient optimization algorithm. Genetic algorithm, rather than being applied blindly with empirical parameters, is tuned with respect to the problem at hand. Following an extensive study, genetic algorithm parameters are selected carefully so as to ensure a robust optimized stacking sequence. The sensitivity of ply angles is also investigated so as to warrant against marginal manufacturing perturbations. The safe limit for variation of ply angles without much hampering the frequency is also recommended. Validation with existing solutions illustrates the efficiency of the procedure. A wide range of results with rectangular/ skew plates of different layers having symmetric/ antisymmetric ply-orientations, subject to different boundary conditions are solved, which demonstrate the efficacy of the approach.

Interplay between short-range correlated disorder and Coulomb interaction in nodal-line semimetals

In nodal-line semimetals, Coulomb interactions and short-range correlated disorder are both marginal perturbations to the clean non-interacting Hamiltonian. We analyze their interplay using a weak-coupling renormalization group approach. In the clean case, the Coulomb interaction has been found to be marginally irrelevant, leading to Fermi liquid behavior. We extend the analysis to incorporate the effects of disorder. The nodal line structure gives rise to kinematical constraints similar to that for a two-dimensional Fermi surface, which plays a crucial role in the one-loop renor- malization of the disorder couplings. For a two-fold degenerate nodal loop (Weyl loop), we show that disorder flows to strong coupling along a unique fixed trajectory in the space of symmetry inequiv- alent disorder couplings. Along this fixed trajectory, all symmetry inequivalent disorder strengths become equal. For a four-fold degenerate nodal loop (Dirac loop), disorder also flows to strong coupling, however the strengths of symmetry inequivalent disorder couplings remain different. We show that feedback from disorder reverses the sign of the beta function for the Coulomb interaction, causing the Coulomb interaction to flow to strong coupling as well. However, the Coulomb interac- tion flows to strong coupling asymptotically more slowly than disorder. Extrapolating our results to strong coupling, we conjecture that at low energies nodal line semimetals should be described by a noninteracting nonlinear sigma model. We discuss the relation of our results with possible many-body localization at zero temperatures in such materials.

On the Kerr-AdS/CFT correspondence

We review the relation between four-dimensional global conformal blocks and field propagation in AdS5. Following the standard argument that marginal perturbations should backreact in the geometry, we turn to the study of scalar fields in the generic Kerr-AdS5 geometry. On one hand, the result for scattering coefficients can be obtained exactly using the isomonodromy technique, giving exact expressions in terms of c = 1 chiral conformal blocks. On the other hand, one can use the analogy between the scalar field equations to the Level 2 null field Ward identity in two dimensional Liouville field theory to write approximate expressions for the same coefficients in terms of semi-classical chiral Liouville conformal blocks. Surprisingly, the conformal block thus constructed has a well-behaved interpretation in terms of Liouville vertex operators.

On exact solution of topological CFT models based on Kazama–Suzuki cosets

We compute the flat coordinates on the Frobenius manifolds arising on the deformation space of Gepner chiral rings. The explicit form of the flat coordinates is important for exact solutions of models of topological CFT and 2D Liouville gravity. We describe the case k = 3, which is of particular interest because apart from the relevant chiral fields it contains a marginal one. Whereas marginal perturbations are relevant in different contexts, their analysis requires additional care compared to the relevant perturbations.

Effect of higher-order stress gradients on the centennial mass evolution of the Greenland ice sheet

Abstract. We use a three-dimensional thermo-mechanically coupled model of the Greenland ice sheet to assess the effects of marginal perturbations on volume changes on centennial timescales. The model is designed to allow for five ice dynamic formulations using different approximations to the force balance. The standard model is based on the shallow ice approximation for both ice deformation and basal sliding. A second model version relies on a higher-order Blatter/Pattyn type of core that resolves effects from gradients in longitudinal stresses and transverse horizontal shearing, i.e. membrane-like stresses. Together with three intermediate model versions, these five versions allow for gradually more dynamic feedbacks from membrane stresses. Idealised experiments are conducted on various resolutions to compare the time-dependent response to imposed accelerations at the marine ice front. If such marginal accelerations are to have an appreciable effect on total mass loss on a century timescale, a fast mechanism to transmit such perturbations inland is required. While the forcing is independent of the model version, inclusion of direct horizontal coupling allows the initial speed-up to reach several tens of kilometres inland. Within one century, effects from gradients in membrane stress alter the inland signal propagation and transmit additional dynamic thinning to the ice sheet interior. But the centennial overall volume loss differs only by some percents from the standard model, as the dominant response is a diffusive inland propagation of geometric changes. For the experiments considered, this volume response is even attenuated by direct horizontal coupling. The reason is a faster adjustment of the sliding regime by instant stress transmission in models that account for the effect of membrane stresses. Ultimately, horizontal coupling decreases the reaction time to perturbations at the ice sheet margin. These findings suggest that for modelling the mass evolution of a large-scale ice sheet, effects from diffusive geometric adjustments dominate effects from successively more complete dynamic approaches.

Renormalization Group Analysis of Nonlinear Diffusion Equations with Time Dependent Coefficients and Marginal Perturbations

In this paper we use a Renormalization Group (RG) method to study the long-time asymptotics of nonlinear diffusion equations with time-dependent diffusion coefficients and nonlinearities which are marginal (or critical) with respect to the RG operator. These equations describe the time evolution of the average concentration of a passive scalar being advected by a random velocity field. We prove that, besides the expected diffusive behavior, there is an extra logarithmic correction which is the imprint of the critical nonlinearity.

Relative Sensitivity of Conditional Distributions to Kurtosis Deviations in the Joint Model

The Multivariate Exponential Power family is considered for n-dimensional random variables, Z, with a known partition Z (Y,X) of dimensions p and n-p, respectively. An infinitesimal variation of any parameter produces both conditional and marginal distributions perturbations. The aim of our study is to determine the local effect of kurtosis deviations by means of the Kullback-Leibler divergence measure between probability distributions. The additive decomposition of this measure in terms of the conditional and marginal distributions, YǀX and X, has been used to define the relative sensitivity of the conditional distributions family {YǀX=x}. The obtained results show that, for large dimensions, it is nearly p/n.

Product CFTs, gravitational cloning, massive gravitons and the space of gravitational duals

AbstractThe question of graviton cloning in the context of the bulk/boundary correspondence is considered. It is shown that multi‐graviton theories can be obtained from products of large‐N CFTs. No more than one interacting massless graviton is possible. There can be however, many interacting massive gravitons that can be arbitrarily light. This is achieved by coupling CFTs via multi‐trace marginal or relevant perturbations. The geometrical structure of the gravitational duals of such theories is that of product manifolds with their boundaries identified. The interpretation of such theories is discussed. Potential applications to massive gravity and cosmology are briefly suggested.

Product CFTs, gravitational cloning, massive gravitons and the space of gravitational duals

The question of graviton cloning in the context of the bulk/boundary correspondence is considered. It is shown that multi-graviton theories can be obtained from products of large-N CFTs. No more than one interacting massless graviton is possible. There can be however, many interacting massive gravitons. This is achieved by coupling CFTs via multi-trace marginal or relevant perturbations. The geometrical structure of the gravitational duals of such theories is that of product manifolds with their boundaries identified. The calculational formalism is described and the interpretation of such theories is discussed.

Constraints on the thermal evolution of continental lithosphere from U-Pb accessory mineral thermochronometry of lower crustal xenoliths, southern Africa

U-Pb isotopic thermochronometry of rutile, apatite and titanite from kimberlite-borne lower crustal granulite xenoliths has been used to constrain the thermal evolution of Archean cratonic and Proterozoic off-craton continental lithosphere beneath southern Africa. The relatively low closure temperature of the U-Pb rutile thermochronometer (~400–450 °C) allows its use as a particularly sensitive recorder of the establishment of "cratonic" lithospheric geotherms, as well as subsequent thermal perturbations to the lithosphere. Contrasting lower crustal thermal histories are revealed between intracratonic and craton margin regions. Discordant Proterozoic (1.8 to 1.0 Ga) rutile ages in Archean (2.9 to 2.7 Ga) granulites from within the craton are indicative of isotopic resetting by marginal orogenic thermal perturbations influencing the deep crust of the cratonic nucleus. In Proterozoic (1.1 to 1.0 Ga) granulite xenoliths from the craton-bounding orogenic belts, rutiles define discordia arrays with Neoproterozoic (0.8 to 0.6 Ga) upper intercepts and lower intercepts equivalent to Mesozoic exhumation upon kimberlite entrainment. In combination with coexisting titanite and apatite dates, these results are interpreted as a record of postorogenic cooling at an integrated rate of approximately 1 °C/Ma, and subsequent variable Pb loss in the apatite and rutile systems during a Mesozoic thermal perturbation to the deep lithosphere. Closure of the rutile thermochronometer signals temperatures of ≤450 °C in the lower crust during attainment of cratonic lithospheric conductive geotherms, and such closure in the examined portions of the "off-craton" Proterozoic domains of southern Africa indicates that their lithospheric thermal profiles were essentially cratonic from the Neoproterozoic through to the Late Jurassic. These results suggest similar lithospheric thickness and potential for diamond stability beneath both Proterozoic and Archean domains of southern Africa. Subsequent partial resetting of U-Pb rutile and apatite systematics in the cratonic margin lower crust records a transient Mesozoic thermal modification of the lithosphere, and modeling of the diffusive Pb loss from lower crustal rutile constrains the temperature and duration of Mesozoic heating to ≤550 °C for ≥50 ka. This result indicates that the thermal perturbation is not simply a kimberlite-related magmatic phenomenon, but is rather a more protracted manifestation of lithospheric heating, likely related to mantle upwelling and rifting of Gondwana during the Late Jurassic to Cretaceous. The manifestation of this thermal pulse in the lower crust is spatially and temporally correlated with anomalously elevated and/or kinked Cretaceous mantle paleogeotherms, and evidence for metasomatic modification in cratonic mantle peridotite suites. It is argued that most of the geographic differences in lithospheric thermal structure inferred from mantle xenolith thermobarometry are likewise due to the heterogeneous propagation of this broad upper mantle thermal anomaly. The differential manifestation of heating between cratonic margin and cratonic interior indicates the importance of advective heat transport along pre-existing lithosphere-scale discontinuities. Within this model, kimberlite magmatism was a similarly complex, space- and time-dependent response to Late Mesozoic lithospheric thermal perturbation.

Multiscaling in Ising quantum chains with random Hilhorst–van Leeuwen perturbations

We consider the influence on the surface critical behaviour of a quantum Ising chain of quenched random surface perturbations decaying as a power of the distance from the surface (random Hilhorst–van Leeuwen models). We study, analytically and numerically, the multiscaling behaviour of the surface magnetization and the surface energy density in the case of marginal perturbations.

Charge instabilities near a Van Hove singularity

The charge instabilities of electron systems in the square lattice are analyzed near the Van Hove singularity by means of a wilsonian renormalization group approach. We show that the method preserves the spin rotational invariance at all scales, allowing a rigorous determination of spin and charge instabilities of the $t-t'$ Hubbard model. For $t'$ above $\approx 0.276 t$, repulsive interactions fall into two different universality classes. One of them has nonsingular response functions in the charge sector, while the other is characterized by the splitting of the Van Hove singularity. At the level of marginal perturbations, the Hubbard model turns out to be at the boundary between the two universality classes, while extended models with nearest-neighbor repulsive interactions belong to the latter class. In the case of open systems allowed to exchange particles with a reservoir, we show the existence of a range of fillings forbidden above and below the Van Hove singularity. This has the property of attracting the Fermi level in the mentioned range, as the system reaches its lowest energy when the Fermi energy is at the singularity.

Conformal profiles in the Hilhorst-van Leeuwen model

We study the critical energy and magnetization profiles for the Ising quantum chain with a marginal extended surface perturbation of the form A/y, y being the distance from the surface (Hilhorst-van Leeuwen model). For weak local couplings, A<A_c, the model displays a continuous surface transition with A-dependent exponents, whereas, for A>A_c, there is surface order at the bulk critical point. If conformal invariance is assumed to hold with such marginal perturbations, it predicts conformal profiles with the same scaling form as for the unperturbed quantum chain, with marginal surface exponents replacing the unperturbed ones. The results of direct analytical and numerical calculations of the profiles confirm the validity of the conformal expressions in the regimes of second- and first-order surface transitions.