Perturbative bosonization from two-point correlation functions

Here we address the problem of bosonizing massive fermions without making expansions in the fermion masses in both massive QED(2) and QED(3) with N fermion flavors including also a Thirring coupling. We start from two-point correlators involving the U(1) fermionic current and the gauge field. From the tensor structure of those correlators we prove that the U(1) current must be identically conserved (topological) in the corresponding bosonized theory in both D=2 and D=3 dimensions. We find an effective generating functional in terms of bosonic fields which reproduces these two-point correlators and from that we obtain a map of the Lagrangian density (ψ) over bar (r)(ipartial derivative-m)psi(r) into a bosonic one in both dimensions. This map is nonlocal but it is independent of the electromagnetic and Thirring couplings, at least in the quadratic approximation for the fermionic determinant.

Field-theory Two-point Functions via Negative Dimension Integration

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the two point Padé table for a distribution

Some additional recurrence relations for the denominator polynomials of two point Padé approximants are derived. An example in which the coefficients of one of the two series, from which the Padé approximants are derived, are moments of a distribution is considered. For this example, properties of the denominator polynomials, and their zeros, are described.

Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the template for embedding the couple (K3, ds2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce into the consideration the function of length between the fluid particles, and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comment the case of a negative Gaussian curvature.

The massless two-loop two-point function and zeta functions in counterterms of Feynman diagrams

The main part of this thesis describes a method of calculating the massless two-loop two-point function which allows expanding the integral up to an arbitrary order in the dimensional regularization parameter epsilon by rewriting it as a double Mellin-Barnes integral. Closing the contour and collecting the residues then transforms this integral into a form that enables us to utilize S. Weinzierl's computer library nestedsums. We could show that multiple zeta values and rational numbers are sufficient for expanding the massless two-loop two-point function to all orders in epsilon. We then use the Hopf algebra of Feynman diagrams and its antipode, to investigate the appearance of Riemann's zeta function in counterterms of Feynman diagrams in massless Yukawa theory and massless QED. The class of Feynman diagrams we consider consists of graphs built from primitive one-loop diagrams and the non-planar vertex correction, where the vertex corrections only depend on one external momentum. We showed the absence of powers of pi in the counterterms of the non-planar vertex correction and diagrams built by shuffling it with the one-loop vertex correction. We also found the invariance of some coefficients of zeta functions under a change of momentum flow through these vertex corrections.

Structure and function in rhodopsin: correct folding and misfolding in two point mutants in the intradiscal domain of rhodopsin identified in retinitis pigmentosa.

The rhodopsin mutants P23H and G188R, identified in autosomal dominant retinitis pigmentosa (ADRP), and the site-specific mutants D190A and DeltaY191-Y192 were expressed in COS cells from synthetic mutant opsin genes containing these mutations. The proteins expressed from P23H and D190A partially regenerated the rhodopsin chromophore with 11-cis-retinal and were mixtures of the correctly folded (retinal-binding) and misfolded (non-retinal-binding) opsins. The mixtures were separated into pure, correctly folded mutant rhodopsins and misfolded opsins. The proteins expressed from the ADRP mutant G188R and the mutant DeltaY191-Y192 were composed of totally misfolded non-retinal-binding opsins. Far-UV CD spectra showed that the correctly folded mutant rhodopsins had helical content similar to that of the wild-type rhodopsin, whereas the misfolded opsins had helical content 50-70% of the wild type. The near-UV CD spectra of the misfolded mutant proteins lack the characteristic band pattern seen in the wild-type opsin, indicative of a different tertiary structure. Further, whereas the folded mutant rhodopsins were essentially resistant to trypsin digestion, the misfolded opsins were degraded to small fragments under the same conditions. Therefore, the misfolded opsins appear to be less compact in their structures than the correctly folded forms. We suggest that most, if not all, of the point mutations in the intradiscal domain identified in ADRP cause partial or complete misfolding of rhodopsin.

Multiplicity results for second-order two-point boundary value problems with nonlinearities across several eigenvalues

We consider the boundary value problems for nonlinear second-order differential equations of the form u '' + a(t)f (u) = 0, 0 < t < 1, u(0) = u (1) = 0. We give conditions on the ratio f (s)/s at infinity and zero that guarantee the existence of solutions with prescribed nodal properties. Then we establish existence and multiplicity results for nodal solutions to the problem. The proofs of our main results are based upon bifurcation techniques. (c) 2004 Elsevier Ltd. All rights reserved.

Multiplicity results for second-order two-point boundary value problems with superlinear or sublinear nonlinearities

We consider boundary value problems for nonlinear second order differential equations of the form u + a(t) f(u) = 0, t epsilon (0, 1), u(0) = u(1) = 0, where a epsilon C([0, 1], (0, infinity)) and f : R --> R is continuous and satisfies f (s)s > 0 for s not equal 0. We establish existence and multiplicity results for nodal solutions to the problems if either f(0) = 0, f(infinity) = infinity or f(0) = infinity, f(0) = 0, where f (s)/s approaches f(0) and f(infinity) as s approaches 0 and infinity, respectively. We use bifurcation techniques to prove our main results. (C) 2004 Elsevier Inc. All rights reserved.

Evaluation of two HbA1c point-of-care analyzers.

BACKGROUND Measurement of HbA1c is the most important parameter to assess glycemic control in diabetic patients. Different point-of-care devices for HbA1c are available. The aim of this study was to evaluate two point-of-care testing (POCT) analyzers (DCA Vantage from Siemens and Afinion from Axis-Shield). We studied the bias and precision as well as interference from carbamylated hemoglobin. METHODS Bias of the POCT analyzers was obtained by measuring 53 blood samples from diabetic patients with a wide range of HbA1c, 4%-14% (20-130 mmol/mol), and comparing the results with those obtained by the laboratory method: HPLC HA 8160 Menarini. Precision was performed by 20 successive determinations of two samples with low 4.2% (22 mmol/mol) and high 9.5% (80 mmol/mol) HbA1c values. The possible interference from carbamylated hemoglobin was studied using 25 samples from patients with chronic renal failure. RESULTS The means of the differences between measurements performed by each POCT analyzer and the laboratory method (95% confidence interval) were: 0.28% (p<0.005) (0.10-0.44) for DCA and 0.27% (p<0.001) (0.19-0.35) for Afinion. Correlation coefficients were: r=0.973 for DCA, and r=0.991 for Afinion. The mean bias observed by using samples from chronic renal failure patients were 0.2 (range -0.4, 0.4) for DCA and 0.2 (-0.2, 0.5) for Afinion. Imprecision results were: CV=3.1% (high HbA1c) and 2.97% (low HbA1c) for DCA, CV=1.95% (high HbA1c) and 2.66% (low HbA1c) for Afinion. CONCLUSIONS Both POCT analyzers for HbA1c show good correlation with the laboratory method and acceptable precision.

Kraichnan–Leith–Batchelor similarity theory and two-dimensional inverse cascades

We study the scaling properties and Kraichnan–Leith–Batchelor (KLB) theory of forced inverse cascades in generalized two-dimensional (2D) fluids (α-turbulence models) simulated at resolution 8192x8192. We consider α=1 (surface quasigeostrophic flow), α=2 (2D Euler flow) and α=3. The forcing scale is well resolved, a direct cascade is present and there is no large-scale dissipation. Coherent vortices spanning a range of sizes, most larger than the forcing scale, are present for both α=1 and α=2. The active scalar field for α=3 contains comparatively few and small vortices. The energy spectral slopes in the inverse cascade are steeper than the KLB prediction −(7−α)/3 in all three systems. Since we stop the simulations well before the cascades have reached the domain scale, vortex formation and spectral steepening are not due to condensation effects; nor are they caused by large-scale dissipation, which is absent. One- and two-point p.d.f.s, hyperflatness factors and structure functions indicate that the inverse cascades are intermittent and non-Gaussian over much of the inertial range for α=1 and α=2, while the α=3 inverse cascade is much closer to Gaussian and non-intermittent. For α=3 the steep spectrum is close to that associated with enstrophy equipartition. Continuous wavelet analysis shows approximate KLB scaling ℰ(k)∝k−2 (α=1) and ℰ(k)∝k−5/3 (α=2) in the interstitial regions between the coherent vortices. Our results demonstrate that coherent vortex formation (α=1 and α=2) and non-realizability (α=3) cause 2D inverse cascades to deviate from the KLB predictions, but that the flow between the vortices exhibits KLB scaling and non-intermittent statistics for α=1 and α=2.

Recording from Two Neurons: Second-Order Stimulus Reconstruction from Spike Trains and Population Coding

We study the reconstruction of visual stimuli from spike trains, representing the reconstructed stimulus by a Volterra series up to second order. We illustrate this procedure in a prominent example of spiking neurons, recording simultaneously from the two H1 neurons located in the lobula plate of the fly Chrysomya megacephala. The fly views two types of stimuli, corresponding to rotational and translational displacements. Second-order reconstructions require the manipulation of potentially very large matrices, which obstructs the use of this approach when there are many neurons. We avoid the computation and inversion of these matrices using a convenient set of basis functions to expand our variables in. This requires approximating the spike train four-point functions by combinations of two-point functions similar to relations, which would be true for gaussian stochastic processes. In our test case, this approximation does not reduce the quality of the reconstruction. The overall contribution to stimulus reconstruction of the second-order kernels, measured by the mean squared error, is only about 5% of the first-order contribution. Yet at specific stimulus-dependent instants, the addition of second-order kernels represents up to 100% improvement, but only for rotational stimuli. We present a perturbative scheme to facilitate the application of our method to weakly correlated neurons.

Light-cone gauge integrals: prescriptionlessness at two loops

The only calculations performed beyond one-loop level in the light-cone gauge make use of the Mandelstam-Leibbrandt (ML) prescription in order to circumvent the notorious gauge dependent poles. Recently we have shown that in the context of negative dimensional integration method (NDIM) such prescription can be altogether abandoned, at least in one-loop order calculations. We extend our approach, now studying two-loop integrals pertaining to two-point functions. While previous works on the subject present only divergent parts for the integrals, we show that our prescriptionless method gives the same results for them, besides finite parts for arbitrary exponents of propagators. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Note on the point-splitting procedure to evaluate vacuum fluctuation in certain cylindrically symmetric backgrounds

We reexamine the two-point function approaches used to study vacuum fluctuation in wedge-shaped regions and conical backgrounds. The appearance of divergent integrals is discussed and circumvented. The issue is considered in the context of a massless scalar field in cosmic string spacetime.

Therapeutic drug monitoring of once daily aminoglycoside dosing: comparison of two methods and investigation of the optimal blood sampling strategy.

PURPOSE Therapeutic drug monitoring of patients receiving once daily aminoglycoside therapy can be performed using pharmacokinetic (PK) formulas or Bayesian calculations. While these methods produced comparable results, their performance has never been checked against full PK profiles. We performed a PK study in order to compare both methods and to determine the best time-points to estimate AUC0-24 and peak concentrations (C max). METHODS We obtained full PK profiles in 14 patients receiving a once daily aminoglycoside therapy. PK parameters were calculated with PKSolver using non-compartmental methods. The calculated PK parameters were then compared with parameters estimated using an algorithm based on two serum concentrations (two-point method) or the software TCIWorks (Bayesian method). RESULTS For tobramycin and gentamicin, AUC0-24 and C max could be reliably estimated using a first serum concentration obtained at 1 h and a second one between 8 and 10 h after start of the infusion. The two-point and the Bayesian method produced similar results. For amikacin, AUC0-24 could reliably be estimated by both methods. C max was underestimated by 10-20% by the two-point method and by up to 30% with a large variation by the Bayesian method. CONCLUSIONS The ideal time-points for therapeutic drug monitoring of once daily administered aminoglycosides are 1 h after start of a 30-min infusion for the first time-point and 8-10 h after start of the infusion for the second time-point. Duration of the infusion and accurate registration of the time-points of blood drawing are essential for obtaining precise predictions.