Mathematical Modeling of Biofilm Structures Using COMSTAT Data

Mathematical modeling holds great potential for quantitatively describing biofilm growth in presence or absence of chemical agents used to limit or promote biofilm growth. In this paper, we describe a general mathematical/statistical framework that allows for the characterization of complex data in terms of few parameters and the capability to (i) compare different experiments and exposures to different agents, (ii) test different hypotheses regarding biofilm growth and interaction with different agents, and (iii) simulate arbitrary administrations of agents. The mathematical framework is divided to submodels characterizing biofilm, including new models characterizing live biofilm growth and dead cell accumulation; the interaction with agents inhibiting or stimulating growth; the kinetics of the agents. The statistical framework can take into account measurement and interexperiment variation. We demonstrate the application of (some of) the models using confocal microscopy data obtained using the computer program COMSTAT

A Two-loop Test of Buscher's T-duality I

We study the two loop quantum equivalence of sigma models related by Buscher's T-duality transformation. The computation of the two loop perturbative free energy density is performed in the case of a certain deformation of the SU(2) principal sigma model, and its T-dual, using dimensional regularization and the geometric sigma model perturbation theory. We obtain agreement between the free energy density expressions of the two models.Comment: 28 pp, Latex, references adde

On the equivalence between Implicit Regularization and Constrained Differential Renormalization

Constrained Differential Renormalization (CDR) and the constrained version of Implicit Regularization (IR) are two regularization independent techniques that do not rely on dimensional continuation of the space-time. These two methods which have rather distinct basis have been successfully applied to several calculations which show that they can be trusted as practical, symmetry invariant frameworks (gauge and supersymmetry included) in perturbative computations even beyond one-loop order. In this paper, we show the equivalence between these two methods at one-loop order. We show that the configuration space rules of CDR can be mapped into the momentum space procedures of Implicit Regularization, the major principle behind this equivalence being the extension of the properties of regular distributions to the regularized ones.Comment: 16 page

Constraints on Beta Functions from Duality

We analyze the way in which duality constrains the exact beta function and correlation length in single-coupling spin systems. A consistency condition we propose shows very concisely the relation between self-dual points and phase transitions, and implies that the correlation length must be duality invariant. These ideas are then tested on the 2-d Ising model, and used towards finding the exact beta function of the $q$-state Potts model. Finally, a generic procedure is given for identifying a duality symmetry in other single-coupling models with a continuous phase transition.Comment: LaTeX, 6 page

O(d,d) invariance at two and three loops

We show that in a two-dimensional sigma-model whose fields only depend on one target space co-ordinate, the O(d,d) invariance of the conformal invariance conditions observed at one loop is preserved at two loops (in the general case with torsion) and at three loops (in the case without torsion).Comment: 21 pages. Plain Tex. Uses Harvmac ("b" option). Revised Version with references added and minor errors correcte

Altered sensorimotor activation patterns in idiopathic dystonia - an activation likelihood estimation meta-analysis of functional brain imaging studies

Dystonia is characterized by sustained or intermittent muscle contractions causing abnormal, often repetitive, movements or postures. Functional neuroimaging studies have yielded abnormal task-related sensorimotor activation in dystonia, but the results appear to be rather variable across studies. Further, study size was usually small including different types of dystonia. Here we performed an activation likelihood estimation (ALE) meta-analysis of functional neuroimaging studies in patients with primary dystonia to test for convergence of dystonia-related alterations in task-related activity across studies. Activation likelihood estimates were based on previously reported regional maxima of task-related increases or decreases in dystonia patients compared to healthy controls. The meta-analyses encompassed data from 179 patients with dystonia reported in 18 functional neuroimaging studies using a range of sensorimotor tasks. Patients with dystonia showed bilateral increases in task-related activation in the parietal operculum and ventral postcentral gyrus as well as right middle temporal gyrus. Decreases in task-related activation converged in left supplementary motor area and left postcentral gyrus, right superior temporal gyrus and dorsal midbrain. Apart from the midbrain cluster, all between-group differences in task-related activity were retrieved in a sub-analysis including only the 14 studies on patients with focal dystonia. For focal dystonia, an additional cluster of increased sensorimotor activation emerged in the caudal cingulate motor zone. The results show that dystonia is consistently associated with abnormal somatosensory processing in the primary and secondary somatosensory cortex along with abnormal sensorimotor activation of mesial premotor and right lateral temporal cortex

Determination of Tobramycin in M₉ Medium by LC-MS/MS: Signal Enhancement by Trichloroacetic Acid

It is well known that ion-pairing reagents cause ion suppression in LC-MS/MS methods. Here, we report that trichloroacetic acid increases the MS signal of tobramycin. To support studies of an in vitro pharmacokinetic/pharmacodynamic simulator for bacterial biofilms, an LC-MS/MS method for determination of tobramycin in M9 media was developed. Aliquots of 25 μL M9 media samples were mixed with the internal standard (IS) tobramycin-d5 (5 µg/mL, 25 µL) and 200 µL 2.5% trichloroacetic acid. The mixture (5 µL) was directly injected onto a PFP column (2.0 × 50 mm, 3 µm) eluted with water containing 20 mM ammonium formate and 0.14% trifluoroacetic acid and acetonitrile containing 0.1% trifluoroacetic acid in a gradient mode. ESI+ and MRM with ion m/z 468 → 324 for tobramycin and m/z 473 → 327 for the IS were used for quantification. The calibration curve concentration range was 50–25000 ng/mL. Matrix effect from M9 media was not significant when compared with injection solvents, but signal enhancement by trichloroacetic acid was significant (∼3 fold). The method is simple, fast, and reliable. Using the method, the in vitro PK/PD model was tested with one bolus dose of tobramycin

Implicit Regularization and Renormalization of QCD

We apply the Implicit Regularization Technique (IR) in a non-abelian gauge theory. We show that IR preserves gauge symmetry as encoded in relations between the renormalizations constants required by the Slavnov-Taylor identities at the one loop level of QCD. Moreover, we show that the technique handles divergencies in massive and massless QFT on equal footing.Comment: (11 pages, 2 figures

RG Flow Irreversibility, C-Theorem and Topological Nature of 4D N=2 SYM

We determine the exact beta function and a RG flow Lyapunov function for N=2 SYM with gauge group SU(n). It turns out that the classical discriminants of the Seiberg-Witten curves determine the RG potential. The radial irreversibility of the RG flow in the SU(2) case and the non-perturbative identity relating the $u$-modulus and the superconformal anomaly, indicate the existence of a four dimensional analogue of the c-theorem for N=2 SYM which we formulate for the full SU(n) theory. Our investigation provides further evidence of the essentially topological nature of the theory.Comment: 9 pages, LaTeX file. Discussion on WDVV and integrability. References added. Version published in PR