Constructive Field Theory and Applications: Perspectives and Open Problems

In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the constructive methods well within the 21st century

The Global Renormalization Group Trajectory in a Critical Supersymmetric Field Theory on the Lattice Z^3

We consider an Euclidean supersymmetric field theory in $Z^3$ given by a supersymmetric $\Phi^4$ perturbation of an underlying massless Gaussian measure on scalar bosonic and Grassmann fields with covariance the Green's function of a (stable) L\'evy random walk in $Z^3$. The Green's function depends on the L\'evy-Khintchine parameter $\alpha={3+\epsilon\over 2}$ with $0<\alpha<2$. For $\alpha ={3\over 2}$ the $\Phi^{4}$ interaction is marginal. We prove for $\alpha-{3\over 2}={\epsilon\over 2}>0$ sufficiently small and initial parameters held in an appropriate domain the existence of a global renormalization group trajectory uniformly bounded on all renormalization group scales and therefore on lattices which become arbitrarily fine. At the same time we establish the existence of the critical (stable) manifold. The interactions are uniformly bounded away from zero on all scales and therefore we are constructing a non-Gaussian supersymmetric field theory on all scales. The interest of this theory comes from the easily established fact that the Green's function of a (weakly) self-avoiding L\'evy walk in $Z^3$ is a second moment (two point correlation function) of the supersymmetric measure governing this model. The control of the renormalization group trajectory is a preparation for the study of the asymptotics of this Green's function. The rigorous control of the critical renormalization group trajectory is a preparation for the study of the critical exponents of the (weakly) self-avoiding L\'evy walk in $Z^3$.Comment: 82 pages, Tex with macros supplied. Revision includes 1. redefinition of norms involving fermions to ensure uniqueness. 2. change in the definition of lattice blocks and lattice polymer activities. 3. Some proofs have been reworked. 4. New lemmas 5.4A, 5.14A, and new Theorem 6.6. 5.Typos corrected.This is the version to appear in Journal of Statistical Physic

Distribution of 5-HT1F Receptors in Monkey Vestibular and Trigeminal Ganglion Cells

Background: Evidence of serotonergic involvement in vestibular pathway contributions to migraine and balance disorders is compelling. Serotonergic 5-HT1B and 5-HT1D receptors are expressed extensively in inner ear ganglia of monkeys and rats. The serotonergic 5-HT1F receptor is also a target of triptans. This study describes its distribution in vestibular and trigeminal ganglia of monkeys. Methods: Using primary polyclonal antibodies raised against oligopeptides specific for the human 5-HT1F receptor, neuronal somatic area and intensity of immunoreactive vestibular and trigeminal ganglia were quantified. Results and Discussion: Virtually all vestibular and considerable trigeminal ganglia showed positive 5-HT1F receptor immunoreactivity. Inferior and superior vestibular ganglia staining appeared confined to distinct cell regions, varying considerably among cells of different sizes: more intense in small, punctate in some medium and regionally polarized in some large cells. Analyses of average somatic vestibular neuronal immunoreactive intensity identified mainly medium sized cells with high standard deviation of intensity corresponding to punctately-stained cells. Less variability occurred in somatic intensity staining and cellular distribution among 5-HT1F receptor immunopositive trigeminal ganglia. Most exhibited similar punctate staining patterns, higher mean somatic immunoreactive intensity and larger neuronal somatic size proportions per size distribution subpopulation compared to vestibular ganglia size distribution populations. Centrally directed vestibular ganglion neuronal processes, cochlear inner hair cells, vestibular hair cells and blood vessels in vestibular maculae and cristae were immunoreactive. The 5-HT1F receptor expression in vestibular ganglia shows complex variable staining intensity patterns associated with cell size of immunopositive neurons, not seen in immunopositive trigeminal ganglia and not previously evident with 5-HT1B and 5-HT1D receptor subtype immunoreactivity in vestibular ganglia. These data motivate exploration of 5-HT1 receptor oligomerization and ligand functional selectivity in differential serotonergic involvement in co-morbidity of migraine and balance disorders. Similar findings in cochlear inner hair cell afferents are applicable to migraine related tinnitus or hypercusis (phonophobia)

Interrelationship of Major Topological Indices Evidenced by Clustering

This study examines the mutual relatedness of 318 major topological indices (TIs) for three sets of molecules: (i) a set of 139 hydrocarbons, (ii) a diverse set of 1029 compounds and (iii) a diverse set of 2887 compounds. The TIs included in this study are those that have been frequently used in the characterization of structure and QSAR/ QSPR studies. After variable reduction based on the elimination of TIs for which all values were zero and those that were completely correlated with another TI, a variable clustering technique was used to cluster the TIs which resulted in 16, 37 and 56 clusters, respectively, for the three data sets mentioned above. Analysis of the correspondence among the clusters derived from the three groups of chemicals has been carried out in an effort to understand the dimensionality of the structure spaces derived for the three different sets of chemicals and the structural aspects characterized by the various TIs

Can adding Ephedrine to Admixture of Propofol & Lidocaine Overcome Propofol Associated Hemodynamic Changes and Injection Pain?

Purpose: There are numerous studies researching ways to alleviate propofol injection pain. In this study, we evaluated and compared the use of propofol-lidocaine admixture vs propofol-lidocaine combined with ephedrine, on vascular pain and hemodynamic changes associated propofol. Methods: This double-blinded, prospective, randomised study was performed on 100 patients with ASA I-II who were divided into two group. The first received admixture consisting of 20 mg of lidocaine and propofol 1% 20 ml (Group L), and the other received admixture consisting of 20 mcg ephedrine, 20 mg lidocaine and propofol 1% 20 ml (Group LE). Baseline and after induction heart rate, mean arterial pressure and rate pressure product (RPP) were recorded per minute. Vascular pain were evaluated with verbal rating scale. Results: Data of 40 patients in group L and 39 patients in Group LE were evaluated in the study. The incidence of pain in group L was 90%, it was 38.4% for Group LE. Mild pain was observed significantly more in Group L when compared to Group LE (p<0.05). Average blood pressure and RPP immediately after induction and 1 min after intubation were significantly higher in group LE compared to group L (p<0.05). Heart rate was higher in Group LE immediately after induction and at initially 4 minutes after intubation. Conclusion: Our study has demonstrated significant decrease in rate of vascular pain and increased hemodynamic stability in patients receiving 20 mg ephedrine added to 20 ml % 1 propofol and 20 mg lidocaine admixture when compared to those who only received the lidocaine-propofol admixtur

Are the Products of Statistical Learning Abstract or Stimulus-Specific?

Learners can segment potential lexical units from syllable streams when statistically variable transitional probabilities between adjacent syllables are the only cues to word boundaries. Here we examine the nature of the representations that result from statistical learning by assessing learners’ ability to generalize across acoustically different stimuli. In three experiments, we compare two possibilities: that the products of statistical segmentation processes are abstract and generalizable representations, or, alternatively, that products of statistical learning are stimulus-bound and restricted to perceptually similar instances. In Experiment 1, learners segmented units from statistically predictable streams, and recognized these units when they were acoustically transformed by temporal reversals. In Experiment 2, learners were able to segment units from temporally reversed syllable streams, but were only able to generalize in conditions of mild acoustic transformation. In Experiment 3, learners were able to recognize statistically segmented units after a voice change but were unable to do so when the novel voice was mildly distorted. Together these results suggest that representations that result from statistical learning can be abstracted to some degree, but not in all listening conditions

Ultraviolet stability of three-dimensional lattice pure gauge field theories

We prove the ultraviolet stability for three-dimensional lattice gauge field theories. We consider only the Wilson lattice approximation for pure Yang-Mills field theories. The proof is based on results of the previous papers on renormalization group method for lattice gauge theories.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46460/1/220_2005_Article_BF01229380.pd

Calculation of Forces at Focal Adhesions from Elastic Substrate Data: The Effect of Localized Force and the Need for Regularization

AbstractForces exerted by stationary cells have been investigated on the level of single focal adhesions by combining elastic substrates, fluorescence labeling of focal adhesions, and the assumption of localized force when solving the inverse problem of linear elasticity theory. Data simulation confirms that the inverse problem is ill-posed in the presence of noise and shows that in general a regularization scheme is needed to arrive at a reliable force estimate. Spatial and force resolution are restricted by the smoothing action of the elastic kernel, depend on the details of the force and displacement patterns, and are estimated by data simulation. Corrections arising from the spatial distribution of force and from finite substrate size are treated in the framework of a force multipolar expansion. Our method is computationally cheap and could be used to study mechanical activity of cells in real time

An Efficient Algorithm for Enumerating Chordless Cycles and Chordless Paths

A chordless cycle (induced cycle) $C$ of a graph is a cycle without any chord, meaning that there is no edge outside the cycle connecting two vertices of the cycle. A chordless path is defined similarly. In this paper, we consider the problems of enumerating chordless cycles/paths of a given graph $G=(V,E),$ and propose algorithms taking $O(|E|)$ time for each chordless cycle/path. In the existing studies, the problems had not been deeply studied in the theoretical computer science area, and no output polynomial time algorithm has been proposed. Our experiments showed that the computation time of our algorithms is constant per chordless cycle/path for non-dense random graphs and real-world graphs. They also show that the number of chordless cycles is much smaller than the number of cycles. We applied the algorithm to prediction of NMR (Nuclear Magnetic Resonance) spectra, and increased the accuracy of the prediction