Tridiagonalized GUE matrices are a matrix model for labeled mobiles

It is well-known that the number of planar maps with prescribed vertex degree distribution and suitable labeling can be represented as the leading coefficient of the $\frac{1}{N}$-expansion of a joint cumulant of traces of powers of an $N$-by-$N$ GUE matrix. Here we undertake the calculation of this leading coefficient in a different way. Firstly, we tridiagonalize the GUE matrix in the manner of Trotter and Dumitriu-Edelman and then alter it by conjugation to make the subdiagonal identically equal to $1$. Secondly, we apply the cluster expansion technique (specifically, the Brydges-Kennedy-Abdesselam-Rivasseau formula) from rigorous statistical mechanics. Thirdly, by sorting through the terms of the expansion thus generated we arrive at an alternate interpretation for the leading coefficient related to factorizations of the long cycle $(12\cdots n)\in S_n$. Finally, we reconcile the group-theoretical objects emerging from our calculation with the labeled mobiles of Bouttier-Di Francesco-Guitter.Comment: 42 pages, LaTeX, 17 figures. The present paper completely supercedes arXiv1203.3185 in terms of methods but addresses a different proble

Feshbach-Villars oscillator (FVO) in Kaluza-Klein Theory (KKT)

This research investigates the relativistic quantum dynamics of spin-0 scalar massive charged particles via the relativistic Feshbach-Villars oscillator in the background of the Kaluza-Klein Theory. We solve the Feshbach-Villars equation in the abckground of a cosmic string spec-time in the context of the Kaluza-Klein and presented the eigenvalue solution. Afterward, we rewrite this system in the case of the Feshbach-Villars quantum oscillator and obtain the eigenvalue analytically. Finally, we study the interaction of the Feshbach-Villars equation and oscillator in a cosmic dislocation in the Som-Raychaudhuri in the context of the Kaluza-Klein Theory and solve the wave equation analytically. We analyze the influence of topological defect in the quantification of energy and wave function of the Feshbach-Villars oscillator and with the external fields in the last oneComment: arXiv admin note: text overlap with arXiv:2304.12496 (Accepted for publication In Nuclear Physics B

The role of the lateral prefrontal cortex and anterior cingulate in stimulus–response association reversals

Many complex tasks require us to flexibly switch between behavioral rules, associations, and strategies. The prefrontal cerebral cortex is thought to be critical to the performance of such behaviors, although the relative contribution of different components of this structure and associated subcortical regions are not fully understood. We used functional magnetic resonance imaging to measure brain activity during a simple task which required repeated reversals of a rule linking a colored cue and a left/right motor response. Each trial comprised three discrete events separated by variable delay periods. A colored cue instructed which response was to be executed, followed by a go signal which told the subject to execute the response and a feedback instruction which indicated whether to ‘‘hold’’ or ‘‘f lip’’ the rule linking the colored cue and response. The design allowed us to determine which brain regions were recruited by the specific demands of preparing a rule contingent motor response, executing such a response, evaluating the significance of the feedback, and reconfiguring stimulus–response (SR) associations. The results indicate that an increase in neural activity occurs within the anterior cingulate gyrus under conditions in which SR associations are labile. In contrast, lateral frontal regions are activated by unlikely/unexpected perceptual events regardless of their significance for behavior. A network of subcortical structures, including the mediodorsal nucleus of the thalamus and striatum were the only regions showing activity that was exclusively correlated with the neurocognitive demands of reversing SR associations. We conclude that lateral frontal regions act to evaluate the behavioral significance of perceptual events, whereas medial frontal–thalamic circuits are involved in monitoring and reconfiguring SR associations when necessary

Generalized Plasmonic Modelling of the Effect of Refractive Index on Laser-Induced Periodic Nanostructures

Laser-induced periodic surface structures (LIPSS) have been studied theoretically employing generalized plasmonic modelling on several dielectric materials such as SiO2, Al2O3, ZnO, AlAs and diamond exposed to 800 nm wavelength multi-pulse femtosecond laser irradiation. The study of the optical properties of the materials during laser irradiation reveals a formation of a metallic like pseudo-material on the irradiated layer during excitation. A study of the grating periodicity of the nanostructures shows that the materials having a high refraction index allow LIPSS formation with a wide range of grating periodicities. Results also show High Spatial Frequency LIPSS formation with periodicities 3 to 8 times lower than the laser wavelength

Parametric Representation of Noncommutative Field Theory

In this paper we investigate the Schwinger parametric representation for the Feynman amplitudes of the recently discovered renormalizable $\phi^4_4$ quantum field theory on the Moyal non commutative ${\mathbb R^4}$ space. This representation involves new {\it hyperbolic} polynomials which are the non-commutative analogs of the usual "Kirchoff" or "Symanzik" polynomials of commutative field theory, but contain richer topological information.Comment: 31 pages,10 figure

Non-semisimple Lie algebras with Levi factor \frak{so}(3), \frak{sl}(2,R) and their invariants

We analyze the number N of functionally independent generalized Casimir invariants for non-semisimple Lie algebras \frak{s}\overrightarrow{% oplus}_{R}\frak{r} with Levi factors isomorphic to \frak{so}(3) and \frak{sl}(2,R) in dependence of the pair (R,\frak{r}) formed by a representation R of \frak{s} and a solvable Lie algebra \frak{r}. We show that for any dimension n >= 6 there exist Lie algebras \frak{s}\overrightarrow{\oplus}_{R}\frak{r} with non-trivial Levi decomposition such that N(\frak{s}% \overrightarrow{oplus}_{R}\frak{r}) = 0.Comment: 16 page

A Physicist's Proof of the Lagrange-Good Multivariable Inversion Formula

We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.Comment: 9 pages, 3 diagram

Casimir invariants for the complete family of quasi-simple orthogonal algebras

A complete choice of generators of the center of the enveloping algebras of real quasi-simple Lie algebras of orthogonal type, for arbitrary dimension, is obtained in a unified setting. The results simultaneously include the well known polynomial invariants of the pseudo-orthogonal algebras $so(p,q)$, as well as the Casimirs for many non-simple algebras such as the inhomogeneous $iso(p,q)$, the Newton-Hooke and Galilei type, etc., which are obtained by contraction(s) starting from the simple algebras $so(p,q)$. The dimension of the center of the enveloping algebra of a quasi-simple orthogonal algebra turns out to be the same as for the simple $so(p,q)$ algebras from which they come by contraction. The structure of the higher order invariants is given in a convenient "pyramidal" manner, in terms of certain sets of "Pauli-Lubanski" elements in the enveloping algebras. As an example showing this approach at work, the scheme is applied to recovering the Casimirs for the (3+1) kinematical algebras. Some prospects on the relevance of these results for the study of expansions are also given.Comment: 19 pages, LaTe

The neural correlates of working memory training in typically developing children.

Working memory training improves children's cognitive performance on untrained tasks; however, little is known about the underlying neural mechanisms. This was investigated in 32 typically developing children aged 10-14 years (19 girls and 13 boys) using a randomized controlled design and multi-modal magnetic resonance imaging (Devon, UK; 2015-2016). Training improved working memory performance and increased intrinsic functional connectivity between the bilateral intraparietal sulci. Furthermore, improvements in working memory were associated with greater recruitment of the left middle frontal gyrus on a complex span task. Repeated engagement of fronto-parietal regions during training may increase their activity and functional connectivity over time, affording greater working memory performance. The plausibility of generalizable cognitive benefits from a neurobiological perspective and implications for neurodevelopmental theory are discussed

A solitary primary subcutaneous hydatid cyst in the abdominal wall of a 70-year-old woman: a case report

<p>Abstract</p> <p>Introduction</p> <p>A solitary primary hydatid cyst in the subcutaneous abdominal wall is an exceptional entity, even in countries where the <it>Echinococcus </it>infestation is endemic.</p> <p>Case presentation</p> <p>We report a case of a 70-year-old Caucasian woman who presented to our hospital with a subcutaneous mass in the para-umbilical area with a non-specific clinical presentation. The diagnosis of subcutaneous hydatid cyst was suspected on the basis of radiological findings. A complete surgical resection of the mass was performed and the patient had an uneventful post-operative recovery. The histopathology confirmed the suspected diagnosis.</p> <p>Conclusion</p> <p>Hydatid cyst should be considered in the differential diagnosis of every subcutaneous cystic mass, especially in regions where the disease is endemic. The best treatment is the total excision of the cyst with an intact wall.</p