Zeta function regularization for a scalar field in a compact domain

We express the zeta function associated to the Laplacian operator on $S^1_r\times M$ in terms of the zeta function associated to the Laplacian on $M$, where $M$ is a compact connected Riemannian manifold. This gives formulas for the partition function of the associated physical model at low and high temperature for any compact domain $M$. Furthermore, we provide an exact formula for the zeta function at any value of $r$ when $M$ is a $D$-dimensional box or a $D$-dimensional torus; this allows a rigorous calculation of the zeta invariants and the analysis of the main thermodynamic functions associated to the physical models at finite temperature.Comment: 19 pages, no figures, to appear in J. Phys.

Spectral analysis and zeta determinant on the deformed spheres

We consider a class of singular Riemannian manifolds, the deformed spheres $S^N_k$, defined as the classical spheres with a one parameter family $g[k]$ of singular Riemannian structures, that reduces for $k=1$ to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian $\Delta_{S^N_k}$, we study the associated zeta functions $\zeta(s,\Delta_{S^N_k})$. We introduce a general method to deal with some classes of simple and double abstract zeta functions, generalizing the ones appearing in $\zeta(s,\Delta_{S^N_k})$. An application of this method allows to obtain the main zeta invariants for these zeta functions in all dimensions, and in particular $\zeta(0,\Delta_{S^N_k})$ and $\zeta'(0,\Delta_{S^N_k})$. We give explicit formulas for the zeta regularized determinant in the low dimensional cases, $N=2,3$, thus generalizing a result of Dowker \cite{Dow1}, and we compute the first coefficients in the expansion of these determinants in powers of the deformation parameter $k$.Comment: 1 figur

Effect of eye lateralization on contralateral suppression of transient evoked otoacoustic emissions

Several studies have previously demonstrated that postural changes modify evoked otoacoustic emission. In order to evaluate a possible interaction between eye muscles and ciliated cells in the inner ear, we studied the effects of eye lateralization on the contralateral suppression of transient evoked otoacoustic emissions (TEOAEs). Thirty-eight normal hearing subjects with TEOAEs were recruited. Their TEAOEs at threshold level were recorded with contralateral suppression (white noise) via straight ahead fixation and right or left lateral fixation. Eye lateralization in the same direction of the white noise significantly decreased the suppression at 4 kHz (p = 0.003). The signal-to-noise ratio in the suppression condition with straight ahead was 1.54 (± 4.610) dB, while the ratio was 3.48 (± 4.631) dB in the suppression condition with gaze toward the white noise. Eye lateralization seems to reduce the contralateral suppression effect of TEOAEs at 4 kHz. However, further studies are necessary to investigate the possible mechanisms of this phenomenon

Multiple Layers of CDK5R1 Regulation in Alzheimer’s Disease Implicate Long Non-Coding RNAs

Cyclin-dependent kinase 5 regulatory subunit 1 (CDK5R1) gene encodes for p35, the main activator of Cyclin-dependent kinase 5 (CDK5). The active p35/CDK5 complex is involved in numerous aspects of brain development and function, and its deregulation is closely associated to Alzheimer\u2019s disease (AD) onset and progression. We recently showed that miR-15/107 family can negatively regulate CDK5R1 expression modifying mRNA stability. Interestingly, miRNAs belonging to miR-15/107 family are downregulated in AD brain while CDK5R1 is upregulated. Long non-coding RNAs (lncRNAs) are emerging as master regulators of gene expression, including miRNAs, and their dysregulation has been implicated in the pathogenesis of AD. Here, we evaluated the existence of an additional layer of CDK5R1 expression regulation provided by lncRNAs. In particular, we focused on three lncRNAs potentially regulating CDK5R1 expression levels, based on existing data: NEAT1, HOTAIR, and MALAT1. We demonstrated that NEAT1 and HOTAIR negatively regulate CDK5R1 mRNA levels, while MALAT1 has a positive effect. We also showed that all three lncRNAs positively control miR-15/107 family of miRNAs. Moreover, we evaluated the expression of NEAT1, HOTAIR, and MALAT1 in AD and control brain tissues. Interestingly, NEAT1 displayed increased expression levels in temporal cortex and hippocampus of AD patients. Interestingly, we observed a strong positive correlation between CDK5R1 and NEAT1 expression levels in brain tissues, suggesting a possible neuroprotective role of NEAT1 in AD to compensate for increased CDK5R1 levels. Overall, our work provides evidence of another level of CDK5R1 expression regulation mediated by lncRNAs and points to NEAT1 as a biomarker, as well as a potential pharmacological target for AD therapy

Irregular singularities in Liouville theory

Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to representations of the Virasoro algebra in which a subset of the annihilation part of the algebra act diagonally. In this paper we define natural bases for the space of conformal blocks in the presence of irregular singularities, describe how to calculate their series expansions, and how such conformal blocks can be constructed by some delicate limiting procedure from ordinary conformal blocks. This leads us to a proposal for the structure functions appearing in the decomposition of physical correlation functions with irregular singularities into conformal blocks. Taken together, we get a precise prediction for the partition functions of some Argyres-Douglas type theories on the four-sphere.Comment: 84 pages, 6 figure

Ultra-high-field targeted imaging of focal cortical dysplasia: The intracortical black line sign in type IIB

BACKGROUND AND PURPOSE: Conventional MR imaging has limitations in detecting focal cortical dysplasia. We assessed the added value of 7T in patients with histologically proved focal cortical dysplasia to highlight correlations between neuropathology and ultra-high-field imaging. MATERIALS AND METHODS: Between 2013 and 2019, we performed a standardized 7T MR imaging protocol in patients with drug-resistant focal epilepsy. We focused on 12 patients in whom postsurgical histopathology revealed focal cortical dysplasia and explored the diagnostic yield of preoperative 7T versus 1.5/3T MR imaging and the correlations of imaging findings with histopathology. We also assessed the relationship between epilepsy surgery outcome and the completeness of surgical removal of the MR imaging-visible structural abnormality. RESULTS: We observed clear abnormalities in 10/12 patients using 7T versus 9/12 revealed by 1.5/3T MR imaging. In patients with focal cortical dysplasia I, 7T MR imaging did not disclose morphologic abnormalities (n = 0/2). In patients with focal cortical dysplasia II, 7T uncovered morphologic signs that were not visible on clinical imaging in 1 patient with focal cortical dysplasia IIa (n = 1/4) and in all those with focal cortical dysplasia IIb (n = 6/6). T2*WI provided the highest added value, disclosing a peculiar intracortical hypointense band (black line) in 5/6 patients with focal cortical dysplasia IIb. The complete removal of the black line was associated with good postsurgical outcome (n = 4/5), while its incomplete removal yielded unsatisfactory results (n = 1/5). CONCLUSIONS: The high sensitivity of 7T T2*-weighted images provides an additional tool in defining potential morphologic markers of high epileptogenicity within the dysplastic tissue of focal cortical dysplasia IIb and will likely help to more precisely plan epilepsy surgery and explain surgical failures

Black hole determinants and quasinormal modes

We derive an expression for functional determinants in thermal spacetimes as a product over the corresponding quasinormal modes. As simple applications we give efficient computations of scalar determinants in thermal AdS, BTZ black hole and de Sitter spacetimes. We emphasize the conceptual utility of our formula for discussing `1/N' corrections to strongly coupled field theories via the holographic correspondence.Comment: 28 pages. v2: slightly improved exposition, references adde