Heat Kernels on the AdS(2) cone and Logarithmic Corrections to Extremal Black Hole Entropy

We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the logarithmic contribution to black hole entropy from an N=4 vector multiplet about a Z(N) orbifold of the near-horizon geometry of quarter--BPS black holes in N=4 supergravity. We find that this vanishes, matching perfectly with the prediction from the microstate counting. We also discuss possible generalisations of our heat kernel results to higher-spin fields over Z(N) orbifolds of higher-dimensional spheres and hyperboloids.Comment: 41 page

Logarithmic Corrections to Extremal Black Hole Entropy in N = 2, 4 and 8 Supergravity

We compute the logarithmic correction to black hole entropy about exponentially suppressed saddle points of the Quantum Entropy Function corresponding to Z(N) orbifolds of the near horizon geometry of the extremal black hole under study. By carefully accounting for zero mode contributions we show that the logarithmic contributions for quarter--BPS black holes in N=4 supergravity and one--eighth BPS black holes in N=8 supergravity perfectly match with the prediction from the microstate counting. We also find that the logarithmic contribution for half--BPS black holes in N = 2 supergravity depends non-trivially on the Z(N) orbifold. Our analysis draws heavily on the results we had previously obtained for heat kernel coefficients on Z(N) orbifolds of spheres and hyperboloids in arXiv:1311.6286 and we also propose a generalization of the Plancherel formula to Z(N) orbifolds of hyperboloids to an expression involving the Harish-Chandra character of SL(2,R), a result which is of possible mathematical interest.Comment: 40 page

Performance Evaluation and Validation of Intelligent Security Mechanism in Software Defined Network

Network attacks are discovered using intrusion detection systems (IDS), one of the most crucial security solutions. Machine learning techniques-based intrusion detection approaches have been rapidly created as a result of the widespread use of standard machine learning algorithms in the security field. Unfortunately, as technology has advanced and there have been faults in the machine learning-based intrusion detection system, the system has consistently failed to fulfill the standards for cyber security. Generative adversarial networks (GANs) have drawn a lot of interest recently and have been utilized widely in anomaly detection due to their enormous capacity for learning difficult high-dimensional real time data distribution. Traditional machine learning algorithms for intrusion detection have a number of drawbacks that deep learning techniques can significantly mitigate. With the help of a real time dataset, this work suggests employing GANs and its variants to detect network intrusions in SDN. The feasibility and comparison results are also presented. For different kinds of datasets, the BiGAN outcomes outperform the GAN

DESIGNING AND OPTIMIZATION OF NAPROXEN SODIUM DEFORMABLE VESICULAR SYSTEMS THROUGH FACTORIAL DESIGN: BOX BEHENKEN MODEL

Objective: The objective of this investigation was to develop and statistically optimize deformable vesicles such as transfersomes and transethosomes of Naproxen sodium by employing 33factorial designs through software Design expert version 12 (Box–Behnken design) for dermal delivery. Methods: The levels of the drug, phosphatidylcholine, and span 80 (independent variables) were varied to study the influence on vesicle size and % entrapment efficiency (dependent variables) of transfersomes and for transethosomes, the levels of phosphatidylcholine, ethanol, and span 80 were selected as independent variables Second-order quadratic polynomial equation, 2D and 3D contour plots represented the relationship between variables and desired response. The optimization process was carried out using desirability plots and point prediction techniques. Results: Results of the present study demonstrated that optimized transfersomes and transethosomes showed vesicle sizes of 114.91 nm and 102.91 nm respectively, while entrapment efficiency of 80.11 % and 86.97%, respectively. Both formulations showed high zeta potential values indicating the stability of the optimized formulation. ANOVA statistical results showed a significant difference (P<0.05). Conclusion: The results indicated that the independent variable plays a crucial role in optimizing a formulation that can be used for further research studies. Present preliminary study data provided strong evidence that the optimized deformable vesicular formulations through box Behnken factorial design can be a potentially useful drug carrier for naproxen sodium dermal delivery with minimum vesicle size and efficient entrapment efficiency

Logarithmic Corrections to Twisted Indices from the Quantum Entropy Function

We compute logarithmic corrections to the twisted index $B^g_6$ in four-dimensional $\mathcal{N}=4$ and $\mathcal{N}=8$ string theories using the framework of the Quantum Entropy Function. We find that these vanish, matching perfectly with the large--charge expansion of the corresponding microscopic expressions.Comment: v2 : 22 pages, presentation significantly improved, published in JHE

STRUCTURE AND TEXTURE SYNTHESIS

An approach for filling-in blocks of missing data in wireless image transmission is presented in this paper. When compression algorithms such as JPEG are used as part of the wireless transmission process, images are first tiled into blocks of 8x8 pixels. When such images are transmitted over fading channels, the effects of noise can destroy entire blocks of the image. Instead of using common retransmission query protocols, we aim to reconstruct the lost data using correlation between the lost block and its neighbours. If the lost block contained structure, it is reconstructed using an image inpainting algorithm, while texture synthesis is used for the textured blocks. The switch between the two schemes is done in a fully automatic fashion based on the surrounding available blocks. The performance of this method is tested for various images and combinations of lost blocks

Timing feedback-inhibition of the male reproductive hormone axis

Hormonal methods of male contraception have addressed feedback-inhbition of the cascade of hormones that has evolved to regulate sperm production but high concentrations of testosterone (T) in the blood have not worked satisfactorily. We hypothesized that an episodic event, such as degranulation of gonadotropin-releasing hormone (GnRH) neurons in the hypothalamus, could be as well inhibited by episodic interference as by continuously-applied suppression. We used a computational model of hypothalamus-pituitary-gonad axis described by Veldhuis et al. to test the hypothesis that episodic administration of T would inhibit GnRH and/or luteinizing hormone (LH) secretion. A set of stochastic differential equations model feedback as well as feed-forward actions of GnRH, LH and T. The model predicted feedback-inhibition of GnRH pulses in a dose and frequency dependent manner when transdermal patches or injections delivering pulsatile T were applied. Since the published model did not address the effect of chronic GnRH deprivation on the viability of pituitary gonadotrophes, we introduced a function to address this issue. Incorporation of this function in the model allowed the prediction of a “holiday period” in the contraceptive regimen, during which exogenous T would not be needed to protect from conception. Pulsatile T delivered by real-life transdermal delivery system applied as per a parsimonious regimen reduced secretion of LH and T and fertility. The vitality function, proposed to account for survival and proliferation of pituitary gonadotrophes correlated with in vivo observations as extensive apoptosis in the anterior pituitary was observed after application of transdermal T

Thanatophoric dysplasia, an enigmatic dilemma: a case report

Thanatophoric dysplasia is a rare, fatal form of skeletal dysplasia that affects fetus in utero. It is characterized by marked underdevelopment of fetal skeleton and short limbs. This disorder can be diagnosed antenatally and the couple should be counselled for termination of pregnancy. 20 years old female came in her second trimester carrying an ultrasound report which showed features of thanatophoric dwarfism. She was advised to terminate her pregnancy but she decided to continue with her pregnancy. She was induced after 40 weeks and she delivered a stillborn baby with dwarf like features, a condition identified as thanatophoric dwarfism. Early diagnosis can be done by ultrasound as early as 13 weeks of gestation and since babies born with thanatophoric dysplasia have a very poor prognosis, couples should be counselled regarding early termination of pregnancy. 3D ultrasound scan and molecular analysis can also help identify this disorder