Some Unique Constants Associated with Extremal Black Holes

In recent papers we had developed a unified picture of black hole entropy and curvature which was shown to lead to Hawking radiation. It was shown that for any black hole mass, holography implies a phase space of just one quantum associated with the interior of the black hole. Here we study extremal rotating and charged black holes and obtain unique values for ratios of angular momentum to entropy, charge to entropy, etc. It turns out that these ratios can be expressed in terms of fundamental constants in nature, having analogies with other physical systems, like in condensed matter physics.Comment: "Accepted for publication in Astrophysics & Space Science" 4 pages, 10 equation

Dieterici gas as a Unified Model for Dark Matter and Dark Energy

The dominance of dark energy in the universe has necessitated the introduction of a repulsive gravity source to make q0 negative. The models for dark energy range from a simple lambda-term to quintessence, Chaplygin gas, etc. We look at the possibility of how change of behaviour of missing energy density, from DM to DE, may be determined by the change in the equation of state of a background fluid instead of a form of potential. The question of cosmic acceleration can be discussed within the framework of theories which do not necessarily include scalar fields.Comment: 9 pages, 38 equation

Phase Space Constraints on Neutrino Luminosities

While the importance of phase space constraints for gravitational clustering of neutrinos (which are fermions) is well recognized, the explicit use of such constraints to limit neutrino emission from ultra energetic sources has not been stressed. Special and general relativistic phase space constraints are shown to limit neutrino luminosities in compact sources in various situations.Comment: 13 pages, 20 equation

HODLRddD: A new Black-box fast algorithm for NN-body problems in dd-dimensions with guaranteed error bounds

In this article, we prove new theorems bounding the rank of different sub-matrices arising from these kernel functions. Bounds like these are often useful for analyzing the complexity of various hierarchical matrix algorithms. We also plot the numerical rank growth of different sub-matrices arising out of various kernel functions in $1$D, $2$D, $3$D and $4$D, which, not surprisingly, agrees with the proposed theorems. Another significant contribution of this article is that, using the obtained rank bounds, we also propose a way to extend the notion of \textbf{\emph{weak-admissibility}} for hierarchical matrices in higher dimensions. Based on this proposed \textbf{\emph{weak-admissibility}} condition, we develop a black-box (kernel-independent) fast algorithm for $N$-body problems, hierarchically off-diagonal low-rank matrix in $d$ dimensions (HODLR$d$D), which can perform matrix-vector products with $\mathcal{O}(pN \log (N))$ complexity in any dimension $d$, where $p$ doesn't grow with any power of $N$. More precisely, our theorems guarantee that $p \in \mathcal{O} (\log (N) \log^d (\log (N)))$, which implies our HODLR$d$D algorithm scales almost linearly. The $\texttt{C++}$ implementation with \texttt{OpenMP} parallelization of the HODLR$d$D is available at \url{https://github.com/SAFRAN-LAB/HODLRdD}. We also discuss the scalability of the HODLR$d$D algorithm and showcase the applicability by solving an integral equation in $4$ dimensions and accelerating the training phase of the support vector machines (SVM) for the data sets with four and five features.Comment: 35 pages, 23 figures, 14 table

Clinical and electrophysiological indices as predictors of fertility in males with spinal cord injury; Experience from a tertiary care hospital in South India

OBJECTIVE: Prospective observational pilot study to assess the fertility spinal cord injured males (SCI) using penile vibrator and to predict the response to PVS using clinical tests and electrophysiological tests. MATERIALS AND METHODS: Paraplegic males, duration > 6 months, T6 or below AIS A were included. Assessment of (i) clinical reflexes → bulbocavernosus response (BCR), hip flexor response (HFR), cremasteric reflex and superficial abdominal reflexes. (ii) somatic responses → abdominal contraction, hip adduction during stimulation. (iii) electrophysiological responses →H reflex from Soleus and F wave from tibial nerve. (iv) Response to PVS. Specificity and sensitivity for Bulbocavernosus reflex (BCR) → 90% (CI = 10%). Total sample size was calculated as 72 (36 → BCR +ve & 36 → BCR -ve). • Statistical analysis → Pearson chi square & Fischers exact test. RESULTS: Among the 23 patients recruited, seven had successful ejaculation with Penile Vibratory Stimulation (responders). All persons with T6-T8 neurological level of injury (n=4) and three among persons with neurological level T9 - T12 (n=19) were responders. Among these seven patients, 6 patients had somatic responses during stimulation, whereas, two of the responders showed correlation with electrophysiological tests. CONCLUSION : Level of injury is a predictor of fertility using PVS in males with spinal cord injury

Multimodality Imaging Training for General and Advanced Cardiology Fellowships

With the growth in multimodality imaging technology, there is heightened interest in advanced imaging training within the cardiology fellow community. The ideal training models for multimodality imaging remain to be determined and there are uncertainties about the manpower needs for cardiologists with advanced multimodality imaging expertise. This commentary discusses several areas pertaining to training of cardiology fellows in multimodality imaging

Bioencapsulation strategy and highly unsaturated fatty acids (HUFA) enrichment in Artemia franciscana nauplii by using marine trash fish Odonus niger liver oil

To investigate the maximum accumulation of highly unsaturated fatty acids (HUFA) in Artemia franciscana nauplii through bioencapsulation process, five different concentrations (0 - 4%) of emulsified Odonus niger liver oil were prepared. The prepared emulsions were used to enrich A. franciscana at different time intervals of 6, 12, 18 and 24 h. After the enrichment period, the fatty acid composition of the nauplii were analysed and estimated individually along with freshly hatched A.franciscana and O. niger liver oil. The HUFA content such as linoleic (18: 2n-6), linolenic (18: 3n-3), arachidonic (20: 4n-3 + n-6), eicosapentaenoic (20: 5-n3) and docosahexaenoic (22: 6n-3) acids were 12.87, 0.21, 2.66, 2.86 and 2.30% dry weight (DW), respectively, in O. niger liver oil, and 8.60, 17.20, 1.80, 2.40 and 0.1% DW, respectively, in freshly hatched A. franciscana. During 6 – 24 h of enrichment period, all the above HUFA increased considerably from 8.76 to 10.84, 17.24 to 23.84, 1.16 to 3.98, 2.45 to 5.88 and 0.30 to 2.69% DW, respectively. The increase in the level of individual HUFA of A. franciscana enriched with various concentrations of emulsified liver oil at different time durations showed a positive linear relationship and the correlation coefficient obtained were statistically significant (P< 0.05)