STDP-driven networks and the \emph{C. elegans} neuronal network

We study the dynamics of the structure of a formal neural network wherein the strengths of the synapses are governed by spike-timing-dependent plasticity (STDP). For properly chosen input signals, there exists a steady state with a residual network. We compare the motif profile of such a network with that of a real neural network of \emph{C. elegans} and identify robust qualitative similarities. In particular, our extensive numerical simulations show that this STDP-driven resulting network is robust under variations of the model parameters.Comment: 16 pages, 14 figure

Cerenkov radiation by neutrinos in a supernova core

Neutrinos with a magnetic dipole moment propagating in a medium with a velocity larger than the phase velocity of light emit photons by the Cerenkov process. The Cerenkov radiation is a helicity flip process via which a left-handed neutrino in a supernova core may change into a sterile right-handed one and freestream out of the core. Assuming that the luminosity of the sterile right-handed neutrinos is less than 10^{53} ergs/sec gives an upper bound on the neutrino magnetic dipole moment \mu_\nu < 0.5 \times 10^{-13} \mu_B. This is two orders of magnitude more stringent than the previously established bounds on \mu_\nu from considerations of supernova cooling rate by right-handed neutrinos

Exploring Foundations of Time-Independent Density Functional Theory for Excited-States

Based on the work of Gorling and that of Levy and Nagy, density-functional formalism for many Fermionic excited-states is explored through a careful and rigorous analysis of the excited-state density to external potential mapping. It is shown that the knowledge of the ground-state density is a must to fix the mapping from an excited-state density to the external potential. This is the excited-state counterpart of the Hohenberg-Kohn theorem, where instead of the ground-state density the density of the excited-state gives the true many-body wavefunctions of the system. Further, the excited-state Kohn-Sham system is defined by comparing it's non-interacting kinetic energy with the true kinetic energy. The theory is demonstrated by studying a large number of atomic systems.Comment: submitted to J. Chem. Phy

The young cluster NGC 2282 : a multi-wavelength perspective

We present the analysis of the stellar content of NGC~2282, a young cluster in the Monoceros constellation, using deep optical $BVI$ and IPHAS photometry along with infrared (IR) data from UKIDSS and $Spitzer$-IRAC. Based on the stellar surface density analysis using nearest neighborhood method, the radius of the cluster is estimated as $\sim$ 3.15\arcmin. From optical spectroscopic analysis of 8 bright sources, we have classified three early B-type members in the cluster, which includes, HD 289120, a previously known B2V type star, a Herbig Ae/Be star (B0.5 Ve) and a B5 V star. From spectrophotometric analyses, the distance to the cluster has been estimated as $\sim$ 1.65 kpc. The $K$-band extinction map is estimated using nearest neighborhood technique, and the mean extinction within the cluster area is found to be A$_V$ $\sim$ 3.9 mag. Using IR colour-colour criteria and H$_\alpha$-emission properties, we have identified a total of 152 candidate young stellar objects (YSOs) in the region, of which, 75 are classified as Class II, 9 are Class I YSOs. Our YSO catalog also includes 50 H$_\alpha$-emission line sources, identified using slitless spectroscopy and IPHAS photometry data. Based on the optical and near-IR colour-magnitude diagram analyses, the cluster age has been estimated to be in the range of 2 $-$ 5 Myr, which is in agreement with the estimated age from disc fraction ($\sim$ 58\%). Masses of these YSOs are found to be $\sim$ 0.1$-$2.0 M$_\odot$. Spatial distribution of the candidate YSOs shows spherical morphology, more or less similar to the surface density map.Comment: 16 pages, 19 Figure