Spiritual Concern in the Works of Manoj Das

My aim through this article is to discuss the issue of spirituality in Manoj Das’s works which can be seen in many forms and ideas in his exquisite narration. He narrates an Indian experience in language which is alien or not Indian at the same time. He does not loose original Indian charm and ethos. In his works he shows his deep concern with spirituality. In his works spirituality is not a figment of imagination or a religious dogma or any firm ideology but it is a domain of realization where we realize (experience) values like truth, goodness, beauty, love, compassion, and also intuition, creativity, insight and focused attention in all walks of life. When he begins his concern with spirituality, he talks about “Soul’”. For him soul- a point of non-material energy, eternal in form and identity. The soul is not subject to change as is the body

Two component WIMP-FImP dark matter model with singlet fermion, scalar and pseudo scalar

We explore a two component dark matter model with a fermion and a scalar. In this scenario the Standard Model (SM) is extended by a fermion, a scalar and an additional pseudo scalar. The fermionic component is assumed to have a global ${\rm U(1)}_{\rm DM}$ and interacts with the pseudo scalar via Yukawa interaction while a $\mathbb{Z}_2$ symmetry is imposed on the other component -- the scalar. These ensure the stability of both the dark matter components. Although the Lagrangian of the present model is CP conserving, however the CP symmetry breaks spontaneously when the pseudo scalar acquires a vacuum expectation value (VEV). The scalar component of the dark matter in the present model also develops a VEV on spontaneous breaking of the $\mathbb{Z}_2$ symmetry. Thus the various interactions of the dark sector and the SM sector are progressed through the mixing of the SM like Higgs boson, the pseudo scalar Higgs like boson and the singlet scalar boson. We show that the observed gamma ray excess from the Galactic Centre, self-interaction of dark matter from colliding clusters as well as the 3.55 keV X-ray line from Perseus, Andromeda etc. can be simultaneously explained in the present two component dark matter model.Comment: 35 pages, 5 figure

Probing the spatial and velocity anisotropies in stellar halos from the Aquarius simulations

We analyze the spatial anisotropy and the velocity anisotropy in a set of mock stellar halos from the Aquarius simulations. The spatial anisotropy in each mock stellar halo rises progressively with the increasing distance from the halo centre, eventually reaching a maximum near the periphery. Excluding the bound satellites leads to a significant reduction of the spatial anisotropy in each halo. We compare the measured anisotropy in the mock stellar halos with that from their sphericalized versions where all the shape and substructure induced anisotropies are erased. The growth of spatial anisotropy persists throughout the entire halo when the bound satellites are present but remains limited within the inner halo ($<60 \, h^{-1}\, {\rm kpc}$) after their exclusion. This indicates that the spatial anisotropy in the inner halo is induced by the diffuse substructures and the halo shape whereas the outer halo anisotropy is dominated by the bound satellites. We find that the outer parts of the stellar halo are kinematically colder than the inner regions. The stellar orbits are predominantly radial but they become rotationally dominated at certain radii that are marked by the prominent $\beta$ dips. Most of the $\beta$ dips disappear after the removal of the satellites. A few shallow and broad $\beta$ dips arise occasionally due to the presence of diffuse streams and clouds. Our analysis suggests that a combined study of the spatial and velocity anisotropies can reveal the structure and the assembly history of the stellar halos.Comment: 15 pages, 9 figures, comments welcom

Algebraic Independence over Positive Characteristic: New Criterion and Applications to Locally Low Algebraic Rank Circuits

The motivation for this work comes from two problems--test algebraic independence of arithmetic circuits over a field of small characteristic, and generalize the structural property of algebraic dependence used by (Kumar, Saraf CCC\u2716) to arbitrary fields. It is known that in the case of zero, or large characteristic, using a classical criterion based on the Jacobian, we get a randomized poly-time algorithm to test algebraic independence. Over small characteristic, the Jacobian criterion fails and there is no subexponential time algorithm known. This problem could well be conjectured to be in RP, but the current best algorithm puts it in NP^#P (Mittmann, Saxena, Scheiblechner Trans.AMS\u2714). Currently, even the case of two bivariate circuits over F_2 is open. We come up with a natural generalization of Jacobian criterion, that works over all characteristic. The new criterion is efficient if the underlying inseparable degree is promised to be a constant. This is a modest step towards the open question of fast independence testing, over finite fields, posed in (Dvir, Gabizon, Wigderson FOCS\u2707). In a set of linearly dependent polynomials, any polynomial can be written as a linear combination of the polynomials forming a basis. The analogous property for algebraic dependence is false, but a property approximately in that spirit is named as ``functional dependence\u27\u27 in (Kumar, Saraf CCC\u2716) and proved for zero or large characteristic. We show that functional dependence holds for arbitrary fields, thereby answering the open questions in (Kumar, Saraf CCC\u2716). Following them we use the functional dependence lemma to prove the first exponential lower bound for locally low algebraic rank circuits for arbitrary fields (a model that strongly generalizes homogeneous depth-4 circuits). We also recover their quasipoly-time hitting-set for such models, for fields of characteristic smaller than the ones known before. Our results show that approximate functional dependence is indeed a more fundamental concept than the Jacobian as it is field independent. We achieve the former by first picking a ``good\u27\u27 transcendence basis, then translating the circuits by new variables, and finally approximating them by truncating higher degree monomials. We give a tight analysis of the ``degree\u27\u27 of approximation needed in the criterion. To get the locally low algebraic rank circuit applications we follow the known shifted partial derivative based methods