Abstract:
A dissipative sandpile model (DSM) is constructed and studied on small world networks (SWN). SWNs are generated adding extra links between two arbitrary sites of a two dimensional square lattice with different shortcut densities $\phi$. Three different regimes are identified as regular lattice (RL) for $\phi\lesssim 2^{-12}$, SWN for $2^{-12}<\phi< 0.1$ and random network (RN) for $\phi\ge 0.1$. In the RL regime, the sandpile dynamics is characterized by usual Bak, Tang, Weisenfeld (BTW) type correlated scaling whereas in the RN regime it is characterized by the mean field (MF) scaling. On SWN, both the scaling behaviors are found to coexist. Small compact avalanches below certain characteristic size $s_c$ are found to belong to the BTW universality class whereas large, sparse avalanches above $s_c$ are found to belong to the MF universality class. A scaling theory for the coexistence of two scaling forms on SWN is developed and numerically verified. Though finite size scaling (FSS) is not valid for DSM on RL as well as on SWN, it is found to be valid on RN for the same model. FSS on RN is appeared to be an outcome of super diffusive sand transport and uncorrelated toppling waves.

Abstract:
In the rotational sandpile model, either the clockwise or the anti-clockwise toppling rule is assigned to all the lattice sites. It has all the features of a stochastic sandpile model but belongs to a different universality class than the Manna class. A crossover from rotational to Manna universality class is studied by constructing a random rotational sandpile model and assigning randomly clockwise and anti-clockwise rotational toppling rules to the lattice sites. The steady state and the respective critical behaviour of the present model are found to have a strong and continuous dependence on the fraction of the lattice sites having the anti-clockwise (or clockwise) rotational toppling rule. As the anti-clockwise and clockwise toppling rules exist in equal proportions, it is found that the model reproduces critical behaviour of the Manna model. It is then further evidence of the existence of the Manna class, in contradiction with some recent observations of the non-existence of the Manna class.

Abstract:
Dr. Patrick Russell, born and brought up in Edinburgh, Scotland, a true product of the Scottish Enlightenment, introduced an original discipline—natural history of serpents—in eighteenth-century British India. He was also indefatigable in his study of Indian botany and ichthyology. Russell‘s brief Indian career, particularly his endeavour in snakology, suggests that the diffusion of modern natural history and knowledge of Western medicine was an intricate process, not confined to any particular epistemological domain. This paper has sought to profile the emergence of Western medical-zoology by individual research, as a constituent of natural history science concerning particularly the snake-poisoning in a colonial empire. The article also critiques the concept of Orientalist‘ strategy to dominate the colonised world through knowledge through European knowledge in India.

Abstract:
At the primary level of reality as described by quantum field theory, a fundamental particle like an electron represents a stable, discrete, propagating excited state of its underlying quantum field. QFT also tells us that the lowest vacuum state as well as the excited states of such a field is always very active with spontaneous, unpredictable quantum fluctuations. Also an underlying quantum field is known to be indestructible and immutable possessing the same value in each element of spacetime comprising the universe. These characteristics of the primary quantum fields together with the fact that the quantum fluctuations can be cogently substantiated to be quantum coherent throughout the universe provide a possible ontology of the quantum theory. In this picture, the wave function of a quantum particle represents the reality of the inherent quantum fluctuations at the core of the universe and endows the particle its counter intuitive quantum behavior.

Abstract:
The intrinsic fluctuations of the underlying, immutable quantum fields that fill all space and time can support the element of reality of a wave function in quantum mechanics. The mysterious non-locality of quantum entanglement may also be understood in terms of these inherent quantum fluctuations, ever-present at the most fundamental level of the universe.

Abstract:
Einstein is considered by many as the father of quantum physics in some sense. Yet there is an unshakable view that he was wrong on quantum physics. Although it may be a subject of considerable debate, the core of his allegedly wrong demurral was the insistence on finding an objective reality underlying the manifestly bizarre behavior of quantum objects. The uncanny wave-particle duality of a quantum particle is a prime example. In view of the latest developments, particularly in quantum field theory, objections of Einstein are substantially corroborated. Careful investigation suggests that a travelling quantum particle is a holistic wave packet consisting of an assemblage of irregular disturbances in quantum fields. It acts as a particle because only the totality of all the disturbances in the wave packet yields the energy momentum with the mass of a particle, along with its other conserved quantities such as charge and spin. Thus the wave function representing a particle is not just a fictitious mathematical construct but embodies a reality of nature as asserted by Einstein.

Abstract:
Let $GO(2n)$ be the general orthogonal group scheme (the group of orthogonal similitudes). In the topological category, Y. Holla and N. Nitsure determined the singular cohomology ring $H^*_{\rm sing}(BGO(2n,\mathbb C),\mathbb F_2)$ of the classifying space $BGO(2n,\mathbb C)$ of the corresponding complex Lie group $GO(2n,\mathbb C)$ in terms of explicit generators and relations. The author of the present note showed that over any algebraically closed field of characteristic not equal to $2$, the smooth-\'etale cohomology ring $H_{\rm sm-\'et}^*(BGO(2n),\mathbb F_2)$ of the classifying algebraic stack $BGO(2n)$ has the same description in terms of generators and relations as the singular cohomology ring $H^*_{\rm sing}(BGO(2n,\mathbb C),\mathbb F_2)$. Totaro defined for any reductive group $G$ over a field, the Chow ring $A^*_G$, which is canonically identified with the ring of characteristic classes in the sense of intersection theory, for principal $G$-bundles, locally trivial in \'etale topology. In this paper, we calculate the Chow group $A^*_{GO(2n)}$ over any field of characteristic different from $2$ in terms of generators and relations.

Abstract:
Let GO(2n) be the general orthogonal group (the group of similitudes) over any algebraically closed field of characteristic not equal to 2. We determine the etale cohomology ring with mod 2 coefficients of the algebraic stack BGO(2n). In the topological category, Y. Holla and N. Nitsure determined the singular cohomology ring of the classifying space BGO(2n) of the complex Lie group GO(2n) in terms of explicit generators and relations. We extend their results to the algebraic category. The chief ingredients in this are (i) an extension to etale cohomology of an idea of Totaro, originally used in the context of Chow groups, which allows us to approximate the classifying stack by quasi projective schemes; and (ii) construction of a Gysin sequence for the G_m fibration BO(2n) to BGO(2n) of algebraic stacks.

Abstract:
Maximum length CA has wide range of applications in design of linear block code, cryptographic primitives and VLSI testing particularly in Built-In-Self-Test. In this paper, an algorithm to compute all $n$-cell maximum length CA-rule vectors is proposed. Also rule vectors for each primitive polynomial in GF(2^2) to GF(2^{12} have been computed by simulation and they have been listed.Programmable rule vectors based maximum length CA can be used to design cryptographic primitives.

Abstract:
The current status of the studies of the origin of the fundamental particles and the universe is presented. These studies indicate the unified field to be the source of both the fundamental particles and the universe itself. Furthermore, as a consequence of the unique properties of the quantum vacuum, the unified field is presumed to exist, in a quantum physical sense, everywhere in the very fabric of spacetime. In an analogy to the characteristics of the human genome, unified field appears to have the basic blueprint of at least everything physical in this universe.