Group fission in Nilgiri langurs (Presbytis johnii)

During a field study on habituated groups of wild Nilgiri langurs (Presbytis johnii), four cases of group fission were observed which differed markedly from group changes reported in other species of the same genus. All fissions occurred in groups with more than one mature male and roughly coincided with the onset of loud call vocalization by the second mature male group member. As a result of the fission the founder group factions acquired the structure of a onemale group. The filial factions consisted of both mature males and females and occupied, at least temporarily, a part of, or an area adjacent to, the founder group. During fission, the amount of aggressive interactions between the two mature males increased. However, the majority of agonistic interactions involved ritualized threat and intimidation behavior without physical aggression. In at least three cases the two mature males involved in the fission had not joined recently but had lived in these groups for three years or more. Although the presence of all male bands and single males in the two study populations indicate that male replacement by invasive takeovers may occur, it is suggested that in Nilgiri langurs, noninvasive fissions are probably another common mechanism for the foundation and maintenance of bisexual one-male groups.

On the achievable rates of sources having a group alphabet in a distributed source coding setting

We consider the problem of compression via homomorphic encoding of a source having a group alphabet. This is motivated by the problem of distributed function computation, where it is known that if one is only interested in computing a function of several sources, then one can at times improve upon the compression rate required by the Slepian-Wolf bound. The functions of interest are those which could be represented by the binary operation in the group. We first consider the case when the source alphabet is the cyclic Abelian group, Zpr. In this scenario, we show that the set of achievable rates provided by Krithivasan and Pradhan [1], is indeed the best possible. In addition to that, we provide a simpler proof of their achievability result. In the case of a general Abelian group, an improved achievable rate region is presented than what was obtained by Krithivasan and Pradhan. We then consider the case when the source alphabet is a non-Abelian group. We show that if all the source symbols have non-zero probability and the center of the group is trivial, then it is impossible to compress such a source if one employs a homomorphic encoder. Finally, we present certain non-homomorphic encoders, which also are suitable in the context of function computation over non-Abelian group sources and provide rate regions achieved by these encoders.

On the Compressibility of non-Abelian-Group Sources in a Distributed Source Coding Setting

We consider the problem of compression of a non-Abelian source.This is motivated by the problem of distributed function computation,where it is known that if one is only interested in computing a function of several sources, then one can often improve upon the compression rate required by the Slepian-Wolf bound. Let G be a non-Abelian group having center Z(G). We show here that it is impossible to compress a source with symbols drawn from G when Z(G) is trivial if one employs a homomorphic encoder and a typical-set decoder.We provide achievable upper bounds on the minimum rate required to compress a non-Abelian group with non-trivial center. Also, in a two source setting, we provide achievable upper bounds for compression of any non-Abelian group, using a non-homomorphic encoder.

Group behaviour in physical, chemical and biological systems

Groups exhibit properties that either are not perceived to exist, or perhaps cannot exist, at the individual level. Such `emergent' properties depend on how individuals interact, both among themselves and with their surroundings. The world of everyday objects consists of material entities. These are, ultimately, groups of elementary particles that organize themselves into atoms and molecules, occupy space, and so on. It turns out that an explanation of even the most commonplace features of this world requires relativistic quantum field theory and the fact that Planck's constant is discrete, not zero. Groups of molecules in solution, in particular polymers ('sols'), can form viscous clusters that behave like elastic solids ('gels'). Sol-gel transitions are examples of cooperative phenomena. Their occurrence is explained by modelling the statistics of inter-unit interactions: the likelihood of either state varies sharply as a critical parameter crosses a threshold value. Group behaviour among cells or organisms is often heritable and therefore can evolve. This permits an additional, typically biological, explanation for it in terms of reproductive advantage, whether of the individual or of the group. There is no general agreement on the appropriate explanatory framework for understanding group-level phenomena in biology.

Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential

We use Floquet theory to study the maximum value of the stroboscopic group velocity in a one-dimensional tight-binding model subjected to an on-site staggered potential varying sinusoidally in time. The results obtained by numerically diagonalizing the Floquet operator are analyzed using a variety of analytical schemes. In the low-frequency limit we use adiabatic theory, while in the high-frequency limit the Magnus expansion of the Floquet Hamiltonian turns out to be appropriate. When the magnitude of the staggered potential is much greater or much less than the hopping, we use degenerate Floquet perturbation theory; we find that dynamical localization occurs in the former case when the maximum group velocity vanishes. Finally, starting from an ``engineered'' initial state where the particles (taken to be hard-core bosons) are localized in one part of the chain, we demonstrate that the existence of a maximum stroboscopic group velocity manifests in a light-cone-like spreading of the particles in real space.