Matrices of finite Lorentz transformations in a noncompact basis. III. Completeness relation for O(2, 1)

A parametrization of the elements of the three-dimensional Lorentz group O(2, 1), suited to the use of a noncompact O(1, 1) basis in its unitary representations, is derived and used to set up the representation matrices for the entire group. The Plancherel formula for O(2, 1) is then expressed in this basis.

Branch-branch connections in trees analogous to hyphal fusions in fungal colonies

the leopard tree Caesalpinia ferrea (Leguminosae) a native of eastern Brazil-some of the leader branches connect to and fuse with neighbouring branches of the same tree. The bridge initials project out as pegs or protuberances and apparently extend in a coordinated manner, connecting branches up to 4 ft apart. The fusion of two branches of the same tree implies intra-plant communication involving signaling factor(s). The bridges resemble fusions between hyphae in a fungal colony. Whereas hyphal fusions are common and the process is apparently completed in <1 h, branch fusions in C. ferrea tree are limited and a slow process, apparently requiring several months to years to complete. Branch fusions in C. ferrea are in accord with Claus Mattheck's analysis that tree branches actually seek contact rather than avoid contacts.

Flat connections, geometric invariants and the symplectic nature of the fundamental group of surfaces

In this paper we associate a new geometric invariant to the space of fiat connections on a G (= SU(2))-bundle on a compact Riemann surface M and relate it tcr the symplectic structure on the space Hom(pi(1)(M), G)/G consisting of representations of the fundamental group pi(1)(M) Of M into G module the conjugate action of G on representations.

On some geometric invariants associated to the space of flat connections on an open space

A geometric invariant is associated to the parabolic moduli space on a marked surface and is related to the symplectic structure of the moduli space.

Flat connections, geometric invariants and energy of harmonic functions on compact Riemann surfaces

A geometric invariant is associated to the space of fiat connections on a G-bundle over a compact Riemann surface and is related to the energy of harmonic functions.

Punching shear strength of flat slab corner column connections .1. Reinforced concrete connections

This paper presents the details of an experimental study on punching shear strength and behaviour of reinforced concrete corner column connections in flat slabs; a quasi-empirical method is proposed for computing the punching shear strength. The method has also been extended for punching shear strength prediction at interior and edge column connections. The test results compare better with the strengths predicted by the proposed method than those by Ingvarson, Zaglool and Pollet available in the literature. Further, the experimental strengths of interior, edge and corner column connections have been compared with the strengths predicted by the proposed method and the two codes of practice, viz. ACI and BS code, to demonstrate the usefulness of the method.

Punching shear strength of flat slab corner column connections .2. Fibre-reinforced concrete connections

This paper gives the details of the studies undertaken to examine the strength and behaviour of fibre-reinforced concrete corner column connections in flat slabs. Tests have been conducted on 16 specimens with varying reinforcement ratio, moment/shear ratio (load eccentricity) and volume fraction of fibres. A quasi-empirical method has been proposed for computing the punching shear strength. The method has also been extended to fibre-reinforced concrete interior column connections, tests on which are available in the literature. The test results have been compared with the strength predicted by the proposed method for corner column as well as interior column connections and a satisfactory agreement noticed.

Analytical model for congestion control and throughput with TCP CUBIC connections

We develop a Markov model for a TCP CUBIC connection. Next we use it to obtain approximate expressions for throughput when there may be queuing in the network. Finally we provide the throughputs different TCP CUBIC and TCP NewReno connections obtain while sharing a channel when they may have different round trip delays and packet loss probabilities.

Performance analysis of data and voice connections in a cognitive radio network

We study the performance of cognitive (secondary) users in a cognitive radio network which uses a channel whenever the primary users are not using the channel. The usage of the channel by the primary users is modelled by an ON-OFF renewal process. The cognitive users may be transmitting data using TCP connections and voice traffic. The voice traffic is given priority over the data traffic. We theoretically compute the mean delay of TCP and voice packets and also the mean throughput of the different TCP connections. We compare the theoretical results with simulations.

Spontaneous Lorentz violation in gauge theories

Frohlich, Morchio and Strocchi long ago proved that the Lorentz invariance is spontaneously broken in QED because of infrared effects. We develop a simple model where the consequences of this breakdown can be explicitly and easily calculated. For this purpose, the superselected U(1) charge group of QED is extended to a superselected ``Sky'' group containing direction-dependent gauge transformations at infinity. It is the analog of the Spi group of gravity. As Lorentz transformations do not commute with Sky, they are spontaneously broken. These Abelian considerations and model are extended to non-Abelian gauge symmetries. Basic issues regarding the observability of twisted non-Abelian gauge symmetries and of the asymptotic ADM symmetries of quantum gravity are raised.

Spontaneous Lorentz violation: the case of infrared QED

It is by now clear that the infrared sector of quantum electrodynamics (QED) has an intriguingly complex structure. Based on earlier pioneering work on this subject, two of us recently proposed a simple modification of QED by constructing a generalization of the U(1) charge group of QED to the ``Sky'' group incorporating the well-known spontaneous Lorentz violation due to infrared photons, but still compatible in particular with locality (Balachandran and Vaidya, Eur Phys J Plus 128:118, 2013). It was shown that the ``Sky'' group is generated by the algebra of angle-dependent charges and a study of its superselection sectors has revealed a manifest description of spontaneous breaking of the Lorentz symmetry. We further elaborate this approach here and investigate in some detail the properties of charged particles dressed by the infrared photons. We find that Lorentz violation due to soft photons may be manifestly codified in an angle-dependent fermion mass, modifying therefore the fermion dispersion relations. The fact that the masses of the charged particles are not Lorentz invariant affects their spin content, and time dilation formulas for decays should also get corrections.

Probing the Neutral Edge Modes in Transport across a Point Contact via Thermal Effects in the Read-Rezayi Non-Abelian Quantum Hall States

Non-Abelian quantum Hall states are characterized by the simultaneous appearance of charge and neutral gapless edge modes, with the structure of the latter being intricately related to the existence of bulk quasiparticle excitations obeying non-Abelian statistics. Here we propose a scenario for detecting the neutral modes by having two point contacts in series separated by a distance set by the thermal equilibration length of the charge mode. We show that by using the first point contact as a heating device, the excess charge noise measured at the second point contact carries a nontrivial signature of the presence of the neutral mode. We also obtain explicit expressions for the thermal conductance and corresponding Lorentz number for transport across a quantum point contact between two edges held at different temperatures and chemical potentials.

Intra and Inter-Molecular Communications Through Protein Structure Network

Communication within and across proteins is crucial for the biological functioning of proteins. Experiments such as mutational studies on proteins provide important information on the amino acids, which are crucial for their function. However, the protein structures are complex and it is unlikely that the entire responsibility of the function rests on only a few amino acids. A large fraction of the protein is expected to participate in its function at some level or other. Thus, it is relevant to consider the protein structures as a completely connected network and then deduce the properties, which are related to the global network features. In this direction, our laboratory has been engaged in representing the protein structure as a network of non-covalent connections and we have investigated a variety of problems in structural biology, such as the identification of functional and folding clusters, determinants of quaternary association and characterization of the network properties of protein structures. We have also addressed a few important issues related to protein dynamics, such as the process of oligomerization in multimers, mechanism on protein folding, and ligand induced communications (allosteric effect). In this review we highlight some of the investigations which we have carried out in the recent past. A review on protein structure graphs was presented earlier, in which the focus was on the graphs and graph spectral properties and their implementation in the study of protein structure graphs/networks (PSN). In this article, we briefly summarize the relevant parts of the methodology and the focus is on the advancement brought out in the understanding of protein structure-function relationships through structure networks. The investigations of structural/biological problems are divided into two parts, in which the first part deals with the analysis of PSNs based on static structures obtained from x-ray crystallography. The second part highlights the changes in the network, associated with biological functions, which are deduced from the network analysis on the structures obtained from molecular dynamics simulations.

On anomalous U(1) gauge theory in four dimensions

We discuss the consistency, unitarity and Lorentz invariance of an anomalous U(1) gauge theory in four dimensions. Our analysis is based on an effective low-energy action valid in the chiral symmetry broken phase. The allegedly bad properties of anomalous theories (except non-renormalizability) are examined. It is shown that, in the low-energy context, the theory can be consistently and unitarily quantised, and is formally Lorentz covariant.