On the compatibility of causality and symmetry (Comments on "Analysis of causality in time-dependent density functional theory")

It is argued that there exists the only one inverse of the linear response function $\chi$, i.e. $\chi^{-1}$, which depends symmetrically of its spatial-times variables, see M.K. Harbola, and A. Banerjee, Phys. Rev. A {\bf 60}, 5101 (1999). Some brief comments on this consideration are presented. We show instead, that it is possible to construct the causal inverse also. At the same time we confirm the main statement of M.K. Harbola and A. Banerjee that in fact there is no contradiction between the symmetry and causality.Comment: 4 pages, LaTe

Covariant anomaly and Hawking radiation from the modified black hole in the rainbow gravity theory

Recently, Banerjee and Kulkarni (R. Banerjee, S. Kulkarni, arXiv:0707.2449 [hep-th]) suggested that it is conceptually clean and economical to use only the covariant anomaly to derive Hawking radiation from a black hole. Based upon this simplified formalism, we apply the covariant anomaly cancellation method to investigate Hawking radiation from a modified Schwarzschild black hole in the theory of rainbow gravity. Hawking temperature of the gravity's rainbow black hole is derived from the energy-momentum flux by requiring it to cancel the covariant gravitational anomaly at the horizon. We stress that this temperature is exactly the same as that calculated by the method of cancelling the consistent anomaly.Comment: 5 page

Book review – The Pathan Unarmed

Book review of The Pathan Unarmed: Opposition and Memory in the North West Frontier by Mukulika Banerjee from Oxford University Press 2001 238pp. This review is reproduced with permission from Bloomsbury Pakistan (www.bloomsburypakistan.org)

Remarks on an Exact Seiberg-Witten map

We obtain the leading derivative corrections to an expression for the Seiberg-Witten map given by Banerjee and Yang and show how they affect the noncommutative deformation of the Maxwell action, as well as the matter coupling in noncommutative emergent gravity.Comment: 8 page

Evasive Properties of Sparse Graphs and Some Linear Equations in Primes

We give an unconditional version of a conditional, on the Extended Riemann Hypothesis, result of L. Babai, A. Banerjee, R. Kulkarni and V. Naik (2010) on the evasiveness of sparse graphs.Comment: This version corrects a mistake made in the previous version, which was pointed out to the author by Laszlo Baba

Two Experiments to Test a Model of Herd Behaviour

We carry out two experiments to test a model of herd behaviour based on the work of Banerjee (1992). He shows that herding occurs as a result of people observing the actions of others and using this information in their own decision rule. However, in our experiments herding does not occur as frequently as Banerjee predicts. Contrary to his results, the subjects' behaviour appears to depend on the probabilities of receiving a signal and of this signal being correct. Furthermore, he finds that the pattern of decision making over a number of rounds of the game is volatile whereas we find that decision making is volatile within rounds.

Nonparametric confidence intervals for monotone functions

We study nonparametric isotonic confidence intervals for monotone functions. In Banerjee and Wellner (2001) pointwise confidence intervals, based on likelihood ratio tests for the restricted and unrestricted MLE in the current status model, are introduced. We extend the method to the treatment of other models with monotone functions, and demonstrate our method by a new proof of the results in Banerjee and Wellner (2001) and also by constructing confidence intervals for monotone densities, for which still theory had to be developed. For the latter model we prove that the limit distribution of the LR test under the null hypothesis is the same as in the current status model. We compare the confidence intervals, so obtained, with confidence intervals using the smoothed maximum likelihood estimator (SMLE), using bootstrap methods. The `Lagrange-modified' cusum diagrams, developed here, are an essential tool both for the computation of the restricted MLEs and for the development of the theory for the confidence intervals, based on the LR tests.Comment: 31 pages, 13 figure