Small Area Shrinkage Estimation

The need for small area estimates is increasingly felt in both the public and private sectors in order to formulate their strategic plans. It is now widely recognized that direct small area survey estimates are highly unreliable owing to large standard errors and coefficients of variation. The reason behind this is that a survey is usually designed to achieve a specified level of accuracy at a higher level of geography than that of small areas. Lack of additional resources makes it almost imperative to use the same data to produce small area estimates. For example, if a survey is designed to estimate per capita income for a state, the same survey data need to be used to produce similar estimates for counties, subcounties and census divisions within that state. Thus, by necessity, small area estimation needs explicit, or at least implicit, use of models to link these areas. Improved small area estimates are found by "borrowing strength" from similar neighboring areas.Comment: Published in at http://dx.doi.org/10.1214/11-STS374 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Methodology for Information Flow Experiments

Information flow analysis has largely ignored the setting where the analyst has neither control over nor a complete model of the analyzed system. We formalize such limited information flow analyses and study an instance of it: detecting the usage of data by websites. We prove that these problems are ones of causal inference. Leveraging this connection, we push beyond traditional information flow analysis to provide a systematic methodology based on experimental science and statistical analysis. Our methodology allows us to systematize prior works in the area viewing them as instances of a general approach. Our systematic study leads to practical advice for improving work on detecting data usage, a previously unformalized area. We illustrate these concepts with a series of experiments collecting data on the use of information by websites, which we statistically analyze

Conversion of neutron stars to strange stars as the central engine of gamma-ray bursts

We study the conversion of a neutron star to a strange star as a possible energy source for gamma-ray bursts. We use different recent models for the equation of state of neutron star matter and strange quark matter. We show that the total amount of energy liberated in the conversion is in the range of (1-4) 10^{53} ergs (one order of magnitude larger than previous estimates) and is in agreement with the energy required to power gamma-ray burst sources at cosmological distances.Comment: ApJ, 530, 2000 February 20, Lxxx (in press

Quantum Markov chains, sufficiency of quantum channels, and Renyi information measures

A short quantum Markov chain is a tripartite state $\rho_{ABC}$ such that system $A$ can be recovered perfectly by acting on system $C$ of the reduced state $\rho_{BC}$. Such states have conditional mutual information $I(A;B|C)$ equal to zero and are the only states with this property. A quantum channel $\mathcal{N}$ is sufficient for two states $\rho$ and $\sigma$ if there exists a recovery channel using which one can perfectly recover $\rho$ from $\mathcal{N}(\rho)$ and $\sigma$ from $\mathcal{N}(\sigma)$. The relative entropy difference $D(\rho\Vert\sigma)-D(\mathcal{N}(\rho)\Vert\mathcal{N}(\sigma))$ is equal to zero if and only if $\mathcal{N}$ is sufficient for $\rho$ and $\sigma$. In this paper, we show that these properties extend to Renyi generalizations of these information measures which were proposed in [Berta et al., J. Math. Phys. 56, 022205, (2015)] and [Seshadreesan et al., J. Phys. A 48, 395303, (2015)], thus providing an alternate characterization of short quantum Markov chains and sufficient quantum channels. These results give further support to these quantities as being legitimate Renyi generalizations of the conditional mutual information and the relative entropy difference. Along the way, we solve some open questions of Ruskai and Zhang, regarding the trace of particular matrices that arise in the study of monotonicity of relative entropy under quantum operations and strong subadditivity of the von Neumann entropy.Comment: v4: 26 pages, 1 figure; reorganized and one open question solved with Choi's inequality (at the suggestion of an anonymous referee

Quantum discord between relatively accelerated observers

We calculate the quantum discord between two free modes of a scalar field which start in a maximally entangled state and then undergo a relative, constant acceleration. In a regime where there is no distillable entanglement due to the Unruh effect, we show that there is a finite amount of quantum discord, which is a measure of purely quantum correlations in a state, over and above quantum entanglement. Even in the limit of infinite acceleration of the observer detecting one of the modes, we provide evidence for a non-zero amount of purely quantum correlations, which might be exploited to gain non-trivial quantum advantages.Comment: 4 pages, 2 figure

A Green-function approach to transport phenomena in quantum pumps

We present a general treatment to study transport phenomena in systems described by tight-binding Hamiltonians coupled to reservoirs and with one or more time-periodic potentials. We apply this treatment to the study of transport phenomena in a double barrier structure with one and two harmonic potentials. Among other properties, we discuss the origin of the sign of the net current.Comment: To appear in PR

On the Observability of "Invisible" / "Nearly Invisible" Charginos

It is shown that if the charginos decay into very soft leptons or hadrons + $\not{E}$ due to degeneracy/ near- degeneracy with the LSP or the sneutrino, the observability of the recently proposed signal via the single photon (+ soft particles) + $\not{E}$ channel crucially depends on the magnitude of the \SNU mass due to destructive interferences in the matrix element squared. If the \SNU's and, consequently, left-sleptons are relatively light, the size of the signal, previously computed in the limit \MSNU \to \infty only, is drastically reduced. We present the formula for the signal cross section in a model independent way and discuss the observability of the signal at LEP 192 and NLC energies.Comment: 27 pages, Late

Probing thermality beyond the diagonal

We investigate the off-diagonal sector of eigenstate thermalization using both local and non-local probes in 2-dimensional conformal field theories. A novel analysis of the asymptotics of OPE coefficients via the modular bootstrap is performed to extract the behaviour of the off-diagonal matrix elements. We also probe this sector using semi-classical heavy-light Virasoro blocks. The results demonstrate signatures of thermality and confirms the entropic suppression of the off-diagonal elements as necessitated by the eigenstate thermalization hypothesis.Comment: 27 pages, 2 figure

Strong converse theorems using R\'enyi entropies

We use a R\'enyi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum or classical communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [arXiv:1404.5940], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the $(e,q)$-plane, where $e$ and $q$ denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a R\'enyi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched R\'enyi divergence. In particular, we obtain novel bounds relating these quantities, as well as the R\'enyi conditional mutual information, to the fidelity of two quantum states.Comment: 40 pages, 5 figures; v4: Accepted for publication in Journal of Mathematical Physic