On Graphical Models via Univariate Exponential Family Distributions

Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly for non-Gaussian and non-categorical data. In this paper, we consider a general sub-class of graphical models where the node-wise conditional distributions arise from exponential families. This allows us to derive multivariate graphical model distributions from univariate exponential family distributions, such as the Poisson, negative binomial, and exponential distributions. Our key contributions include a class of M-estimators to fit these graphical model distributions; and rigorous statistical analysis showing that these M-estimators recover the true graphical model structure exactly, with high probability. We provide examples of genomic and proteomic networks learned via instances of our class of graphical models derived from Poisson and exponential distributions.Comment: Journal of Machine Learning Researc

On Local Equivalence, Surface Code States and Matroids

Recently, Ji et al disproved the LU-LC conjecture and showed that the local unitary and local Clifford equivalence classes of the stabilizer states are not always the same. Despite the fact this settles the LU-LC conjecture, a sufficient condition for stabilizer states that violate the LU-LC conjecture is missing. In this paper, we investigate further the properties of stabilizer states with respect to local equivalence. Our first result shows that there exist infinitely many stabilizer states which violate the LU-LC conjecture. In particular, we show that for all numbers of qubits $n\geq 28$, there exist distance two stabilizer states which are counterexamples to the LU-LC conjecture. We prove that for all odd $n\geq 195$, there exist stabilizer states with distance greater than two which are LU equivalent but not LC equivalent. Two important classes of stabilizer states that are of great interest in quantum computation are the cluster states and stabilizer states of the surface codes. To date, the status of these states with respect to the LU-LC conjecture was not studied. We show that, under some minimal restrictions, both these classes of states preclude any counterexamples. In this context, we also show that the associated surface codes do not have any encoded non-Clifford transversal gates. We characterize the CSS surface code states in terms of a class of minor closed binary matroids. In addition to making connection with an important open problem in binary matroid theory, this characterization does in some cases provide an efficient test for CSS states that are not counterexamples.Comment: LaTeX, 13 pages; Revised introduction, minor changes and corrections mainly in section V

Knowledge and Awareness of Thirdhand Smoke among Smokers and Non-smokers - A Comparative cross-sectional study

Third-hand smoke (THS) is the residual tobacco smoke contaminant that remains after a cigarette is extinguished. It can react with the indoor air pollutant nitrous acid to produce a carcinogen. THS exposure may occur long after second-hand smoke appears (SHS). A cross sectional questionnaire study was conducted in which a close-ended self- administered 20 item questionnaire was prepared. The data was collected from the smokers and non-smokers. Demographic characteristics, tobacco use status, attitudes toward awareness of third hand smoke and its adverse effects, was filled by the surveyed subjects. A total of 100 members with the mean age of 15-45 years participated in the study. The awareness of Third hand smoke is more among the non-smokers than compared with the smokers. The precautionary principle, which is a “strategy to cope with possible risks where scientific understanding is yet incomplete,” is widely used in Europe and in radiation protection in the United States. Extended producer responsibility promotes total-lifecycle environmental improvements, placing economic, physical, and informational responsibilities onto the tobacco industry. Efforts to further reduce THS exposure may ultimately reduce tobacco- related diseases and preserve the health of non-smoking adults and children

Evolution of dynamical motions in monolayer protected metal-clusters

Here we report orientational dynamics in monolayer protected metal-cluster (MPC) systems as studied by quasielastic neutron scattering (QENS) technique. Experiments carried out using two different instruments having very different energy windows, thus covering a time scale of 10-9-10-12 s. Clear evidence of absence of 'rotator phase' has been found in isolated MPCs (Au-SC18H37, Au-SC12H25, Au-SC8H17 and Au-SC6H13), a superlattice MPC (Ag-SC18H37) as well as planar thiolates (Ag-SC6H13, Ag-SC12H25, Ag-SC18H37) at room temperature. However, dynamics were found to evolve on increase of temperature and its behaviour is found to be different in the superlattice and isolated cluster systems. Detailed dynamical informations for MPCs are obtained for the first time in these systems