We show that a number of graph-theoretic counting problems remain NP-hard, indeed #P-complete, in very restricted classes of graphs. In particular, it is shown that the problems of counting matchings, vertex covers, independent sets, and extremal variants of these all remain hard when restricted to planar bipartite graphs of bounded degree or regular graphs of constant degree. To achieve these ...

The uncertainty in measurements of gross alpha and beta activities in water samples by liquid scintillation counting with alpha/beta discrimination has been evaluated considering the problems typical of low-level measurements of environmental samples. The use of a pulse shape analysis device to discriminate alpha and beta events introduces a correlation between some of the input quantities, and...

Over the last few decades many techniques have been developed for determination of Sr/Y in the environment. Čerenkov counting technique (developed in the 1960s) is widely used, but can be further developed by the application of emerging technologies. For example, it is believed that the application of the triple-to-double coincidence ratio (TDCR) liquid scintillation counting method can be used...

Propositional model counting is a fundamental problem in artificial intelligence with a wide variety of applications, such as probabilistic inference, decision making under uncertainty, and probabilistic databases. Consequently, the problem is of theoretical as well as practical interest. When the constraints are expressed as DNF formulas, Monte Carlo-based techniques have been shown to provide...

The conjectural equivalence of curve counting on Calabi-Yau 3-folds via stable maps and stable pairs is discussed. By considering Calabi-Yau 3-folds with K3 fibrations, the correspondence naturally connects curve and sheaf counting on K3 surfaces. New results and conjectures (with D. Maulik) about descendent integration on K3 surfaces are announced. The recent proof of the Yau-Zaslow conjecture...

Estimates for products of the zeros of polynomials and entire functions are derived. By these estimates, new upper bounds for the counting function are suggested. In appropriate situations we improve the Jensen inequality for the counting functions and the Mignotte inequality for products of the zeros of polynomials. Mathematics subject classification (2010): 26C10, 30C15, 30D20.