On input read-modes of alternating Turing machines

AbstractA number of input read-modes of Turing machines have appeared in the literature. To investigate the differences among these input read-modes, we study log-time alternating Turing machines of constant alternations. For each fixed integer k ⩾ 1 and for each read-mode, a precise circuit characterization is established for log-time alternating Turing machines of k alternations, which is a nontrivial refinement of Ruzzo's circuit characterization of alternating Turing machines. These circuit characterizations indicate clearly the differences among the input read-modes. Complete languages in strong sense for each level of the log-time hierarchy are presented, refining a result by Buss. An application of these results to computational optimization problems is described

FRACTURE PARAMETERS EVALUATION FOR THE CRACKED NONHOMOGENEOUS ENAMEL BASED ON THE FINITE ELEMENT METHOD AND VIRTUAL CRACK CLOSURE TECHNIQUE

To accurately solve the fracture parameters of enamel, we have established computational nonhomogeneous enamel models and constructed the fracture element of enamel dumb nodes, based on the enamel mineral concentration, nonhomogeneous mechanical properties, and virtual crack closure technique. Through the commercial finite element software ABAQUS and the fracture element of the enamel dumb nodes, we have established the user subroutines UMAT and UEL, which enabled solving of the energy release rates of the nonhomogeneous enamel structure with cracks. The stress intensity factors of central cracks, three-point bend and compact stretched enamels, and double-edge notched stretched enamels are determined. By comparing them with analytical solutions, we have proved that the fracture element of the enamel dumb nodes is highly accurate, simple, and convenient. In addition, the cracks can be other elements rather than singular or special elements; they show versatility and other advantages. The stress intensity factor of the dental enamel can be solved more realistically. Thus, a new numerical method for prevention and treatment of dental diseases is provided

Estimation of multi-state life table functions and their variability from complex survey data using the SPACE Program

The multistate life table (MSLT) model is an important demographic method to document life cycle processes. In this study, we present the SPACE (Stochastic Population Analysis for Complex Events) program to estimate MSLT functions and their sampling variability. It has several advantages over other programs, including the use of microsimulation and the bootstrap method to estimate the sampling variability. Simulation enables researchers to analyze a broader array of statistics than the deterministic approach, and may be especially advantageous in investigating distributions of MSLT functions. The bootstrap method takes sample design into account to correct the potential bias in variance estimates.bootstrap, health expectancy, multi-state life table, population aging

Exponential Time Complexity of the Permanent and the Tutte Polynomial

We show conditional lower bounds for well-studied #P-hard problems: (a) The number of satisfying assignments of a 2-CNF formula with n variables cannot be counted in time exp(o(n)), and the same is true for computing the number of all independent sets in an n-vertex graph. (b) The permanent of an n x n matrix with entries 0 and 1 cannot be computed in time exp(o(n)). (c) The Tutte polynomial of an n-vertex multigraph cannot be computed in time exp(o(n)) at most evaluation points (x,y) in the case of multigraphs, and it cannot be computed in time exp(o(n/polylog n)) in the case of simple graphs. Our lower bounds are relative to (variants of) the Exponential Time Hypothesis (ETH), which says that the satisfiability of n-variable 3-CNF formulas cannot be decided in time exp(o(n)). We relax this hypothesis by introducing its counting version #ETH, namely that the satisfying assignments cannot be counted in time exp(o(n)). In order to use #ETH for our lower bounds, we transfer the sparsification lemma for d-CNF formulas to the counting setting