20 research outputs found
Cardiovascular risk estimation and eligibility for statins in primary prevention comparing different strategies.
Recommendations for statin use for primary prevention of coronary heart disease (CHD) are based on estimation of the 10-year CHD risk. It is unclear which risk algorithm and guidelines should be used in European populations. Using data from a population-based study in Switzerland, we first assessed 10-year CHD risk and eligibility for statins in 5,683 women and men 35 to 75 years of age without cardiovascular disease by comparing recommendations by the European Society of Cardiology without and with extrapolation of risk to age 60 years, the International Atherosclerosis Society, and the US Adult Treatment Panel III. The proportions of participants classified as high-risk for CHD were 12.5% (15.4% with extrapolation), 3.0%, and 5.8%, respectively. Proportions of participants eligible for statins were 9.2% (11.6% with extrapolation), 13.7%, and 16.7%, respectively. Assuming full compliance to each guideline, expected relative decreases in CHD deaths in Switzerland over a 10-year period would be 16.4% (17.5% with extrapolation), 18.7%, and 19.3%, respectively; the corresponding numbers needed to treat to prevent 1 CHD death would be 285 (340 with extrapolation), 380, and 440, respectively. In conclusion, the proportion of subjects classified as high risk for CHD varied over a fivefold range across recommendations. Following the International Atherosclerosis Society and the Adult Treatment Panel III recommendations might prevent more CHD deaths at the cost of higher numbers needed to treat compared with European Society of Cardiology guidelines
Balancing Bounded Treewidth Circuits
Algorithmic tools for graphs of small treewidth are used to address questions
in complexity theory. For both arithmetic and Boolean circuits, it is shown
that any circuit of size and treewidth can be
simulated by a circuit of width and size , where , if , and otherwise. For our main construction,
we prove that multiplicatively disjoint arithmetic circuits of size
and treewidth can be simulated by bounded fan-in arithmetic formulas of
depth . From this we derive the analogous statement for
syntactically multilinear arithmetic circuits, which strengthens a theorem of
Mahajan and Rao. As another application, we derive that constant width
arithmetic circuits of size can be balanced to depth ,
provided certain restrictions are made on the use of iterated multiplication.
Also from our main construction, we derive that Boolean bounded fan-in circuits
of size and treewidth can be simulated by bounded fan-in
formulas of depth . This strengthens in the non-uniform setting
the known inclusion that . Finally, we apply our
construction to show that {\sc reachability} for directed graphs of bounded
treewidth is in
Unary Pushdown Automata and Straight-Line Programs
We consider decision problems for deterministic pushdown automata over a
unary alphabet (udpda, for short). Udpda are a simple computation model that
accept exactly the unary regular languages, but can be exponentially more
succinct than finite-state automata. We complete the complexity landscape for
udpda by showing that emptiness (and thus universality) is P-hard, equivalence
and compressed membership problems are P-complete, and inclusion is
coNP-complete. Our upper bounds are based on a translation theorem between
udpda and straight-line programs over the binary alphabet (SLPs). We show that
the characteristic sequence of any udpda can be represented as a pair of
SLPs---one for the prefix, one for the lasso---that have size linear in the
size of the udpda and can be computed in polynomial time. Hence, decision
problems on udpda are reduced to decision problems on SLPs. Conversely, any SLP
can be converted in logarithmic space into a udpda, and this forms the basis
for our lower bound proofs. We show coNP-hardness of the ordered matching
problem for SLPs, from which we derive coNP-hardness for inclusion. In
addition, we complete the complexity landscape for unary nondeterministic
pushdown automata by showing that the universality problem is -hard, using a new class of integer expressions. Our techniques have
applications beyond udpda. We show that our results imply -completeness for a natural fragment of Presburger arithmetic and coNP lower
bounds for compressed matching problems with one-character wildcards
e{open}-productions in context-free grammars
The effect of e{open}-productions on the space complexity of various context-free language problems is investigated. It is shown that the removal of e{open}-productions from a context-free grammar can probably not be achieved with small storage space. This explains the apparent discrepancy between two different results in the literature on the membership problem. By way of contrast, it is shown that the space complexity of the emptiness and the finiteness problems are independent of the presence of e{open}-productions
The maximum flow problem is log space complete for P
The space complexity of the maximum flow problem is investigated. It is shown that the problem is log space complete for deterministic polynomial time. Thus the maximum flow problem probably has no algorithm which needs only O(logk n) storage space for any constant k. Another consequence is that there is probably no fast parallel algorithm for the maximum flow problem
Electronic Colloquium on Computational Complexity, Report No. 130 (2006) One-input-face MPCVP is Hard for L, but in
Abstract. A monotone planar circuit (MPC) is a Boolean circuit that can be embedded in a plane, and that has only AND and OR gates. Yang showed that the one-input-face monotone planar circuit value problem (MPCVP) is in NC 2, and Limaye et. al. improved the bound to LogCFL. Barrington et. al. showed that evaluating monotone upward stratified circuits, a restricted version of the one-input-face MPCVP, is in LogDCFL. In this paper, we prove that the unrestricted one-input-face MPCVP is also in LogDCFL. We also show this problem to be L-hard under quantifier free projections. Key Words: L, LogDCFL, monotone planar circuits.