67 research outputs found
Variation of Cross-Section Enhancement in Decay Spectra of CO under Resonant Raman Conditions
We have measured participator and spectator decay at several photon energies within the range of the lifetime-broadened first vibrational component of the C 1s→π* resonance in CO. From the branching ratios it is evident that the resonant enhancement is different for single-hole and two-hole–one-electron states: The maximum in the resonant intensity peaks at different photon energies. It now becomes necessary to calculate energy-dependent transition matrix elements within the lifetime-broadening range
A parametric integer programming algorithm for bilevel mixed integer programs
We consider discrete bilevel optimization problems where the follower solves
an integer program with a fixed number of variables. Using recent results in
parametric integer programming, we present polynomial time algorithms for pure
and mixed integer bilevel problems. For the mixed integer case where the
leader's variables are continuous, our algorithm also detects whether the
infimum cost fails to be attained, a difficulty that has been identified but
not directly addressed in the literature. In this case it yields a ``better
than fully polynomial time'' approximation scheme with running time polynomial
in the logarithm of the relative precision. For the pure integer case where the
leader's variables are integer, and hence optimal solutions are guaranteed to
exist, we present two algorithms which run in polynomial time when the total
number of variables is fixed.Comment: 11 page
Silly Questions and Arguments for the Implicit, Cinematic Narrator
My chapter aims to advance the debate on a problem often raised by philosophers who are skeptical of implied narrators in movies. This is the concern that positing such elusive narrators gives rise to absurd imaginings (Gaut 2004: 242; Carroll 2006: 179-180).
Friends of the implied cinematic narrator reply that the questions critics raise about the workings of the implied cinematic narrator are "silly ones" to ask.
I examine how the "absurd imaginings" problem arises for all the central arguments for the elusive cinematic narrator and discuss why the questions critics pose about this narrator are legitimate ones to ask
Nonlinear Integer Programming
Research efforts of the past fifty years have led to a development of linear
integer programming as a mature discipline of mathematical optimization. Such a
level of maturity has not been reached when one considers nonlinear systems
subject to integrality requirements for the variables. This chapter is
dedicated to this topic.
The primary goal is a study of a simple version of general nonlinear integer
problems, where all constraints are still linear. Our focus is on the
computational complexity of the problem, which varies significantly with the
type of nonlinear objective function in combination with the underlying
combinatorial structure. Numerous boundary cases of complexity emerge, which
sometimes surprisingly lead even to polynomial time algorithms.
We also cover recent successful approaches for more general classes of
problems. Though no positive theoretical efficiency results are available, nor
are they likely to ever be available, these seem to be the currently most
successful and interesting approaches for solving practical problems.
It is our belief that the study of algorithms motivated by theoretical
considerations and those motivated by our desire to solve practical instances
should and do inform one another. So it is with this viewpoint that we present
the subject, and it is in this direction that we hope to spark further
research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G.
Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50
Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art
Surveys, Springer-Verlag, 2009, ISBN 354068274
Automatic Design of Synthetic Gene Circuits through Mixed Integer Non-linear Programming
Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver sub-optimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer non-linear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and user-defined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective function given by the user. We evaluated the proposed method in the design of three synthetic circuits (a toggle switch, a transcriptional cascade, and a band detector), with both experimentally constructed and synthetic promoter libraries. Scalability and robustness analysis shows that the proposed framework scales well with the library size and the solution space. The work described here is a step towards a unifying, realistic framework for the automated design of biological circuits
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