734 research outputs found
Cooperativity and Stability in a Langevin Model of Protein Folding
We present two simplified models of protein dynamics based on Langevin's
equation of motion in a viscous medium. We explore the effect of the potential
energy function's symmetry on the kinetics and thermodynamics of simulated
folding. We find that an isotropic potential energy function produces, at best,
a modest degree of cooperativity. In contrast, a suitable anisotropic potential
energy function delivers strong cooperativity.Comment: 45 pages, 16 figures, 2 tables. LaTeX. Submitted to the Journal of
Chemical Physic
Multidimensional Binary Vector Assignment problem: standard, structural and above guarantee parameterizations
In this article we focus on the parameterized complexity of the
Multidimensional Binary Vector Assignment problem (called \BVA). An input of
this problem is defined by disjoint sets , each
composed of binary vectors of size . An output is a set of disjoint
-tuples of vectors, where each -tuple is obtained by picking one vector
from each set . To each -tuple we associate a dimensional vector by
applying the bit-wise AND operation on the vectors of the tuple. The
objective is to minimize the total number of zeros in these vectors. mBVA
can be seen as a variant of multidimensional matching where hyperedges are
implicitly locally encoded via labels attached to vertices, but was originally
introduced in the context of integrated circuit manufacturing.
We provide for this problem FPT algorithms and negative results (-based
results, [2]-hardness and a kernel lower bound) according to several
parameters: the standard parameter i.e. the total number of zeros), as well
as two parameters above some guaranteed values.Comment: 16 pages, 6 figure
A Discrete State Transition Algorithm for Generalized Traveling Salesman Problem
Generalized traveling salesman problem (GTSP) is an extension of classical
traveling salesman problem (TSP), which is a combinatorial optimization problem
and an NP-hard problem. In this paper, an efficient discrete state transition
algorithm (DSTA) for GTSP is proposed, where a new local search operator named
\textit{K-circle}, directed by neighborhood information in space, has been
introduced to DSTA to shrink search space and strengthen search ability. A
novel robust update mechanism, restore in probability and risk in probability
(Double R-Probability), is used in our work to escape from local minima. The
proposed algorithm is tested on a set of GTSP instances. Compared with other
heuristics, experimental results have demonstrated the effectiveness and strong
adaptability of DSTA and also show that DSTA has better search ability than its
competitors.Comment: 8 pages, 1 figur
Parameterized pre-coloring extension and list coloring problems
Golovach, Paulusma and Song (Inf. Comput. 2014) asked to determine the parameterized complexity of the following problems parameterized by k: (1) Given a graph G, a clique modulator D (a clique modulator is a set of vertices, whose removal results in a clique) of size k for G, and a list L(v) of colors for every v ∈ V(G), decide whether G has a proper list coloring; (2) Given a graph G, a clique modulator D of size k for G, and a pre-coloring λ_P: X → Q for X ⊆ V(G), decide whether λ_P can be extended to a proper coloring of G using only colors from Q. For Problem 1 we design an O*(2^k)-time randomized algorithm and for Problem 2 we obtain a kernel with at most 3k vertices. Banik et al. (IWOCA 2019) proved the following problem is fixed-parameter tractable and asked whether it admits a polynomial kernel: Given a graph G, an integer k, and a list L(v) of exactly n-k colors for every v ∈ V(G), decide whether there is a proper list coloring for G. We obtain a kernel with O(k²) vertices and colors and a compression to a variation of the problem with O(k) vertices and O(k²) colors
The radiating part of circular sources
An analysis is developed linking the form of the sound field from a circular
source to the radial structure of the source, without recourse to far-field or
other approximations. It is found that the information radiated into the field
is limited, with the limit fixed by the wavenumber of source multiplied by the
source radius (Helmholtz number). The acoustic field is found in terms of the
elementary fields generated by a set of line sources whose form is given by
Chebyshev polynomials of the second kind, and whose amplitude is found to be
given by weighted integrals of the radial source term. The analysis is
developed for tonal sources, such as rotors, and, for Helmholtz number less
than two, for random disk sources. In this case, the analysis yields the
cross-spectrum between two points in the acoustic field. The analysis is
applied to the problems of tonal radiation, random source radiation as a model
problem for jet noise, and to noise cancellation, as in active control of noise
from rotors. It is found that the approach gives an accurate model for the
radiation problem and explicitly identifies those parts of a source which
radiate.Comment: Submitted to Journal of the Acoustical Society of Americ
Spanning directed trees with many leaves
The {\sc Directed Maximum Leaf Out-Branching} problem is to find an
out-branching (i.e. a rooted oriented spanning tree) in a given digraph with
the maximum number of leaves. In this paper, we obtain two combinatorial
results on the number of leaves in out-branchings. We show that
- every strongly connected -vertex digraph with minimum in-degree at
least 3 has an out-branching with at least leaves;
- if a strongly connected digraph does not contain an out-branching with
leaves, then the pathwidth of its underlying graph UG() is .
Moreover, if the digraph is acyclic, the pathwidth is at most .
The last result implies that it can be decided in time whether a strongly connected digraph on vertices has an
out-branching with at least leaves. On acyclic digraphs the running time of
our algorithm is
A New Approach to Population Sizing for Memetic Algorithms: A Case Study for the Multidimensional Assignment Problem
Memetic algorithms are known to be a powerful technique in solving hard optimization problems. To design a memetic algorithm, one needs to make a host of decisions. Selecting the population size is one of the most important among them. Most of the algorithms in the literature fix the population size to a certain constant value. This reduces the algorithm's quality since the optimal population size varies for different instances, local search procedures, and runtimes. In this paper we propose an adjustable population size. It is calculated as a function of the runtime of the whole algorithm and the average runtime of the local search for the given instance. Note that in many applications the runtime of a heuristic should be limited and, therefore, we use this bound as a parameter of the algorithm. The average runtime of the local search procedure is measured during the algorithm's run. Some coefficients which are independent of the instance and the local search are to be tuned at the design time;we provide a procedure to find these coefficients. The proposed approach was used to develop a memetic algorithm for the multidimensional assignment problem (MAP). We show that our adjustable population size makes the algorithm flexible to perform efficiently for a wide range of running times and local searches and this does not require any additional tuning of the algorithm
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