562 research outputs found
Trichotomy for Integer Linear Systems Based on Their Sign Patterns
In this paper, we consider solving the integer linear systems, i.e.,
given a matrix A in R^{m*n}, a vector b in R^m, and a positive integer d, to compute an integer vector x in D^n such that Ax <= b,
where m and n denote positive integers, R denotes the set of reals, and D={0,1,..., d-1}. The problem is one of the most fundamental NP-hard problems in computer science.
For the problem, we propose a complexity index h which is based only on the sign pattern of A. For a real r, let ILS_=(r) denote the family of the problem instances I with h(I)=r. We then show the following trichotomy:
- ILS_=(r) is linearly solvable, if r < 1,
- ILS_=(r) is weakly NP-hard and pseudo-polynomially solvable, if r = 1, and
- ILS_=(r) is strongly NP-hard, if r > 1.
This, for example, includes the existing results that quadratic systems and Horn systems can be solved in pseudo-polynomial time
A Combinatorial Certifying Algorithm for Linear Programming Problems with Gainfree Leontief Substitution Systems
Linear programming (LP) problems with gainfree Leontief substitution systems
have been intensively studied in economics and operations research, and include
the feasibility problem of a class of Horn systems, which arises in, e.g.,
polyhedral combinatorics and logic. This subclass of LP problems admits a
strongly polynomial time algorithm, where devising such an algorithm for
general LP problems is one of the major theoretical open questions in
mathematical optimization and computer science. Recently, much attention has
been paid to devising certifying algorithms in software engineering, since
those algorithms enable one to confirm the correctness of outputs of programs
with simple computations. In this paper, we provide the first combinatorial
(and strongly polynomial time) certifying algorithm for LP problems with
gainfree Leontief substitution systems. As a by-product, we answer
affirmatively an open question whether the feasibility problem of the class of
Horn systems admits a combinatorial certifying algorithm
Visualization of Au Nanoparticles Buried in a Polymer Matrix by Scanning Thermal Noise Microscopy
We demonstrated visualization of Au nanoparticles buried 300 nm into a
polymer matrix by measurement of the thermal noise spectrum of a
microcantilever with a tip in contact to the polymer surface. The subsurface Au
nanoparticles were detected as the variation in the contact stiffness and
damping reflecting the viscoelastic properties of the polymer surface. The
variation in the contact stiffness well agreed with the effective stiffness of
a simple one-dimensional model, which is consistent with the fact that the
maximum depth range of the technique is far beyond the extent of the contact
stress field.Comment: 13 pages, 4 figures in main text; 7 pages, 5 figures in supplementary
informatio
Relaxed Bell inequalities as a trade-off relation between measurement dependence and hiddenness
Quantum correlations that violate the Bell inequality cannot be explained by
any (measurement independent) local hidden variable theory. However, the
violation only implies incompatibility of the underlying assumptions of
reality, locality, and measurement independence, and does not address the
extent to which each assumption is violated quantitatively. In contrast, Hall
(2010,2011) gave a quantification of each assumption and generalized the
Bell-CHSH inequality that gives a trade-off relationship between the underlying
assumptions. In this paper, we introduce a quantification of hidden variables
(hiddenness) and derive a new trade-off relation between the hiddenness and the
measurement dependency that holds for any local hidden variable theory.Comment: 10 page
Quantaloidal approach to constraint satisfaction
The constraint satisfaction problem (CSP) is a computational problem that
includes a range of important problems in computer science. We point out that
fundamental concepts of the CSP, such as the solution set of an instance and
polymorphisms, can be formulated abstractly inside the 2-category
of finite sets and sets of functions between them.
The 2-category is a quantaloid, and the
formulation relies mainly on structure available in any quantaloid. This
observation suggests a formal development of generalisations of the CSP and
concomitant notions of polymorphism in a large class of quantaloids. We extract
a class of optimisation problems as a special case, and show that their
computational complexity can be classified by the associated notion of
polymorphism.Comment: 17 page
The Fewest Clues Problem of Picross 3D
Picross 3D is a popular single-player puzzle video game for the Nintendo DS. It is a 3D variant of Nonogram, which is a popular pencil-and-paper puzzle. While Nonogram provides a rectangular grid of squares that must be filled in to create a picture, Picross 3D presents a rectangular parallelepiped (i.e., rectangular box) made of unit cubes, some of which must be removed to construct an image in three dimensions. Each row or column has at most one integer on it, and the integer indicates how many cubes in the corresponding 1D slice remain when the image is complete. It is shown by Kusano et al. that Picross 3D is NP-complete. We in this paper show that the fewest clues problem of Picross 3D is Sigma_2^P-complete and that the counting version and the another solution problem of Picross 3D are #P-complete and NP-complete, respectively
Molecular cloning and expression analysis of a gene encoding KUP/HAK/KT-type potassium uptake transporter from Cryptomeria japonica
Potassium ion (K+) is an essential and the most abundant intracellular cation in plants. The roles of K+ in various aspects of plant life are closely linked to its transport across biological membranes such as the plasma membrane and the tonoplast, which is mediated by membrane-bound transport proteins known as transporters and channels. Information on the molecular basis of K+ membrane transport in trees, especially in conifers, is currently limited. In this study, we isolated one complementary DNA, CjKUP1, which is homologous to known plant K+ transporters, from Cryptomeria japonica. Complementation tests using an Escherichia coli mutant, which is deficient in K+ uptake activity, was conducted to examine the K+ uptake function of the protein encoded by CjKUP1. Transformation of the K+-uptake-deficient mutant with CjKUP1 complemented the deficiency of this mutant. This result indicates that CjKUP1 has a function of K+ uptake. The expression levels of CjKUP1 in male strobili were markedly higher from late September to early October than in other periods. The expression levels in male and female strobili were higher than those in other organs such as needles, inner bark, differentiating xylem, and roots. These results indicate that CjKUP1 is mainly involved in K+ membrane transport in the cells of reproductive organs of C. japonica trees, especially in male strobili during pollen differentiation.ArticleTrees-Struct. Funct. 28(5):1527-1537 (2014)journal articl
Algorithms for Coloring Reconfiguration Under Recolorability Digraphs
In the k-Recoloring problem, we are given two (vertex-)colorings of a graph using k colors, and asked to transform one into the other by recoloring only one vertex at a time, while at all times maintaining a proper k-coloring. This problem is known to be solvable in polynomial time if k ? 3, and is PSPACE-complete if k ? 4. In this paper, we consider a (directed) recolorability constraint on the k colors, which forbids some pairs of colors to be recolored directly. The recolorability constraint is given in terms of a digraph R, whose vertices correspond to the colors and whose arcs represent the pairs of colors that can be recolored directly. We provide algorithms for the problem based on the structure of recolorability constraints R, showing that the problem is solvable in linear time when R is a directed cycle or is in a class of multitrees
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