100,853 research outputs found
On the Triality Theory for a Quartic Polynomial Optimization Problem
This paper presents a detailed proof of the triality theorem for a class of
fourth-order polynomial optimization problems. The method is based on linear
algebra but it solves an open problem on the double-min duality left in 2003.
Results show that the triality theory holds strongly in a tri-duality form if
the primal problem and its canonical dual have the same dimension; otherwise,
both the canonical min-max duality and the double-max duality still hold
strongly, but the double-min duality holds weakly in a symmetrical form. Four
numerical examples are presented to illustrate that this theory can be used to
identify not only the global minimum, but also the largest local minimum and
local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011.
arXiv admin note: substantial text overlap with arXiv:1104.297
Analytical Solutions to General Anti-Plane Shear Problems In Finite Elasticity
This paper presents a pure complementary energy variational method for
solving anti-plane shear problem in finite elasticity. Based on the canonical
duality-triality theory developed by the author, the nonlinear/nonconex partial
differential equation for the large deformation problem is converted into an
algebraic equation in dual space, which can, in principle, be solved to obtain
a complete set of stress solutions. Therefore, a general analytical solution
form of the deformation is obtained subjected to a compatibility condition.
Applications are illustrated by examples with both convex and nonconvex stored
strain energies governed by quadratic-exponential and power-law material
models, respectively. Results show that the nonconvex variational problem could
have multiple solutions at each material point, the complementary gap function
and the triality theory can be used to identify both global and local extremal
solutions, while the popular (poly-, quasi-, and rank-one) convexities provide
only local minimal criteria, the Legendre-Hadamard condition does not guarantee
uniqueness of solutions. This paper demonstrates again that the pure
complementary energy principle and the triality theory play important roles in
finite deformation theory and nonconvex analysis.Comment: 23 pages, 4 figures. Mathematics and Mechanics of Solids, 201
Interacting cells driving the evolution of multicellular life cycles
Author summary Multicellular organisms are ubiquitous. But how did the first multicellular organisms arise? It is typically argued that this occurred due to benefits coming from interactions between cells. One example of such interactions is the division of labour. For instance, colonial cyanobacteria delegate photosynthesis and nitrogen fixation to different cells within the colony. In this way, the colony gains a growth advantage over unicellular cyanobacteria. However, not all cell interactions favour multicellular life. Cheater cells residing in a colony without any contribution will outgrow other cells. Then, the growing burden of cheaters may eventually destroy the colony. Here, we ask what kinds of interactions promote the evolution of multicellularity? We investigated all interactions captured by pairwise games and for each of them, we look for the evolutionarily optimal life cycle: How big should the colony grow and how should it split into offspring cells or colonies? We found that multicellularity can evolve with interactions far beyond cooperation or division of labour scenarios. More surprisingly, most of the life cycles found fall into either of two categories: A parent colony splits into two multicellular parts, or it splits into multiple independent cells
Astronomy: Starbursts near and far
Observations of intensely bright star-forming galaxies both close by and in
the distant Universe at first glance seem to emphasize their similarity. But
look a little closer, and differences emerge.Comment: 6 pages including 1 figur
An Analysis of Phase Transition in NK Landscapes
In this paper, we analyze the decision version of the NK landscape model from
the perspective of threshold phenomena and phase transitions under two random
distributions, the uniform probability model and the fixed ratio model. For the
uniform probability model, we prove that the phase transition is easy in the
sense that there is a polynomial algorithm that can solve a random instance of
the problem with the probability asymptotic to 1 as the problem size tends to
infinity. For the fixed ratio model, we establish several upper bounds for the
solubility threshold, and prove that random instances with parameters above
these upper bounds can be solved polynomially. This, together with our
empirical study for random instances generated below and in the phase
transition region, suggests that the phase transition of the fixed ratio model
is also easy
Meter-baseline tests of sterile neutrinos at Daya Bay
We explore the sensitivity of an experiment at the Daya Bay site, with a
point radioactive source and a few meter baseline, to neutrino oscillations
involving one or more eV mass sterile neutrinos. We find that within a year,
the entire 3+2 and 1+3+1 parameter space preferred by global fits can be
excluded at the 3\sigma level, and if an oscillation signal is found, the 3+1
and 3+2 scenarios can be distinguished from each other at more than the 3\sigma
level provided one of the sterile neutrinos is lighter than 0.5 eV.Comment: 4 pages, 5 figures, 1 table. Version to appear in PL
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