4,777 research outputs found
NP-complete Problems and Physical Reality
Can NP-complete problems be solved efficiently in the physical universe? I
survey proposals including soap bubbles, protein folding, quantum computing,
quantum advice, quantum adiabatic algorithms, quantum-mechanical
nonlinearities, hidden variables, relativistic time dilation, analog computing,
Malament-Hogarth spacetimes, quantum gravity, closed timelike curves, and
"anthropic computing." The section on soap bubbles even includes some
"experimental" results. While I do not believe that any of the proposals will
let us solve NP-complete problems efficiently, I argue that by studying them,
we can learn something not only about computation but also about physics.Comment: 23 pages, minor correction
Issues of Reggeization in Back-Angle Scattering
The Kirschner-Lipatov result for the DLLA of high-energy backward
scattering is re-derived without the use of integral equations. It is shown
that part of the inequalities between the variables in the
logarithmically-divergent integrals is inconsequential. The light-cone
wave-function interpretation under the conditions of backward scattering is
discussed. It is argued that for hadron-hadron scattering in the valence-quark
model the reggeization should manifest itself at full strength starting from
.Comment: 10 Pages, 2 Figures. To appear in Proc. of Int. Conf. "New Trends in
High Energy Physics", 27 Sept.-4 Oct. 2008, Yalta, Crimea, Ukrain
Epistemic virtues, metavirtues, and computational complexity
I argue that considerations about computational complexity show that all finite agents need characteristics like those that have been called epistemic virtues. The necessity of these virtues follows in part from the nonexistence of shortcuts, or efficient ways of finding shortcuts, to cognitively expensive routines. It follows that agents must possess the capacities – metavirtues –of developing in advance the cognitive virtues they will need when time and memory are at a premium
Why Philosophers Should Care About Computational Complexity
One might think that, once we know something is computable, how efficiently
it can be computed is a practical question with little further philosophical
importance. In this essay, I offer a detailed case that one would be wrong. In
particular, I argue that computational complexity theory---the field that
studies the resources (such as time, space, and randomness) needed to solve
computational problems---leads to new perspectives on the nature of
mathematical knowledge, the strong AI debate, computationalism, the problem of
logical omniscience, Hume's problem of induction, Goodman's grue riddle, the
foundations of quantum mechanics, economic rationality, closed timelike curves,
and several other topics of philosophical interest. I end by discussing aspects
of complexity theory itself that could benefit from philosophical analysis.Comment: 58 pages, to appear in "Computability: G\"odel, Turing, Church, and
beyond," MIT Press, 2012. Some minor clarifications and corrections; new
references adde
Long Proteins with Unique Optimal Foldings in the H-P Model
It is widely accepted that (1) the natural or folded state of proteins is a
global energy minimum, and (2) in most cases proteins fold to a unique state
determined by their amino acid sequence. The H-P (hydrophobic-hydrophilic)
model is a simple combinatorial model designed to answer qualitative questions
about the protein folding process. In this paper we consider a problem
suggested by Brian Hayes in 1998: what proteins in the two-dimensional H-P
model have unique optimal (minimum energy) foldings? In particular, we prove
that there are closed chains of monomers (amino acids) with this property for
all (even) lengths; and that there are open monomer chains with this property
for all lengths divisible by four.Comment: 22 pages, 18 figure
Defect-induced local electronic structure modifications within the system SrO - SrTiO3 - TiO2: symmetry and disorder
Owing to their versatile orbital character with both local and highly dispersive degrees of freedom, transition metal oxides span the range of ionic, covalent and metallic bonding. They exhibit a vast diversity of electronic phenomena such as high dielectric, piezoelectric, pyroelectric, ferroelectric, magnetic, multiferroic, catalytic, redox, and superconductive properties. The nature of these properties arises from sensitive details in the electronic structure, e.g. orbital mixing and orbital hybridization, due to non-stoichiometry, atomic displacements, broken symmetries etc., and their coupling with external perturbations.
In the work presented here, these variations of the electronic structure of crystals due to structural and electronic defects have been investigated, exemplarily for the quasi-binary system SrO - SrTiO3 - TiO2. A number of binary and ternary structures have been studied, both experimentally as well as by means of electronic modeling. The applied methods comprise Resonant X-ray Scattering techniques like Diffraction Anomalous Fine Structure, Anisotropy of Anomalous Scattering and X-ray Absorption Fine Structure, and simultaneously extensive electronic calculations by means of Density Functional Theory and Finite Difference Method Near-Edge Structure to gain a thorough physical understanding of the underlying processes, interactions and dynamics.
It is analyzed in detail how compositional variations, e.g. manifesting as oxygen vacancies or ordered stacking faults, alter the short-range order and affect the electronic structure, and how the severe changes in mechanical, optical, electrical as well as electrochemical properties evolve. Various symmetry-property relations have been concluded and interpreted on the basis of these modifications in electronic structure for the orbital structure in rutile TiO2, for distorted TiO6 octahedra and related switching mechanisms of the Ti valence, for elasticity and resistivity in strontium titanate, and for surface relaxations in Ruddlesden-Popper phases.
Highlights of the thesis include in particular the methodical development regarding Resonant X-Ray Diffraction, such as the first use of partially forbidden reflections to get the complete phase information not only of the tensorial structure factor but of each individual atomic scattering tensor for a whole spectrum of energies, as well as the determination of orbital degrees of freedom and details of the partial local density of states from these tensors.
On the material side, the most prominent results are the identification of the migration-induced field-stabilized polar phase and the exergonic redox behavior in SrTiO3 caused by defect migration and defect separation
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