3,871 research outputs found
Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces
We study the general deformed conformal-Poincare (Galilean) symmetries
consistent with relativistic (nonrelativistic) canonical noncommutative spaces.
In either case we obtain deformed generators, containing arbitrary free
parameters, which close to yield new algebraic structures. We show that a
particular choice of these parameters reproduces the undeformed algebra. The
modified coproduct rules and the associated Hopf algebra are also obtained.
Finally, we show that for the choice of parameters leading to the undeformed
algebra, the deformations are represented by twist functions.Comment: 9 pages, LaTeX, shortened, version appearing in Phys. Rev.
Metastable tight knots in a worm-like polymer
Based on an estimate of the knot entropy of a worm-like chain we predict that
the interplay of bending energy and confinement entropy will result in a
compact metastable configuration of the knot that will diffuse, without
spreading, along the contour of the semi-flexible polymer until it reaches one
of the chain ends. Our estimate of the size of the knot as a function of its
topological invariant (ideal aspect ratio) agrees with recent experimental
results of knotted dsDNA. Further experimental tests of our ideas are proposed.Comment: 4 pages, 3 figure
Remarks on the Noncommutative Gravitational Quantum Well
A planar phase space having both position and momentum noncommutativity is
defined in a more inclusive setting than that considered elsewhere. The
dynamics of a particle in a gravitational quantum well in this space is
studied. The use of the WKB approximation and the virial theorem enable
analytic discussions on the effect of noncommutativity. Consistent results are
obtained following either commutative space or noncommutative space
descriptions. Comparison with recent experimental data with cold neutrons at
Grenoble imposes an upper bound on the noncommutative parameter. Also, our
results are compared with a recent numerical analysis of a similar problem.Comment: Latex, 17 pages, Title changed, minor modifications, 3 new references
added, To appear in Phys. Rev.
The Mythology of Game Theory
Non-cooperative game theory is at its heart a theory of cognition, specifically a theory of how decisions are made. Game theory\u27s leverage is that we can design different payoffs, settings, player arrays, action possibilities, and information structures, and that these differences lead to different strategies, outcomes, and equilibria. It is well-known that, in experimental settings, people do not adopt the predicted strategies, outcomes, and equilibria. The standard response to this mismatch of prediction and observation is to add various psychological axioms to the game-theoretic framework. Regardless of the differing specific proposals and results, game theory uniformly makes certain cognitive assumptions that seem rarely to be acknowledged, much less interrogated. Indeed, it is not widely understood that game theory is essentially a cognitive theory. Here, we interrogate those cognitive assumptions. We do more than reject specific predictions from specific games. More broadly, we reject the underlying cognitive model implicitly assumed by game theory
DNA in nanopore-counterion condensation and coion depletion
Molecular dynamics simulations are used to study the equilibrium distribution
of monovalent ions in a nanopore connecting two water reservoirs separated by a
membrane, both for the empty pore and that with a single stranded DNA molecule
inside. In the presence of DNA, the counterions condense on the stretched
macromolecule effectively neutralizing it, and nearly complete depletion of
coions from the pore is observed. The implications of our results for
experiments on DNA translocation through alpha-hemolysin nanopores are
discussed.Comment: 8 pages, 2 figure
Verification of PCP-Related Computational Reductions in Coq
We formally verify several computational reductions concerning the Post
correspondence problem (PCP) using the proof assistant Coq. Our verifications
include a reduction of a string rewriting problem generalising the halting
problem for Turing machines to PCP, and reductions of PCP to the intersection
problem and the palindrome problem for context-free grammars. Interestingly,
rigorous correctness proofs for some of the reductions are missing in the
literature
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