4,299 research outputs found
The Number of Different Binary Functions Generated by NK-Kauffman Networks and the Emergence of Genetic Robustness
We determine the average number , of \textit{NK}-Kauffman
networks that give rise to the same binary function. We show that, for , there exists a connectivity critical value such that () for and
for . We find that is not a
constant, but scales very slowly with , as . The problem of genetic robustness emerges as a statistical property
of the ensemble of \textit{NK}-Kauffman networks and impose tight constraints
in the average number of epistatic interactions that the genotype-phenotype map
can have.Comment: 4 figures 18 page
Self-Reduction Rate of a Microtubule
We formulate and study a quantum field theory of a microtubule, a basic
element of living cells. Following the quantum theory of consciousness by
Hameroff and Penrose, we let the system to reduce to one of the classical
states without measurement if certain conditions are
satisfied(self-reductions), and calculate the self-reduction time (the
mean interval between two successive self-reductions) of a cluster consisting
of more than neighboring tubulins (basic units composing a microtubule).
is interpreted there as an instance of the stream of consciousness. We
analyze the dependence of upon and the initial conditions, etc.
For relatively large electron hopping amplitude, obeys a power law
, which can be explained by the percolation theory. For
sufficiently small values of the electron hopping amplitude, obeys an
exponential law, . By using this law, we estimate the
condition for to take realistic values
\raisebox{-0.5ex}{} sec as \raisebox{-0.5ex}
{} 1000.Comment: 7 pages, 9 figures, Extended versio
On the Quantum Computational Complexity of the Ising Spin Glass Partition Function and of Knot Invariants
It is shown that the canonical problem of classical statistical
thermodynamics, the computation of the partition function, is in the case of
+/-J Ising spin glasses a particular instance of certain simple sums known as
quadratically signed weight enumerators (QWGTs). On the other hand it is known
that quantum computing is polynomially equivalent to classical probabilistic
computing with an oracle for estimating QWGTs. This suggests a connection
between the partition function estimation problem for spin glasses and quantum
computation. This connection extends to knots and graph theory via the
equivalence of the Kauffman polynomial and the partition function for the Potts
model.Comment: 8 pages, incl. 2 figures. v2: Substantially rewritte
The Asymptotic Number of Attractors in the Random Map Model
The random map model is a deterministic dynamical system in a finite phase
space with n points. The map that establishes the dynamics of the system is
constructed by randomly choosing, for every point, another one as being its
image. We derive here explicit formulas for the statistical distribution of the
number of attractors in the system. As in related results, the number of
operations involved by our formulas increases exponentially with n; therefore,
they are not directly applicable to study the behavior of systems where n is
large. However, our formulas lend themselves to derive useful asymptotic
expressions, as we show.Comment: 16 pages, 1 figure. Minor changes. To be published in Journal of
Physics A: Mathematical and Genera
Quantum logic as superbraids of entangled qubit world lines
Presented is a topological representation of quantum logic that views
entangled qubit spacetime histories (or qubit world lines) as a generalized
braid, referred to as a superbraid. The crossing of world lines is purely
quantum in nature, most conveniently expressed analytically with
ladder-operator-based quantum gates. At a crossing, independent world lines can
become entangled. Complicated superbraids are systematically reduced by
recursively applying novel quantum skein relations. If the superbraid is closed
(e.g. representing quantum circuits with closed-loop feedback, quantum lattice
gas algorithms, loop or vacuum diagrams in quantum field theory), then one can
decompose the resulting superlink into an entangled superposition of classical
links. In turn, for each member link, one can compute a link invariant, e.g.
the Jones polynomial. Thus, a superlink possesses a unique link invariant
expressed as an entangled superposition of classical link invariants.Comment: 4 page
Canonical quantization of general relativity in discrete space-times
It has long been recognized that lattice gauge theory formulations, when
applied to general relativity, conflict with the invariance of the theory under
diffeomorphisms. Additionally, the traditional lattice field theory approach
consists in fixing the gauge in a Euclidean action, which does not appear
appropriate for general relativity. We analyze discrete lattice general
relativity and develop a canonical formalism that allows to treat constrained
theories in Lorentzian signature space-times. The presence of the lattice
introduces a ``dynamical gauge'' fixing that makes the quantization of the
theories conceptually clear, albeit computationally involved. Among other
issues the problem of a consistent algebra of constraints is automatically
solved in our approach. The approach works successfully in other field theories
as well, including topological theories like BF theory. We discuss a simple
cosmological application that exhibits the quantum elimination of the
singularity at the big bang.Comment: 4 pages, RevTeX, no figures, final version to appear in Physical
Review Letter
Self-organized Networks of Competing Boolean Agents
A model of Boolean agents competing in a market is presented where each agent
bases his action on information obtained from a small group of other agents.
The agents play a competitive game that rewards those in the minority. After a
long time interval, the poorest player's strategy is changed randomly, and the
process is repeated. Eventually the network evolves to a stationary but
intermittent state where random mutation of the worst strategy can change the
behavior of the entire network, often causing a switch in the dynamics between
attractors of vastly different lengths.Comment: 4 pages, 3 included figures. Some text revision and one new figure
added. To appear in PR
Distinguishing scalar from pseudoscalar Higgs production at the LHC
In this letter we examine the production channels for the scalar or
pseudoscalar Higgs plus two jets at the CERN Large Hadron Collider (LHC). We
identify possible signals for distinguishing between a scalar and a
pseudoscalar Higgs boson.Comment: 7 pages, REVTeX4, 4 eps figures. Figure 1 and 4 replaced. Typos
corrected, additional reference adde
Lens Spaces and Handlebodies in 3D Quantum Gravity
We calculate partition functions for lens spaces L_{p,q} up to p=8 and for
genus 1 and 2 handlebodies H_1, H_2 in the Turaev-Viro framework. These can be
interpreted as transition amplitudes in 3D quantum gravity. In the case of lens
spaces L_{p,q} these are vacuum-to-vacuum amplitudes \O -> \O, whereas for
the 1- and 2-handlebodies H_1, H_2 they represent genuinely topological
transition amplitudes \O -> T^2 and \O -> T^2 # T^2, respectively.Comment: 14 pages, LaTeX, 5 figures, uses eps
Critical Networks Exhibit Maximal Information Diversity in Structure-Dynamics Relationships
Network structure strongly constrains the range of dynamic behaviors
available to a complex system. These system dynamics can be classified based on
their response to perturbations over time into two distinct regimes, ordered or
chaotic, separated by a critical phase transition. Numerous studies have shown
that the most complex dynamics arise near the critical regime. Here we use an
information theoretic approach to study structure-dynamics relationships within
a unified framework and how that these relationships are most diverse in the
critical regime
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