5,294 research outputs found
Closing probabilities in the Kauffman model: an annealed computation
We define a probabilistic scheme to compute the distributions of periods,
transients and weigths of attraction basins in Kauffman networks. These
quantities are obtained in the framework of the annealed approximation, first
introduced by Derrida and Pomeau. Numerical results are in good agreement with
the computed values of the exponents of average periods, but show also some
interesting features which can not be explained whithin the annealed
approximation.Comment: latex, 36 pages, figures added in uufiles format,error in epsffile
nam
Schechter vs. Schechter: Sub-Arcsecond Gravitational Lensing and Inner Halo Profiles
Sub-arcsecond lensing statistics depend sensitively on the inner mass
profiles of low-mass objects and the faint-end slopes of the Schechter
luminosity function and the Press-Schechter mass function. By requiring the
luminosity and mass functions to give consistent predictions for the
distribution of image separation below 1'', we show that dark matter halos with
masses below 10^12 M_sun cannot have a single type of profile, be it the
singular isothermal sphere (SIS) or the shallower ``universal'' dark matter
profile. Instead, consistent results are achieved if we allow a fraction of the
halos at a given mass to be luminous with the SIS profile, and the rest be dark
with an inner logarithmic slope shallower than -1.5 to compensate for the
steeper faint-end slope of the mass function compared with the luminosity
function. We quantify how rapidly the SIS fraction must decrease with
decreasing halo mass, thereby providing a statistical measure for the
effectiveness of feedback processes on the baryon content in low-mass halos.Comment: 13 pages, 4 figures. CLASS lensing data added; minor revisions. ApJL
in pres
A determinant formula for the Jones polynomial of pretzel knots
This paper presents an algorithm to construct a weighted adjacency matrix of
a plane bipartite graph obtained from a pretzel knot diagram. The determinant
of this matrix after evaluation is shown to be the Jones polynomial of the
pretzel knot by way of perfect matchings (or dimers) of this graph. The weights
are Tutte's activity letters that arise because the Jones polynomial is a
specialization of the signed version of the Tutte polynomial. The relationship
is formalized between the familiar spanning tree setting for the Tait graph and
the perfect matchings of the plane bipartite graph above. Evaluations of these
activity words are related to the chain complex for the Champanerkar-Kofman
spanning tree model of reduced Khovanov homology.Comment: 19 pages, 12 figures, 2 table
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
Spiders for rank 2 Lie algebras
A spider is an axiomatization of the representation theory of a group,
quantum group, Lie algebra, or other group or group-like object. We define
certain combinatorial spiders by generators and relations that are isomorphic
to the representation theories of the three rank two simple Lie algebras,
namely A2, B2, and G2. They generalize the widely-used Temperley-Lieb spider
for A1. Among other things, they yield bases for invariant spaces which are
probably related to Lusztig's canonical bases, and they are useful for
computing quantities such as generalized 6j-symbols and quantum link
invariants.Comment: 33 pages. Has color figure
Family Preservation: Perceptions of Effectiveness
This qualitative study examines the attributes or perceptions of service providers and overseers as to the effectiveness of intensive family preservation services provided by a social services agency in Tucson, Arizona. The services provided are patterned after the Homebuilders\u27 model developed in 1974 in Tacoma, Washington. Data collection was generated from interviews and focus groups with the in-home service providers, the program supervisor, and investigators and case managers with Child Protective Services (CPS). Although placement prevention rates (PPR) are the dependent variable in most studies on this form of intervention, this study seeks to understand those characteristics of the model that contribute to successful outcomes with client families. Those appear to be the short-term intervention coupled with a non-judgmental approach to client families and the clinical supervision provided by the program supervisor
Relevant elments, Magnetization and Dynamical Properties in Kauffman Networks: a Numerical Study
This is the first of two papers about the structure of Kauffman networks. In
this paper we define the relevant elements of random networks of automata,
following previous work by Flyvbjerg and Flyvbjerg and Kjaer, and we study
numerically their probability distribution in the chaotic phase and on the
critical line of the model. A simple approximate argument predicts that their
number scales as sqrt(N) on the critical line, while it is linear with N in the
chaotic phase and independent of system size in the frozen phase. This argument
is confirmed by numerical results. The study of the relevant elements gives
useful information about the properties of the attractors in critical networks,
where the pictures coming from either approximate computation methods or from
simulations are not very clear.Comment: 22 pages, Latex, 8 figures, submitted to Physica
The computational complexity of Kauffman nets and the P versus NP problem
Complexity theory as practiced by physicists and computational complexity
theory as practiced by computer scientists both characterize how difficult it
is to solve complex problems. Here it is shown that the parameters of a
specific model can be adjusted so that the problem of finding its global energy
minimum is extremely sensitive to small changes in the problem statement. This
result has implications not only for studies of the physics of random systems
but may also lead to new strategies for resolving the well-known P versus NP
question in computational complexity theory.Comment: 4 pages, no figure
The Great Tone Split and Central Karen
This thesis is a comparative reconstruction of the tones and initial consonants of Proto-Central Karen based on the languages Eastern Kayah, Wetern Kayah, Geba, and Padaung. Other Karen languages are referred to but not studied to the same detail.
The study focuses on the great tone split that affected nearly all the languages of Southeast Asia, including Central Karen. I show that an understanding of the great tone split is crucial if one is to discover the phonological characteristics of Proto-Central Karen syllable-initial consonants.
In agreement with Haudricourt\u27s (1946) analysis of Proto-Karen, I conclude that Proto-Central Karen had three proto-tones and a series of voiceless sonorants, and was affected by a great tone split in which the sets of voiced and voiceless consonants merged and the three proto-tones split. These are different conclusions than those drawn by two other major reconstructions of Proto-Karen, Jones (1961) and Burling (1969)
Quantum entanglement, unitary braid representation and Temperley-Lieb algebra
Important developments in fault-tolerant quantum computation using the
braiding of anyons have placed the theory of braid groups at the very
foundation of topological quantum computing. Furthermore, the realization by
Kauffman and Lomonaco that a specific braiding operator from the solution of
the Yang-Baxter equation, namely the Bell matrix, is universal implies that in
principle all quantum gates can be constructed from braiding operators together
with single qubit gates. In this paper we present a new class of braiding
operators from the Temperley-Lieb algebra that generalizes the Bell matrix to
multi-qubit systems, thus unifying the Hadamard and Bell matrices within the
same framework. Unlike previous braiding operators, these new operators
generate {\it directly}, from separable basis states, important entangled
states such as the generalized Greenberger-Horne-Zeilinger states, cluster-like
states, and other states with varying degrees of entanglement.Comment: 5 pages, no figur
- …