5,738 research outputs found
The phase transition in random catalytic sets
The notion of (auto) catalytic networks has become a cornerstone in
understanding the possibility of a sudden dramatic increase of diversity in
biological evolution as well as in the evolution of social and economical
systems. Here we study catalytic random networks with respect to the final
outcome diversity of products. We show that an analytical treatment of this
longstanding problem is possible by mapping the problem onto a set of
non-linear recurrence equations. The solution of these equations show a crucial
dependence of the final number of products on the initial number of products
and the density of catalytic production rules. For a fixed density of rules we
can demonstrate the existence of a phase transition from a practically
unpopulated regime to a fully populated and diverse one. The order parameter is
the number of final products. We are able to further understand the origin of
this phase transition as a crossover from one set of solutions from a quadratic
equation to the other.Comment: 7 pages, ugly eps files due to arxiv restriction
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
On the Robustness of NK-Kauffman Networks Against Changes in their Connections and Boolean Functions
NK-Kauffman networks {\cal L}^N_K are a subset of the Boolean functions on N
Boolean variables to themselves, \Lambda_N = {\xi: \IZ_2^N \to \IZ_2^N}. To
each NK-Kauffman network it is possible to assign a unique Boolean function on
N variables through the function \Psi: {\cal L}^N_K \to \Lambda_N. The
probability {\cal P}_K that \Psi (f) = \Psi (f'), when f' is obtained through f
by a change of one of its K-Boolean functions (b_K: \IZ_2^K \to \IZ_2), and/or
connections; is calculated. The leading term of the asymptotic expansion of
{\cal P}_K, for N \gg 1, turns out to depend on: the probability to extract the
tautology and contradiction Boolean functions, and in the average value of the
distribution of probability of the Boolean functions; the other terms decay as
{\cal O} (1 / N). In order to accomplish this, a classification of the Boolean
functions in terms of what I have called their irreducible degree of
connectivity is established. The mathematical findings are discussed in the
biological context where, \Psi is used to model the genotype-phenotype map.Comment: 17 pages, 1 figure, Accepted in Journal of Mathematical Physic
Postcard: Hand Written Message Requesting an Agriculture Report
This black and white printed postcard contains correspondence from a man seeking information from another man. Handwriting is on the front and back of the card.https://scholars.fhsu.edu/tj_postcards/2169/thumbnail.jp
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
Quantum entanglement: The unitary 8-vertex braid matrix with imaginary rapidity
We study quantum entanglements induced on product states by the action of
8-vertex braid matrices, rendered unitary with purely imaginary spectral
parameters (rapidity). The unitarity is displayed via the "canonical
factorization" of the coefficients of the projectors spanning the basis. This
adds one more new facet to the famous and fascinating features of the 8-vertex
model. The double periodicity and the analytic properties of the elliptic
functions involved lead to a rich structure of the 3-tangle quantifying the
entanglement. We thus explore the complex relationship between topological and
quantum entanglement.Comment: 4 pages in REVTeX format, 2 figure
Attractors in fully asymmetric neural networks
The statistical properties of the length of the cycles and of the weights of
the attraction basins in fully asymmetric neural networks (i.e. with completely
uncorrelated synapses) are computed in the framework of the annealed
approximation which we previously introduced for the study of Kauffman
networks. Our results show that this model behaves essentially as a Random Map
possessing a reversal symmetry. Comparison with numerical results suggests that
the approximation could become exact in the infinite size limit.Comment: 23 pages, 6 figures, Latex, to appear on J. Phys.
Teleportation, Braid Group and Temperley--Lieb Algebra
We explore algebraic and topological structures underlying the quantum
teleportation phenomena by applying the braid group and Temperley--Lieb
algebra. We realize the braid teleportation configuration, teleportation
swapping and virtual braid representation in the standard description of the
teleportation. We devise diagrammatic rules for quantum circuits involving
maximally entangled states and apply them to three sorts of descriptions of the
teleportation: the transfer operator, quantum measurements and characteristic
equations, and further propose the Temperley--Lieb algebra under local unitary
transformations to be a mathematical structure underlying the teleportation. We
compare our diagrammatical approach with two known recipes to the quantum
information flow: the teleportation topology and strongly compact closed
category, in order to explain our diagrammatic rules to be a natural
diagrammatic language for the teleportation.Comment: 33 pages, 19 figures, latex. The present article is a short version
of the preprint, quant-ph/0601050, which includes details of calculation,
more topics such as topological diagrammatical operations and entanglement
swapping, and calls the Temperley--Lieb category for the collection of all
the Temperley--Lieb algebra with physical operations like local unitary
transformation
Landscape statistics of the p-spin Ising model
The statistical properties of the local optima (metastable states) of the
infinite range Ising spin glass with p-spin interactions in the presence of an
external magnetic field h are investigated analytically. The average number of
optima as well as the typical overlap between pairs of identical optima are
calculated for general p. Similarly to the thermodynamic order parameter, for
p>2 and small h the typical overlap q_t is a discontinuous function of the
energy. The size of the jump in q_t increases with p and decreases with h,
vanishing at finite values of the magnetic field.Comment: 12 pages,te
RE-ARCHITECTING AND RE-ENGINEERING TRADING AND TREASURY SYSTEMS IN THE MERGER OF CHEMICAL BANK AND MANUFACTURERS HANOVER TRUST -- An Interview with Brian Slater, Vice-President, Chemical Bank
This chapter presents an edited transcript of an interview held in
August 1993 with Brian Slater, a vice-president in the Global Bank at
Chemical Bank. Slater is responsible for the firm's U.S.-based trading
and global risk management systems. The interview was conducted in
the context of Project 1990s -- the U.S. Council for International
Banking's Study on Information Technology Investment and International
Banking Performance. The purpose of the discussion was to develop
background information on the issues the bank's senior management
team faced in merging the trading and treasury functions of Chemical
Bank and Manufacturers Hanover Trust. The new Global Bank faces
challenges in the areas of global risk management, cost-effective
delivery of in formation technology-based products, trading infrastructure
application functionality gaps, and human resource management that can be best addressed by a shift to a new paradigm for trading and
treasury application software development: reuse of object-oriented
representations of the bank's systems. We now turn to the details of
the discussion that develops these themes.Information Systems Working Papers Serie
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