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 $\vartheta (N, K)$, of \textit{NK}-Kauffman networks that give rise to the same binary function. We show that, for $N \gg 1$, there exists a connectivity critical value $K_c$ such that $\vartheta(N,K) \approx e^{\phi N}$ ($\phi > 0$) for $K < K_c$ and $\vartheta(N,K) \approx 1$ for $K > K_c$. We find that $K_c$ is not a constant, but scales very slowly with $N$, as $K_c \approx \log_2 \log_2 (2N / \ln 2)$. 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