The emergence of dynamical complexity: An exploration using elementary cellular automata

This work concerns the interaction between two classical problems: the forecasting of the dynamical behaviors of elementary cellular automata (ECA) from its intrinsic mathematical laws and the conditions that determine the emergence of complex dynamics. To approach these problems, and inspired by the theory of reversible logical gates, we decompose the ECA laws in a “spectrum” of dyadic Boolean gates. Emergent properties due to interactions are captured generating another spectrum of logical gates. The combined analysis of both spectra shows the existence of characteristic bias in the distribution of Boolean gates for ECA belonging to different dynamical classes. These results suggest the existence of signatures capable to indicate the propensity to develop complex dynamics. Logical gates “exclusive‐or” and “equivalence” are among these signatures of complexity. An important conclusion is that within ECA space, interactions are not capable to generate signatures of complexity in the case these signatures are absent in the intrinsic law of the automaton. © 2004 Wiley Periodicals, Inc. Complexity 9: 33–42, 2004     

Dihalodimethyltin(IV) complexes of 2‐(pyrazol‐1‐ylmethyl)pyridine

Reaction of dichloro‐ and dibromodimethyltin(IV) with 2‐(pyrazol‐1‐ylmethyl)pyridine (PMP) afforded [SnMe₂Cl₂(PMP)] and [SnMe₂Br₂(PMP)] respectively. The new complexes were characterized by elemental analysis and mass spectrometry and by IR, Raman and NMR (¹H, ¹³C) spectroscopies. Structural studies by X‐ray diffraction techniques show that the compounds consist of discrete units with the tin atom octahedrally coordinated to the carbon atoms of the two methyl groups in a trans disposition (Sn? C = 2.097(5), 2.120(5) Å and 2.110(6), 2.121(6) Å in the chloro and in the bromo compounds respectively), two cis halogen atoms (Sn? Cl = 2.4908(16), 2.5447(17) Å; Sn? Br = 2.6875(11), 2.7464(9) Å) and the two donor atoms of the ligand (Sn? N = 2.407(4), 2.471(4) Å and 2.360(5), 2.455(5) Å). In both cases, the Sn? N(pyridine) bond length is markedly longer than the Sn? N(pyrazole) distance. Copyright © 2003 John Wiley & Sons, Ltd.     

Applications of density functional theory methods in millimeter‐wave spectroscopy

Density functional theory (DFT), using the most common functionals, and ab initio quantum chemistry methods are used to calculate the rotational constants and dipole moments of the astrophysically important molecules HCN, CH₃CN, CH₃CNH⁺, HCCCN, and HCCNC. As far as millimeter‐wave spectroscopy is of interest the DFT methods performed well with most functionals, giving results within ±1% of experiments for rotational constants and ±3% for dipole moments. Analyzing the results obtained with all theoretical models, it may be concluded that the Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Paar (B3LYP) and Becke's three‐parameter functional with Perdew–Wang correlational functional [B3PW91/6‐31G(d, p)] give the best performances. A detailed analysis of the electron correlation effects shows that HCCCN is more stable than is HCCNC, by 1.16 eV, with important contribution arising from triple excitations. This result is also compared with those obtained with DFT methods. Despite occasional difficulties, DFT with the currently available functionals are of great utility in quickly assessing spectroscopic parameters of astrophysical interest. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Reactions on the dimethylphenylbenzacridinones. VI. Hydrogenation of ortho-nitrophenyl derivatives

Catalytic hydrogenation of o-nitrophenylbenz[a], benz[c], dibenz[a,h] and dibenz[a,g]acridinones using Pd/C as catalyst, at 60 psi of pressure, gave the hiterto unknown benzoquinoacridine N-oxides and benzo-pyranonaphthyridine N-oxides. The structure of all products was corroborated by ir, ¹H- and ¹³C-nmr and mass spectra data.     

A Characterization of Cosmological Time Functions

A characterization of time functions on a spacetime is made by using theMöbius equation. It is shown that a time function characterized in this wayyields past timelike geodesic incompleteness and local Lorentzian warpedproduct decomposition of spacetime, provided that the stress-energy tensoris a fluid. Also, by imposing additional assumptions on the stress-energytensor and global analytic structure of the spacetime, more restrictivedecompositions closer to Robertson–Walker spacetimes are obtained.     

Formulation of N- and ν-representable density functional theory. V. Exchange-only self-consistent field

The concept of a self-consistent field is developed within the version of density functional theory based on local-scaling transformations. It is shown that in this context there arise two types of consistency: one relating to the charge-consistency within an orbit and another to “orbit jumping.” The latter is analyzed in terms of one-particle equations. The connection with other methods is discussed. © 1992 John Wiley & Sons, Inc.     

An infinite-time relaxation theorem for differential inclusions

The fundamental relaxation result for Lipschitz differential inclusions is the Filippov-Wazewski Relaxation Theorem, which provides approximations of trajectories of a relaxed inclusion on finite intervals. A complementary result is presented, which provides approximations on infinite intervals, but does not guarantee that the approximation and the reference trajectory satisfy the same initial condition.

     

Reference priors for exponential families with simple quadratic variance function

Reference analysis is one of the most successful general methods to derive noninformative prior distributions. In practice, however, reference priors are often difficult to obtain. Recently developed theory for conditionally reducible natural exponential families identifies an attractive reparameterization which allows one, among other things, to construct an enriched conjugate prior. In this paper, under the assumption that the variance function is simple quadratic, the order-invariant group reference prior for the above parameter is found. Furthermore, group reference priors for the mean- and natural parameter of the families are obtained. A brief discussion of the frequentist coverage properties is also presented. The theory is illustrated for the multinomial and negative-multinomial family. Posterior computations are especially straightforward due to the fact that the resulting reference distributions belong to the corresponding enriched conjugate family. A substantive application of the theory relates to the construction of reference priors for the Bayesian analysis of two-way contingency tables with respect to two alternative parameterizations.     

Diffusion in three-dimensional random systems at their percolation thresholds

Extensive Monte Carlo simulations of theant-in-the-labyrinth problem on randomL* L* L simple cubic lattices are performed, forL up to 960 on a CRAY-YMP supercomputer. The exponentk for the rms displacementr witht inrt ^k is found to bek=0.190±0.003. As a second approach, large percolation clusters with chemical shells up to 300 are generated on a simple cubic lattice at criticality. The diffusion equation is then solved by using the exact enumeration technique. The corresponding critical exponentd ^w is found to be 1/d ^w =0.250±0.003.On leave from I. Institut für Theoretische für Physik, Universität Hamburg, D-2000 Hamburg, Federal Republic of Germany.     

Monotone Chemical Reaction Networks

We analyze certain chemical reaction networks and show that every solution converges to some steady state. The reaction kinetics are assumed to be monotone but otherwise arbitrary. When diffusion effects are taken into account, the conclusions remain unchanged. The main tools used in our analysis come from the theory of monotone dynamical systems. We review some of the features of this theory and provide a self-contained proof of a particular attractivity result which is used in proving our main result.