Computing with cells: membrane systems - some complexity issues.

Membrane computing is a branch of natural computing which abstracts computing models from the structure and the functioning of the living cell. The main ingredients of membrane systems, called P systems, are (i) the membrane structure, which consists of a hierarchical arrangements of membranes which delimit compartments where (ii) multisets of symbols, called objects, evolve according to (iii) sets of rules which are localised and associated with compartments. By using the rules in a nondeterministic/deterministic maximally parallel manner, transitions between the system configurations can be obtained. A sequence of transitions is a computation of how the system is evolving. Various ways of controlling the transfer of objects from one membrane to another and applying the rules, as well as possibilities to dissolve, divide or create membranes have been studied. Membrane systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems once future biotechnology gives way to a practical bio-realization. In this paper we survey some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism

Experimental analysis of lateral impact on planar brittle material

The fragmentation of alumina and glass plates due to lateral impact is studied. A few hundred plates have been fragmented at different impact velocities and the produced fragments are analyzed. The method employed in this work allows one to investigate some geometrical properties of the fragments, besides the traditional size distribution usually studied in former experiments. We found that, although both materials exhibit qualitative similar fragment size distribution function, their geometrical properties appear to be quite different. A schematic model for two-dimensional fragmentation is also presented and its predictions are compared to our experimental results. The comparison suggests that the analysis of the fragments' geometrical properties constitutes a more stringent test of the theoretical models' assumptions than the size distribution

Statistical Mechanics of Linear and Nonlinear Time-Domain Ensemble Learning

Conventional ensemble learning combines students in the space domain. In this paper, however, we combine students in the time domain and call it time-domain ensemble learning. We analyze, compare, and discuss the generalization performances regarding time-domain ensemble learning of both a linear model and a nonlinear model. Analyzing in the framework of online learning using a statistical mechanical method, we show the qualitatively different behaviors between the two models. In a linear model, the dynamical behaviors of the generalization error are monotonic. We analytically show that time-domain ensemble learning is twice as effective as conventional ensemble learning. Furthermore, the generalization error of a nonlinear model features nonmonotonic dynamical behaviors when the learning rate is small. We numerically show that the generalization performance can be improved remarkably by using this phenomenon and the divergence of students in the time domain.Comment: 11 pages, 7 figure

Ensemble learning of linear perceptron; Online learning theory

Within the framework of on-line learning, we study the generalization error of an ensemble learning machine learning from a linear teacher perceptron. The generalization error achieved by an ensemble of linear perceptrons having homogeneous or inhomogeneous initial weight vectors is precisely calculated at the thermodynamic limit of a large number of input elements and shows rich behavior. Our main findings are as follows. For learning with homogeneous initial weight vectors, the generalization error using an infinite number of linear student perceptrons is equal to only half that of a single linear perceptron, and converges with that of the infinite case with O(1/K) for a finite number of K linear perceptrons. For learning with inhomogeneous initial weight vectors, it is advantageous to use an approach of weighted averaging over the output of the linear perceptrons, and we show the conditions under which the optimal weights are constant during the learning process. The optimal weights depend on only correlation of the initial weight vectors.Comment: 14 pages, 3 figures, submitted to Physical Review

Theoretical Investigation of Laser Induced Desorption of Small Molecules from Oxide Surfaces: A First Principles Study

State resolved laser induced desorption of NO molecules from a NiO(100) surface is studied theoretically. A full potential energy surface for the excited state was constructed by means of ab initio cluster calculations in addition to the potential energy surface for the ground state. Multidimensional wave packet calculations on these two surfaces allow a detailed simulation of experimental observables, such as velocity distributions and desorption probabilities, on a full ab initio basis

Magnetism and d-wave superconductivity on the half-filled square lattice with frustration

The role of frustration and interaction strength on the half-filled Hubbard model is studied on the square lattice with nearest and next-nearest neighbour hoppings t and t' using the Variational Cluster Approximation (VCA). At half-filling, we find two phases with long-range antiferromagnetic (AF) order: the usual Neel phase, stable at small frustration t'/t, and the so-called collinear (or super-antiferromagnet) phase with ordering wave-vector $(\pi,0)$ or $(0,\pi)$, stable for large frustration. These are separated by a phase with no detectable long-range magnetic order. We also find the d-wave superconducting (SC) phase ($d_{x^2-y^2}$), which is favoured by frustration if it is not too large. Intriguingly, there is a broad region of coexistence where both AF and SC order parameters have non-zero values. In addition, the physics of the metal-insulator transition in the normal state is analyzed. The results obtained with the help of the VCA method are compared with the large-U expansion of the Hubbard model and known results for the frustrated J1-J2 Heisenberg model. These results are relevant for pressure studies of undoped parents of the high-temperature superconductors: we predict that an insulator to d-wave SC transition may appear under pressure.Comment: 12 pages, 10 figure

Mott transition in one dimension: Benchmarking dynamical cluster approaches

The variational cluster approach (VCA) is applied to the one-dimensional Hubbard model at zero temperature using clusters (chains) of up to ten sites with full diagonalization and the Lanczos method as cluster solver. Within the framework of the self-energy-functional theory (SFT), different cluster reference systems with and without bath degrees of freedom, in different topologies and with different sets of variational parameters are considered. Static and one-particle dynamical quantities are calculated for half-filling as a function of U as well as for fixed U as a function of the chemical potential to study the interaction- and filling-dependent metal-insulator (Mott) transition. The recently developed Q-matrix technique is used to compute the SFT grand potential. For benchmarking purposes we compare the VCA results with exact results available from the Bethe ansatz, with essentially exact dynamical DMRG data, with (cellular) dynamical mean-field theory and full diagonalization of isolated Hubbard chains. Several issues are discussed including convergence of the results with cluster size, the ability of cluster approaches to access the critical regime of the Mott transition, efficiency in the optimization of correlated-site vs. bath-site parameters and of multi-dimensional parameter optimization. We also study the role of bath sites for the description of excitation properties and as charge reservoirs for the description of filling dependencies. The VCA turns out to be a computationally cheap method which is competitive with established cluster approaches.Comment: 19 pages, 19 figures, v3 with minor corrections, extended discussio