Self-assembly of discrete self-similar fractals

In this paper, we search for theoretical limitations of the Tile Assembly Model (TAM), along with techniques to work around such limitations. Specifically, we investigate the self-assembly of fractal shapes in the TAM. We prove that no self-similar fractal weakly self-assembles at temperature 1 in a locally deterministic tile assembly system, and that certain kinds of discrete self-similar fractals do not strictly self-assemble at any temperature. Additionally, we extend the fiber construction of Lathrop et al. (2009) to show that any discrete self-similar fractal belonging to a particular class of “nice” discrete self-similar fractals has a fibered version that strictly self-assembles in the TAM.     

Representation before computation

My main objective is to point out a fundamental weakness in the conventional conception of computation and suggest a promising way out. This weakness is directly related to a gross underestimation of the role of object representation in a computational model, hence confining such models to an unrealistic (input) environment, which, in turn, leads to “unnatural” computational models. This lack of appreciation of the role of structural object representation has been inherited from logic and partly from mathematics, where, in the latter, the centuries-old tradition is to represent objects as unstructured “points”. I also discuss why the appropriate fundamental reorientation in the conception of computational models will bring the resulting study of computation closer to the “natural” computational constrains. An example of the pertinent, class-oriented, representational formalism developed by our group over many years—Evolving Transformation System (ETS)—is briefly outlined here, and several related general lines of research are suggested.     

Optimization–Simulation Model for Planning Supply Transport to Large Infrastructure Public Works Located in Congested Urban Areas

This article proposes an optimization–simulation model for planning the transport of supplies to large public infrastructure works located in congested urban areas. The purpose is to minimize their impact on the environment and on private transportation users on the local road network. To achieve this goal, the authors propose and solve an optimization problem for minimizing the total system cost made up of operating costs for various alternatives for taking supplies to the worksite and the costs supported by private vehicle users as a result of increased congestion due to the movement of heavy goods vehicles transporting material to the worksite. The proposed optimization problem is a bi-level Math Program model. The upper level defines the total cost of the system, which is minimized taking into account environmental constraints on atmospheric and noise pollution. The lower level defines the optimization problem representing the private transportation user behavior, assuming they choose the route that minimizes their total individual journey costs. Given the special characteristics of the problem, a heuristic algorithm is proposed for finding optimum solutions. Both the model developed and the specific solution algorithm are applied to the real case of building a new port at Laredo (Northern Spain). A series of interesting conclusions are obtained from the corresponding sensitivity analysis.     

Solving Stochastic Transportation Network Protection Problems Using the Progressive Hedging-based Method

This research focuses on pre-disaster transportation network protection against uncertain future disasters. Given limited resources, the goal of the central planner is to choose the best set of network components to protect while allowing the network users to follow their own best-perceived routes in any resultant network configuration. This problem is formulated as a two-stage stochastic programming problem with equilibrium constraints, where the objective is to minimize the total expected physical and social losses caused by potential disasters. Developing efficient solution methods for such a problem can be challenging. In this work, we will demonstrate the applicability of progressive hedging-based method for solving large scale stochastic network optimization problems with equilibrium constraints. In the proposed solution procedure, we solve each modified scenario sub-problem as a mathematical program with complementary constraints and then gradually aggregate scenario-dependent solutions to the final optimal solution.     

Protected subspaces in quantum information

In certain situations the state of a quantum system, after transmission through a quantum channel, can be perfectly restored. This can be done by “coding” the state space of the system before transmission into a “protected” part of a larger state space, and by applying a proper “decoding” map afterwards. By a version of the Heisenberg Principle, which we prove, such a protected space must be “dark” in the sense that no information leaks out during the transmission. We explain the role of the Knill–Laflamme condition in relation to protection and darkness, and we analyze several degrees of protection, whether related to error correction, or to state restauration after a measurement. Recent results on higher rank numerical ranges of operators are used to construct examples. In particular, dark spaces are constructed for any map of rank 2, for a biased permutations channel and for certain separable maps acting on multipartite systems. Furthermore, error correction subspaces are provided for a class of tri-unitary noise models.     

Robust finite-time <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of stochastic jump systems

This paper provides the stochastic finite-time stabilization and H _∞ control problem of Markov jump systems with norm-bounded uncertainties and state delays that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. The finite-time H _∞ controller via state feedback is provided to guarantee the stochastic finite-time bounded-ness and stochastic finite-time stabilization of the resulting closed-loop system for all admissible uncertainties and unknown time-delays. The control criterion is formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. Simulation results illustrate the effectiveness of the developed approaches.     

Unified parametrization for the solutions to the polynomial diophantine matrix equation and the generalized Sylvester matrix equation

The polynomial Diophantine matrix equation and the generalized Sylvester matrix equation are important for controller design in frequency domain linear system theory and time domain linear system theory, respectively. By using the so-called generalized Sylvester mapping, right coprime factorization and Bezout identity associated with certain polynomial matrices, we present in this note a unified parametrization for the solutions to both of these two classes of matrix equations. Moreover, it is shown that solutions to the generalized Sylvester matrix equation can be obtained if solutions to the Diophantine matrix equation are available. The results disclose a relationship between the polynomial Diophantine matrix equation and generalized Sylvester matrix equation that are respectively studied and used in frequency domain linear system theory and time domain linear system theory.     

Position control of a mobile inverted pendulum system using radial basis function network

This article presents the implementation of position control of a mobile inverted pendulum (MIP) system by using the radial basis function (RBF) network. The MIP has two wheels to move on the plane and to balance the pendulum. The MIP is a nonlinear system whose dynamics is nonholonomic. The goal of this study was to control the MIP to maintain the balance of the pendulum while tracking a desired position of the cart. The reference compensation technique scheme is used as a neural network control method for the MIP. The back-propagation learning algorithm of the RBF network is derived for online learning and control. The control algorithm has been embedded on a DSP 2812 board to achieve real-time control. Experimental results are conducted and show successful control performances of both balancing and tracking the desired position of the MIP.