Synchronous Counting and Computational Algorithm Design

Consider a complete communication network on $n$ nodes, each of which is a state machine. In synchronous 2-counting, the nodes receive a common clock pulse and they have to agree on which pulses are "odd" and which are "even". We require that the solution is self-stabilising (reaching the correct operation from any initial state) and it tolerates $f$ Byzantine failures (nodes that send arbitrary misinformation). Prior algorithms are expensive to implement in hardware: they require a source of random bits or a large number of states. This work consists of two parts. In the first part, we use computational techniques (often known as synthesis) to construct very compact deterministic algorithms for the first non-trivial case of $f = 1$. While no algorithm exists for $n < 4$, we show that as few as 3 states per node are sufficient for all values $n \ge 4$. Moreover, the problem cannot be solved with only 2 states per node for $n = 4$, but there is a 2-state solution for all values $n \ge 6$. In the second part, we develop and compare two different approaches for synthesising synchronous counting algorithms. Both approaches are based on casting the synthesis problem as a propositional satisfiability (SAT) problem and employing modern SAT-solvers. The difference lies in how to solve the SAT problem: either in a direct fashion, or incrementally within a counter-example guided abstraction refinement loop. Empirical results suggest that the former technique is more efficient if we want to synthesise time-optimal algorithms, while the latter technique discovers non-optimal algorithms more quickly.Comment: 35 pages, extended and revised versio

A New Algorithm for Protein Design

We apply a new approach to the reverse protein folding problem. Our method uses a minimization function in the design process which is different from the energy function used for folding. For a lattice model, we show that this new approach produces sequences that are likely to fold into desired structures. Our method is a significant improvement over previous attempts which used the energy function for designing sequences.Comment: 10 pages latex 2.09 no figures. Use uufiles to decod

A Fast Algorithm for Sparse Controller Design

We consider the task of designing sparse control laws for large-scale systems by directly minimizing an infinite horizon quadratic cost with an $\ell_1$ penalty on the feedback controller gains. Our focus is on an improved algorithm that allows us to scale to large systems (i.e. those where sparsity is most useful) with convergence times that are several orders of magnitude faster than existing algorithms. In particular, we develop an efficient proximal Newton method which minimizes per-iteration cost with a coordinate descent active set approach and fast numerical solutions to the Lyapunov equations. Experimentally we demonstrate the appeal of this approach on synthetic examples and real power networks significantly larger than those previously considered in the literature

Genetic algorithm search for stent design improvements

Copyright @ 2002 SpringerThis paper presents an optimisation process for finding improved stent design using Genetic Algorithms. An optimisation criterion based on dissipated power is used which fits with the accepted principle that arterial flows follow a minimum energy loss. The GA shows good convergence and the solution found exhibits improved performance over proprietary designs used for comparison purposes

An algorithm for cooperative probabilistic control design

This paper deals with the decentralized closed loop control in a pure probabilistic framework. In this framework, a system is a controlled Markov chain whose transition probabilities depend on the actions of the agents. The agents are also described in a probabilistic way. The objective is to drive the system so that the joint state and agents actions are close to a set of given target probability distributions. The Kullback-Leibler divergence is used as a performance measure. The resulting algorithm uses dynamic programming interleaved with an iterative process that computes the behavior of each agent

The Majorization Arrow in Quantum Algorithm Design

We apply majorization theory to study the quantum algorithms known so far and find that there is a majorization principle underlying the way they operate. Grover's algorithm is a neat instance of this principle where majorization works step by step until the optimal target state is found. Extensions of this situation are also found in algorithms based in quantum adiabatic evolution and the family of quantum phase-estimation algorithms, including Shor's algorithm. We state that in quantum algorithms the time arrow is a majorization arrow.Comment: REVTEX4.b4 file, 4 color figures (typos corrected.