Parameterizing cut sets in a graph by the number of their components

For a connected graph G=(V,E), a subset U⊆V is a disconnected cut if U disconnects G and the subgraph G[U] induced by U is disconnected as well. A cut U is a k-cut if G[U] contains exactly k(≥1) components. More specifically, a k-cut U is a (k,?)-cut if V?U induces a subgraph with exactly ?(≥2) components. The Disconnected Cut problem is to test whether a graph has a disconnected cut and is known to be NP-complete. The problems k-Cut and (k,?)-Cut are to test whether a graph has a k-cut or (k,?)-cut, respectively. By pinpointing a close relationship to graph contractibility problems we show that (k,?)-Cut is in P for k=1 and any fixed constant ?≥2, while it is NP-complete for any fixed pair k,?≥2. We then prove that k-Cut is in P for k=1 and NP-complete for any fixed k≥2. On the other hand, for every fixed integer g≥0, we present an FPT algorithm that solves (k,?)-Cut on graphs of Euler genus at most g when parameterized by k+?. By modifying this algorithm we can also show that k-Cut is in FPT for this graph class when parameterized by k. Finally, we show that Disconnected Cut is solvable in polynomial time for minor-closed classes of graphs excluding some apex graph.     

Editorial

Higher-Order and Symbolic Computation -     

Codevelopmental learning between human and humanoid robot using a dynamic neural-network model.

This paper examines characteristics of interactive learning between human tutors and a robot having a dynamic neural-network model, which is inspired by human parietal cortex functions. A humanoid robot, with a recurrent neural network that has a hierarchical structure, learns to manipulate objects. Robots learn tasks in repeated self-trials with the assistance of human interaction, which provides physical guidance until the tasks are mastered and learning is consolidated within the neural networks. Experimental results and the analyses showed the following: 1) codevelopmental shaping of task behaviors stems from interactions between the robot and a tutor; 2) dynamic structures for articulating and sequencing of behavior primitives are self-organized in the hierarchically organized network; and 3) such structures can afford both generalization and context dependency in generating skilled behaviors.     

A study on a quantum-inspired evolutionary algorithm based on pair swap

A quantum-inspired evolutionary algorithm (QEA) is proposed as a stochastic algorithm to perform combinatorial optimization problems. The QEA is evolutionary computation that uses quantum bits and superposition states in quantum computation. Although the QEA is a coarse-grained parallel algorithm, it involves many parameters that must be adjusted manually. This paper proposes a new method, named pair swap, which exchanges each best solution information between two individuals instead of migration in the QEA. Experimental results show that our proposed method is a simpler algorithm and can find a high quality solution in the 0-1 knapsack problem. This work was presented in part at the 12th International Symposium on Artificial Life and Robotics, Oita, Japan, January 25–27, 2007     

Bottom-up pyramid cellular acceptors with three-dimensional layers

In 1997, C.R. Dyer and A. Rosenfeld introduced an acceptor on a two-dimensional pattern (or tape), called the pyramid cellular acceptor, and demonstrated that many useful recognition tasks are executed by pyramid cellular acceptors in time proportional to the logarithm of the diameter of the input. They also introduced a bottom-up pyramid cellular acceptor which is a restricted version of the pyramid cellular acceptor, and proposed some interesting open problems of the bottom-up pyramid cellular acceptors. On the other hand, we think that the study of threedimensional automata has been meaningful as the computational model of three-dimensional information processing such as computer vision, robotics, and so forth. In this paper, we investigate about bottom-up pyramid cellular acceptors with three-dimensional layers, and show their some accepting powers. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Making Java work for microcontroller applications

The authors investigate complete system development using a Java machine aimed at FPGA devices. A new design strategy targets a single FPGA chip, within which the dedicated Java microcontroller-FemtoJava-is synthesized     

Minimum cost source location problem with vertex-connectivity requirements in digraphs

Given a digraph (or an undirected graph) G=(V,E) with a set V of vertices v with nonnegative real costs w(v), and a set E of edges and a positive integer k, we deal with the problem of finding a minimum cost subset SV such that, for each vertex vV−S, there are k vertex-disjoint paths from S to v. In this paper, we show that the problem can be solved by a greedy algorithm in time in a digraph (or in time in an undirected graph), where n=|V| and m=|E|. Based on this, given a digraph and two integers k and ℓ, we also give a polynomial time algorithm for finding a minimum cost subset SV such that for each vertex vV−S, there are k vertex-disjoint paths from S to v as well as ℓ vertex-disjoint paths from v to S.     

Group weighted finite transducers

We consider weighted finite transducers over arbitrary groups, that is finite transducers having a counter in which, at any step, a value of the group is stored but no information regarding the content of this counter is available until the computation is finished. The computation is valid if the counter value is the neutral element of the group. We generalize here some results from [8] and [17]. Received: 28 January 2001 / 5 June 2001     

A high-field adiabatic fast passage ultracold neutron spin flipper for the UCNA experiment

The UCNA collaboration is making a precision measurement of the β asymmetry (A) in free neutron decay using polarized ultracold neutrons (UCN). A critical component of this experiment is an adiabatic fast passage neutron spin flipper capable of efficient operation in ambient magnetic fields on the order of 1 T. The requirement that it operate in a high field necessitated the construction of a free neutron spin flipper based, for the first time, on a birdcage resonator. The design, construction, and initial testing of this spin flipper prior to its use in the first measurement of A with UCN during the 2007 run cycle of the Los Alamos Neutron Science Center's 800 MeV proton accelerator is detailed. These studies determined the flipping efficiency of the device, averaged over the UCN spectrum present at the location of the spin flipper, to be ε=0.9985(4).