In a bounded valence graph every vertex has O(1) neighbours. Testing isomorphism of bounded valence graphs is known to be in P [15], something that is not clear to hold for graph isomorphism in general. We show that testing isomorphism for undirected, directed and colored graphs of valence 2 is logspace complete. We also prove the following: If a special version of bounded valence GI is hard fo...

A new solvable many-body problem is identified. It is characterized by nonlinear Newtonian equations of motion (“acceleration equal force”) featuring one-body and twobody velocity-dependent forces “of goldfish type” which determine the motion of an arbitrary number N of unit-mass point-particles in a plane. The N (generally complex ) values zn(t) at time t of the N coordinates of these moving p...

In this paper, the problems of semi-global leaderless consensus for continuous-time multi-agent systems under input saturation restraints are investigated. We consider the leaderless consensus problems under fixed undirected communication topology. New necessary synthesis conditions are established for achieving semi-global leaderless consensus via the distributed adaptive protocols, which is d...

Dana H. Ballard This paper provides a systematic analysis of the recurrent backpropagation (RBP) algorithm, introducing a number of new results. The main limitation of the RBP algorithm is that it assumes the convergence of the network to a stable fixed point in order to backpropagate the error signals. We show by experiment and eigenvalue analysis that this condition can be violated and that c...

In Slovenia, textbooks are an integral part of the curriculum. Nationally certified guarantee both teachers and students that they provide all necessary knowledge in each subject. There many available for subject must decide which will be source instruction their students. Our research question is whether groups who use different as mandatory learning resource differ attitudes towards learning....

Cabri is characterized by an attractive advantage and provides wide-ranging benefits in the teaching of mathematics. Although today there have been many studies on edges Cabri, experiments Cabri-Express not widely explored. For this reason, a quasi-experimental study with randomized posttest only design involving 80 grade VII junior high school students Ruteng, Indonesia, was conducted to analy...

Engineering Technology (ET) is often combined with that of Engineering. Although based on a more hands-on approach and theoretical approach, the two majors share very similar pedagogy in teaching students same engineering scientific principles. An observation by an ET professor found than not would eschew use mathematical computations instead provide answers they believe to be correct, without ...

“Computational mathematics” (algorithmic mathematics) is the part of mathematics that strives at the solution of mathematical problems by algorithms. In a superficial view, some people might believe that computational mathematics is the easy part of mathematics in which trivial mathematics is made useful by repeating trivial steps sufficiently many times on current powerful machines in order to...

We count the number of alignments of N ≥ 1 sequences when match-up types are from a specified set S ⊆ N . Equivalently, we count the number of nonnegative integer matrices whose rows sum to a given fixed vector and each of whose columns lie in S. We provide a new asymptotic formula for the case S = {(s1, . . . , sN ) | 1 ≤ si ≤ 2}.