Decorous lower bounds for minimum linear arrangement

Minimum Linear Arrangement is a classical basic combinatorial optimization problem from the 1960s, which turns out to be extremely challenging in practice. In particular, for most of its benchmark instances, even the order of magnitude of the optimal solution value is unknown, as testified by the surveys on the problem that contain tables in which the best known solution value often has one more digit than the best known lower bound value. In this paper, we propose a linear-programming based approach to compute lower bounds on the optimum. This allows us, for the first time, to show that the best known solutions are indeed not far from optimal for most of the benchmark instances

A 3D Printed Toolbox for Opto-Mechanical Components

Nowadays is very common to find headlines in the media where it is stated that 3D printing is a technology called to change our lives in the near future. For many authors, we are living in times of a third industrial revolution. Howerver, we are currently in a stage of development where the use of 3D printing is advantageous over other manufacturing technologies only in rare scenarios. Fortunately, scientific research is one of them. Here we present the development of a set of opto-mechanical components that can be built easily using a 3D printer based on Fused Filament Fabrication (FFF) and parts that can be found on any hardware store. The components of the set presented here are highly customizable, low-cost, require a short time to be fabricated and offer a performance that compares favorably with respect to low-end commercial alternatives.Comment: 9 pages, 9 figure

Constant of Motion for several one-dimensional systems and outlining the problem associated with getting their Hamiltonians

The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation, a no-relativistic particle with a time explicitly depending force, a no-relativistic particle with a constant force and time depending mass, and a relativistic particle under a conservative force with position depending mass. The problem of getting the Hamiltonian for these systems is determined by getting the velocity as an explicit function of position and generalized linear momentum, and this problem can be solved a first approximation for the first above system.Comment: 15 pages, Te