Anymatrix: an extensible MATLAB matrix collection

Anymatrix is a MATLAB toolbox that provides an extensible collection of matrices with the ability to search the collection by matrix properties. Each matrix is implemented as a MATLAB function and the matrices are arranged in groups. Compared with previous collections, Anymatrix offers three novel features. First, it allows a user to share a collection of matrices by putting them in a group, annotating them with properties, and placing the group on a public repository, for example on GitHub; the group can then be incorporated into another user’s local Anymatrix installation. Second, it provides a tool to search for matrices by their properties, with Boolean expressions supported. Third, it provides organization into sets, which are subsets of matrices from the whole collection appended with notes, which facilitate reproducible experiments. Anymatrix comes with 146 built-in matrices organized into 7 groups with 49 recognized properties. The authors continue to extend the collection and welcome contributions from the community.

All-Optical Logic Gates and Boolean Expressions in a Photonic Mach–Zehnder Interferometer

In this paper, we numerically investigate the behavior of solitons in a Mach–Zehnder interferometer made of dual-core photonic crystal fibers. The goal was to obtain logic gates with modulated information in ON-OFF keying (OOK). We considered ultra-short solitonic pulses propagating throughout the system in two distinct regimes of pump power and obtained the OR and XOR gates with fundamental solitons. In addition, the A→B and A←B Boolean expressions were obtained with high peak power. As these logical expressions were obtained with the same length of the obtained logic gates, they are important and therefore can be used to save space in the design of complex circuits.

Vaex: big data exploration in the era of Gaia

We present a new Python library, called vaex, intended to handle extremely large tabular datasets such as astronomical catalogues like the Gaia catalogue, N-body simulations, or other datasets which can be structured in rows and columns. Fast computations of statistics on regular N-dimensional grids allows analysis and visualization in the order of a billion rows per second, for a high-end desktop computer. We use streaming algorithms, memory mapped files, and a zero memory copy policy to allow exploration of datasets larger than memory, for example out-of-core algorithms. Vaex allows arbitrary (mathematical) transformations using normal Python expressions and (a subset of) numpy functions which are “lazily” evaluated and computed when needed in small chunks, which avoids wasting of memory. Boolean expressions (which are also lazily evaluated) can be used to explore subsets of the data, which we call selections. Vaex uses a similar DataFrame API as Pandas, a very popular library, which helps migration from Pandas. Visualization is one of the key points of vaex, and is done using binned statistics in 1d (e.g. histogram), in 2d (e.g. 2d histograms with colourmapping) and 3d (using volume rendering). Vaex is split in in several packages: vaex-core for the computational part, vaex-viz for visualization mostly based on matplotlib, vaex-jupyter for visualization in the Jupyter notebook/lab based in IPyWidgets, vaex-server for the (optional) client-server communication, vaex-ui for the Qt based interface, vaex-hdf5 for HDF5 based memory mapped storage, vaex-astro for astronomy related selections, transformations, and memory mapped (column based) FITS storage.

A Nonlinear Integer Programming Approach for the Minimization of Boolean Expressions

A novel approach is suggested in this paper for the minimization of Boolean expressions. This is particularly useful in logic synthesis, since it leads to simpler logic circuit implementations. Although the proposed method is general, emphasis is given on Exclusive-or Sum Of Products (ESOPs) functions. A transformation is derived to convert the problem from the Boolean algebra area to the classical algebraic area. The resulting problem becomes a nonlinear, integer program and an original branch-and-bound procedure with several relaxations is developed for its solution. The suggested methodology is especially suitable for the minimization of incompletely specified functions, which is a difficult problem in the Boolean area. Numerical examples are provided to demonstrate the applicability and performance of the approach and possible future directions are described. The resulting nonlinear problems can sometimes be very demanding but their challenging solutions could solve open ESOP problems.