Towards Automated Boundary Value Testing with Program Derivatives and Search

A natural and often used strategy when testing software is to use input values at boundaries, i.e. where behavior is expected to change the most, an approach often called boundary value testing or analysis (BVA). Even though this has been a key testing idea for long it has been hard to clearly define and formalize. Consequently, it has also been hard to automate. In this research note we propose one such formalization of BVA by, in a similar way as to how the derivative of a function is defined in mathematics, considering (software) program derivatives. Critical to our definition is the notion of distance between inputs and outputs which we can formalize and then quantify based on ideas from Information theory. However, for our (black-box) approach to be practical one must search for test inputs with specific properties. Coupling it with search-based software engineering is thus required and we discuss how program derivatives can be used as and within fitness functions. This brief note does not allow a deeper, empirical investigation but we use a simple illustrative example throughout to introduce the main ideas. By combining program derivatives with search, we thus propose a practical as well as theoretically interesting technique for automated boundary value (analysis and) testing

Convolution algebras and the deformation theory of infinity-morphisms

Given a coalgebra C over a cooperad, and an algebra A over an operad, it is often possible to define a natural homotopy Lie algebra structure on hom(C,A), the space of linear maps between them, called the convolution algebra of C and A. In the present article, we use convolution algebras to define the deformation complex for infinity-morphisms of algebras over operads and coalgebras over cooperads. We also complete the study of the compatibility between convolution algebras and infinity-morphisms of algebras and coalgebras. We prove that the convolution algebra bifunctor can be extended to a bifunctor that accepts infinity-morphisms in both slots and which is well defined up to homotopy, and we generalize and take a new point of view on some other already known results. This paper concludes a series of works by the two authors dealing with the investigation of convolution algebras.Comment: 17 pages, 1 figure; (v2): Expanded some proofs, corrected typos, updated references. Final versio

Homotopy morphisms between convolution homotopy Lie algebras

In previous works by the authors, a bifunctor was associated to any operadic twisting morphism, taking a coalgebra over a cooperad and an algebra over an operad, and giving back the space of (graded) linear maps between them endowed with a homotopy Lie algebra structure. We build on this result by using a more general notion of $\infty$-morphism between (co)algebras over a (co)operad associated to a twisting morphism, and show that this bifunctor can be extended to take such $\infty$-morphisms in either one of its two slots. We also provide a counterexample proving that it cannot be coherently extended to accept $\infty$-morphisms in both slots simultaneously. We apply this theory to rational models for mapping spaces.Comment: 37 pages; v2: minor typo corrections, updated bibliography, final versio

Phase Diagram of Bosons in Two-Color Superlattices from Experimental Parameters

We study the zero-temperature phase diagram of a gas of bosonic 87-Rb atoms in two-color superlattice potentials starting directly from the experimental parameters, such as wavelengths and intensities of the two lasers generating the superlattice. In a first step, we map the experimental setup to a Bose-Hubbard Hamiltonian with site-dependent parameters through explicit band-structure calculations. In the second step, we solve the many-body problem using the density-matrix renormalization group (DMRG) approach and compute observables such as energy gap, condensate fraction, maximum number fluctuations and visibility of interference fringes. We study the phase diagram as function of the laser intensities s_2 and s_1 as control parameters and show that all relevant quantum phases, i.e. superfluid, Mott-insulator, and quasi Bose-glass phase, and the transitions between them can be investigated through a variation of these intensities alone.Comment: 4 pages, 3 figure

Resummed Kinetic Field Theory: Using Mesoscopic Particle Hydrodynamics to Describe Baryonic Matter in a Cosmological Framework

Recently, Bartelmann et al. presented a 'Kinetic Field Theory' (KFT) formalism to tackle the difficulties of large scale structure formation. In this approach, the dynamics of a non-equilibrium ensemble of classical particles are examined based on methods of statistical field theory. So far, only contributions coming from dark matter were considered, which is assumed to pose an accurate description of our universe on very large scales. Nevertheless, going to smaller scales, also baryonic contributions have to be taken into account. Building on the ideas of Viermann et al. we present an effective particle model of hydrodynamics to describe baryonic matter in a cosmological framework. Using this model, the baryonic density contrast power spectrum is computed to lowest perturbative order within the resummed KFT framework of Lilow et al. We discuss the qualitative differences to the dark matter case and perform a quantitative comparison to the baryonic spectrum obtained from Eulerian perturbation theory. A subsequent paper will resolve the problem of coupling both theories describing dark and baryonic matter, respectively, to gain a full model of cosmic matter. Even though our focus is on cosmological systems only, we want to emphasize that all methods presented here are of a quite general fashion, making it applicable also to other fields.Comment: 24 pages, 2 figures, current version: added more explanatory material (especially on the underlying RKFT-formalism), added references to literature on non-linear structure formation, make difference to pure dark matter model clearer, further minor changes; content matches published versio