Elective course planning

Efficient planning increasingly becomes an indispensable tool for management of both companies and public organizations. This is also the case for high school management in Denmark, because the growing individual freedom of the students to choose courses makes planning much more complex. Due to reforms, elective courses are today an important part of the curriculum, and elective courses are a good way to make high school education more attractive for the students. In this article, the problem of planning the elective courses is modeled using integer programming and three different solution approaches are suggested, including a Branch-and-Price framework using partial Dantzig-Wolfe decomposition. Explicit Constraint Branching is used to enhance the solution process, both on the original IP model and in the Branch-and-Price algorithm. To the best of our knowledge, no exact algorithm for the Elective Course Planning Problem has been described in the literature before. The proposed algorithms are tested on data sets from 98 of the 150 high schools in Denmark. The tests show that for the majority of the problems, the optimal solution can be obtained within the one hour time bound. Furthermore the suggested algorithms achieve better results than the currently applied meta-heuristic.     

Establishing strong connectivity using optimal radius half-disk antennas

Given a set S of points in the plane representing wireless devices, each point equipped with a directional antenna of radius r and aperture angle $\alpha ?180\mathrm{°}$, our goal is to find orientations and a minimum r for these antennas such that the induced communication graph is strongly connected. We show that $r=\sqrt{3}$ if $\alpha \in [180\mathrm{°},240\mathrm{°})$, $r=\sqrt{2}$ if $\alpha \in [240\mathrm{°},270\mathrm{°})$, $r=2\sin (36\mathrm{°})$ if $\alpha \in [270\mathrm{°},288\mathrm{°})$, and $r=1$ if $\alpha ?288\mathrm{°}$ suffices to establish strong connectivity, assuming that the longest edge in the Euclidean minimum spanning tree of S is 1. These results are worst-case optimal and match the lower bounds presented in [I. Caragiannis, C. Kaklamanis, E. Kranakis, D. Krizanc, A. Wiese, Communication in wireless networks with directional antennae, in: Proc. of the 20th Symp. on Parallelism in Algorithms and Architectures, 2008, pp. 344–351]. In contrast, $r=2$ is sometimes necessary when $\alpha <180\mathrm{°}$.     

Lower semicontinuity and relaxation of signed functionals with linear growth in the context of {\mathcal A}-quasiconvexity

A lower semicontinuity and relaxation result with respect to weak-* convergence of measures is derived for functionals of the form $$\mu \in \mathcal{M}(\Omega; \mathbb{R}^d) \to \int \limits_\Omega f(\mu^a(x))\,{\rm {d}}x +\int \limits_\Omega f^\infty \left( \frac{{\rm{d}}\mu^s}{d|\mu^s|}(x)\right) \, d| \mu^s|(x),$$ where admissible sequences {μ _n } are such that ${\{{\mathcal{A}}\mu_{n}\}}$ converges to zero strongly in ${W^{-1 q}_{\rm loc}(\Omega)}$ and ${\mathcal {A}}$ is a partial differential operator with constant rank. The integrand f has linear growth and L ^∞-bounds from below are not assumed.     

The consultation timetabling problem at Danish high schools

In the different stages of the educational system, the demand for efficient planning is increasing. This article treats the $\mathcal NP $ NP -hard Consultation Timetabling Problem, a recurrent planning problem for the high schools in Denmark, which has not been described in the literature before. Two versions of the problem are considered, the Parental Consultation Timetabling Problem (PCTP) and the Supervisor Consultation Timetabling Problem (SCTP). It is shown that both problems can be modeled using the same Integer Programming model. Solutions are found using the state-of-the-art MIP solver Gurobi and Adaptive Large Neighborhood Search (ALNS), and computational results are established using 300 real-life datasets. These tests show that the developed ALNS algorithm is significantly outperforming both Gurobi and a currently applied heuristic for the PCTP. For both the PCTP and the SCTP, it is shown that the ALNS algorithm in average provides results within 5 % of optimum. The developed algorithm has been implemented in the commercial product Lectio, and is therefore available for approximately 95 % of the Danish high schools.     

Investigations of mechanical vibrations for beamlines at the Canadian Light Source

Vibration is often a problem causing poor quality of photon beams at synchrotron radiation facilities, since beamlines are quite sensitive to vibrations. Therefore, vibration analysis and control at synchrotron radiation facilities is crucial. This paper presents investigations on mechanical vibrations at four beamlines and endstations at the Canadian Light Source, i.e. the Canadian Macromolecular Crystallography Facility 08ID‐1 beamline, the Hard X‐ray MicroAnalysis 06ID‐1 beamline, the Resonant Elastic and Inelastic Soft X‐ray Scattering 10ID‐2 beamline, and the Scanning Transmission X‐ray Microscope endstation at the Spectromicroscopy 10ID‐1 beamline. This study identifies vibration sources and investigates the influence of mechanical vibrations on beamline performance. The results show that vibrations caused by movable mechanical equipment significantly affect the data acquired from beamlines.     

On the Relation between Enhanced Dissipation Timescales and Mixing Rates

We study diffusion and mixing in different linear fluid dynamics models, mainly related to incompressible flows. In this setting, mixing is a purely advective effect that causes a transfer of energy to high frequencies. When diffusion is present, mixing enhances the dissipative forces. This phenomenon is referred to as enhanced dissipation, namely the identification of a timescale faster than the purely diffusive one. We establish a precise connection between quantitative mixing rates in terms of decay of negative Sobolev norms and enhanced dissipation timescales. The proofs are based on a contradiction argument that takes advantage of the cascading mechanism due to mixing, an estimate of the distance between the inviscid and viscous dynamics, and an optimization step in the frequency cutoff. Thanks to the generality and robustness of our approach, we are able to apply our abstract results to a number of problems. For instance, we prove that contact Anosov flows obey logarithmically fast dissipation timescales. To the best of our knowledge, this is the first example of a flow that induces an enhanced dissipation timescale faster than polynomial. Other applications include passive scalar evolution in both planar and radial settings and fractional diffusion. © 2019 Wiley Periodicals, Inc.     

Null screen quasi-conformal hypersurfaces in semi-Riemannian manifolds and applications

We introduce a class of null hypersurfaces of a semi-Riemannian manifold, namely, screen quasi-conformal hypersurfaces, whose geometry may be studied through the geometry of its screen distribution. In particular, this notion allows us to extend some results of previous works to the case in which the sectional curvature of the ambient space is different from zero. As applications, we study umbilical, isoparametric and Einstein null hypersurfaces in Lorentzian space forms and provide several classification results.