The Resource-Constrained Project Scheduling Problem with Work-Content Constraints

For executing the activities of a project, one or several resources are required, which are in general scarce. Many resource-allocation methods assume that the usage of these resources by an activity is constant during execution; in practice, however, the project manager may vary resource usage by individual activities over time within prescribed bounds. This variation gives rise to the project scheduling problem which consists in allocating the scarce resources to the project activities over time such that the project duration is minimized, the total number of resource units allocated equals the prescribed work content of each activity, and precedence and various work-content-related constraints are met.

Stringy origin of diboson and dijet excesses at the LHC

Very recently, the ATLAS and CMS Collaborations reported diboson and dijet excesses above standard model expectations in the invariant mass region of 1.8–2.0 TeV. Interpreting the diboson excess of events in a model independent fashion suggests that the vector boson pair production searches are best described by WZ or ZZ topologies, because states decaying into W+W− pairs are strongly constrained by semileptonic searches. Under the assumption of a low string scale, we show that both the diboson and dijet excesses can be steered by an anomalous U(1) field with very small coupling to leptons. The Drell–Yan bounds are then readily avoided because of the leptophobic nature of the massive Z′ gauge boson. The non-negligible decay into ZZ required to accommodate the data is a characteristic footprint of intersecting D-brane models, wherein the Landau–Yang theorem can be evaded by anomaly-induced operators involving a longitudinal Z. The model presented herein can be viewed purely field-theoretically, although it is particularly well motivated from string theory. Should the excesses become statistically significant at the LHC13, the associated Zγ topology would become a signature consistent only with a stringy origin.

Consistency of Concave Regression with an Application to Current-Status Data

We consider the problem of nonparametric estimation of a concave regression function F. We show that the supremum distance between the least square s estimatorand F on a compact interval is typically of order(log(n)/n)2/5. This entails rates of convergence for the estimator’s derivative. Moreover, we discuss the impact of additional constraints on F such as monotonicity and pointwise bounds. Then we apply these results to the analysis of current status data, where the distribution function of the event times is assumed to be concave.

Energy Efficient Multimedia Communications in IEEE 802.11 Networks

During the last decade wireless mobile communications have progressively become part of the people’s daily lives, leading users to expect to be “alwaysbest-connected” to the Internet, regardless of their location or time of day. This is indeed motivated by the fact that wireless access networks are increasingly ubiquitous, through different types of service providers, together with an outburst of thoroughly portable devices, namely laptops, tablets, mobile phones, among others. The “anytime and anywhere” connectivity criterion raises new challenges regarding the devices’ battery lifetime management, as energy becomes the most noteworthy restriction of the end-users’ satisfaction. This wireless access context has also stimulated the development of novel multimedia applications with high network demands, although lacking in energy-aware design. Therefore, the relationship between energy consumption and the quality of the multimedia applications perceived by end-users should be carefully investigated. This dissertation addresses energy-efficient multimedia communications in the IEEE 802.11 standard, which is the most widely used wireless access technology. It advances the literature by proposing a unique empirical assessment methodology and new power-saving algorithms, always bearing in mind the end-users’ feedback and evaluating quality perception. The new EViTEQ framework proposed in this thesis, for measuring video transmission quality and energy consumption simultaneously, in an integrated way, reveals the importance of having an empirical and high-accuracy methodology to assess the trade-off between quality and energy consumption, raised by the new end-users’ requirements. Extensive evaluations conducted with the EViTEQ framework revealed its flexibility and capability to accurately report both video transmission quality and energy consumption, as well as to be employed in rigorous investigations of network interface energy consumption patterns, regardless of the wireless access technology. Following the need to enhance the trade-off between energy consumption and application quality, this thesis proposes the Optimized Power save Algorithm for continuous Media Applications (OPAMA). By using the end-users’ feedback to establish a proper trade-off between energy consumption and application performance, OPAMA aims at enhancing the energy efficiency of end-users’ devices accessing the network through IEEE 802.11. OPAMA performance has been thoroughly analyzed within different scenarios and application types, including a simulation study and a real deployment in an Android testbed. When compared with the most popular standard power-saving mechanisms defined in the IEEE 802.11 standard, the obtained results revealed OPAMA’s capability to enhance energy efficiency, while keeping end-users’ Quality of Experience within the defined bounds. Furthermore, OPAMA was optimized to enable superior energy savings in multiple station environments, resulting in a new proposal called Enhanced Power Saving Mechanism for Multiple station Environments (OPAMA-EPS4ME). The results of this thesis highlight the relevance of having a highly accurate methodology to assess energy consumption and application quality when aiming to optimize the trade-off between energy and quality. Additionally, the obtained results based both on simulation and testbed evaluations, show clear benefits from employing userdriven power-saving techniques, such as OPAMA, instead of IEEE 802.11 standard power-saving approaches.

hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.

The Complexity of Non-Iterated Probabilistic Justification Logic

The logic PJ is a probabilistic logic defined by adding (noniterated) probability operators to the basic justification logic J. In this paper we establish upper and lower bounds for the complexity of the derivability problem in the logic PJ. The main result of the paper is that the complexity of the derivability problem in PJ remains the same as the complexity of the derivability problem in the underlying logic J, which is π[p/2] -complete. This implies that the probability operators do not increase the complexity of the logic, although they arguably enrich the expressiveness of the language.

Uniqueness of minimisers for a Grötzsch-Belinskiĭ type inequality in the Heisenberg group

The modulus method introduced by H. Grötzsch yields bounds for a mean distortion functional of quasiconformal maps between two annuli mapping the respective boundary components onto each other. P. P. Belinskiĭ studied these inequalities in the plane and identified the family of all minimisers. Beyond the Euclidean framework, a Grötzsch-Belinskiĭ-type inequality has been previously considered for quasiconformal maps between annuli in the Heisenberg group whose boundaries are Korányi spheres. In this note we show that--in contrast to the planar situation--the minimiser in this setting is essentially unique.

Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.