Properties of Gauss Digitized Shapes and Digital Surface Integration

This paper presents new topological and geometric properties of Gauss digitizations of Euclidean shapes, most of them holding in arbitrary dimension d. We focus on r-regular shapes sampled by Gauss digitization at gridstep h. The digitized boundary is shown to be close to the Euclidean boundary in the Hausdorff sense, the minimum distance \(\frac{\sqrt{d}}{2}h\) being achieved by the projection map \(\xi \) induced by the Euclidean distance. Although it is known that Gauss digitized boundaries may not be manifold when \(d \ge 3\), we show that non-manifoldness may only occur in places where the normal vector is almost aligned with some digitization axis, and the limit angle decreases with h. We then have a closer look at the projection of the digitized boundary onto the continuous boundary by \(\xi \). We show that the size of its non-injective part tends to zero with h. This leads us to study the classical digital surface integration scheme, which allocates a measure to each surface element that is proportional to the cosine of the angle between an estimated normal vector and the trivial surface element normal vector. We show that digital integration is convergent whenever the normal estimator is multigrid convergent, and we explicit the convergence speed. Since convergent estimators are now available in the literature, digital integration provides a convergent measure for digitized objects.     

Generating heavy particles with energy and momentum conservation

We propose a novel algorithm, called REGGAE, for the generation of momenta of a given sample of particle masses, evenly distributed in Lorentz-invariant phase space and obeying energy and momentum conservation. In comparison to other existing algorithms, REGGAE is designed for the use in multiparticle production in hadronic and nuclear collisions where many hadrons are produced and a large part of the available energy is stored in the form of their masses. The algorithm uses a loop simulating multiple collisions which lead to production of configurations with reasonably large weights.

Program summary

Program title: REGGAE (REscattering-after-Genbod GenerAtor of Events)Catalogue identifier: AEJR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJR_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 1523No. of bytes in distributed program, including test data, etc.: 9608Distribution format: tar.gzProgramming language: C++Computer: PC Pentium 4, though no particular tuning for this machine was performed.Operating system: Originally designed on Linux PC with g++, but it has been compiled and ran successfully on OS X with g++ and MS Windows with Microsoft Visual C++ 2008 Express Edition, as well.RAM: This depends on the number of particles which are generated. For 10 particles like in the attached example it requires about 120 kB.Classification: 11.2Nature of problem: The task is to generate momenta of a sample of particles with given masses which obey energy and momentum conservation. Generated samples should be evenly distributed in the available Lorentz-invariant phase space.Solution method: In general, the algorithm works in two steps. First, all momenta are generated with the GENBOD algorithm. There, particle production is modeled as a sequence of two-body decays of heavy resonances. After all momenta are generated this way, they are reshuffled. Each particle undergoes a collision with some other partner such that in the pair center of mass system the new directions of momenta are distributed isotropically. After each particle collides only a few times, the momenta are distributed evenly across the whole available phase space. Starting with GENBOD is not essential for the procedure but it improves the performance.Running time: This depends on the number of particles and number of events one wants to generate. On a LINUX PC with 2 GHz processor, generation of 1000 events with 10 particles each takes about 3 s.     

An auto-generated real-time iteration algorithm for nonlinear MPC in the microsecond range

In this paper, we present an automatic C-code generation strategy for real-time nonlinear model predictive control (NMPC), which is designed for applications with kilohertz sample rates. The corresponding code export module has been implemented within the software package ACADO Toolkit. It is capable of exporting fixed step-size integrators together with their sensitivities as well as a real-time Gauss–Newton method. Here, we employ the symbolic representation of optimal control problems in ACADO in order to auto-generate plain C-code which is optimized for final production. The exported code has been tested for model predictive control scenarios comprising constrained nonlinear dynamic systems with four states and a control horizon of ten samples. The numerical simulations show a promising performance of the exported code being able to provide feedback in much less than a millisecond.     

Odometry-Based Viterbi Localization with Artificial Neural Networks and Laser Range Finders for Mobile Robots

This paper proposes an approach that solves the Robot Localization problem by using a conditional state-transition Hidden Markov Model (HMM). Through the use of Self Organized Maps (SOMs) a Tolerant Observation Model (TOM) is built, while odometer-dependent transition probabilities are used for building an Odometer-Dependent Motion Model (ODMM). By using the Viterbi Algorithm and establishing a trigger value when evaluating the state-transition updates, the presented approach can easily take care of Position Tracking (PT), Global Localization (GL) and Robot Kidnapping (RK) with an ease of implementation difficult to achieve in most of the state-of-the-art localization algorithms. Also, an optimization is presented to allow the algorithm to run in standard microprocessors in real time, without the need of huge probability gridmaps.     

2D structured grid generation method producing a mesh with prescribed properties near boundary

A variational method of generating a structured mesh on a two-dimensional domain is considered. To this end, a quasiconformal mapping of the parametric domain with a given Cartesian mesh onto the underlying physical domain is used. The functions implementing the mapping are sought by solving the Dirichlet problem for the system of elliptic second-order partial differential equations. An additional control for the cell shape is executed by introducing a local mapping which induces a control metric. In some particular cases, instead of an additional local mapping, a global mapping of the parametric domain onto the intermediate domain is used, where the curvilinear mesh is produced, and next this domain is mapped onto the underlying physical domain. The control metric allows to obtain a mesh with required properties: grid line orthogonality and prescribed mesh point clustering near the domain boundary. Examples of mesh in the annulus and near airfoil are presented.     

Kalman filter for controlled hybrid systems

The linear partially observed discrete-continuous (hybrid) stochastic controllable system described by differential equations with measures is considered. The optimal filtering equations in the form of generalized Kalman filter are obtained in the case of non-anticipating control. This result could be a theoretical basis for the optimal control in stochastic hybrid systems with incomplete information.     

Patterns of self-stabilization in database consistency maintenance

A substantial portion of the database programming efforts are invested in integrity constraints enforcement. Traditionally, both the constraint semantics and their enforcement were embedded inside application programs. In recent years several studies have dealt with specifying integrity constraints as separate entities (e.g. rules), and relating the database consistency requirements to these rules. In this paper we deal with the complementary issue of stabilizing the database when update exceptions occur. While a simplistic approach is to abort any transaction that inflicts consistency violations, this is not always the desired action. We take advantage of the empirical observation that most of the exception-handling policies follow a small number of behavior patterns. Unlike some previous approaches that base their repair solution on syntactic analysis of the constraints and performance issues, we base our approach on the application semantics as reflected in these behavioral patterns. We describe a model that uses high-level abstractions called stabilizer types denoting these behavior patterns for consistency restorations, whose exact semantics is case dependent. It follows the fault tolerance's self-stabilization approach. An inference mechanism translates these abstractions into executable active rules. This approach provides high-level language to the exception handling portion of the application and substantially reduces the required programming.     

Ellipsoidal parameter or state estimation under model uncertainty

Ellipsoidal outer-bounding of the set of all feasible state vectors under model uncertainty is a natural extension of state estimation for deterministic models with unknown-but-bounded state perturbations and measurement noise. The technique described in this paper applies to linear discrete-time dynamic systems; it can also be applied to weakly non-linear systems if non-linearity is replaced by uncertainty. Many difficulties arise because of the non-convexity of feasible sets. Combined quadratic constraints on model uncertainty and additive disturbances are considered in order to simplify the analysis. Analytical optimal or suboptimal solutions of the basic problems involved in parameter or state estimation are presented, which are counterparts in this context of uncertain models to classical approximations of the sum and intersection of ellipsoids. The results obtained for combined quadratic constraints are extended to other types of model uncertainty.     

On quadratic two-parameter families of spheres and their envelopes

In the present paper we investigate rational two-parameter families of spheres and their envelope surfaces in Euclidean . The four dimensional cyclographic model of the set of spheres in is an appropriate framework to show that a quadratic triangular Bézier patch in corresponds to a two-parameter family of spheres with rational envelope surface. The construction shows also that the envelope has rational offsets. Further we outline how to generalize the construction to obtain a much larger class of surfaces with similar properties.     

330 GHz FMCW Image Sensor for Homeland Security Applications

A single-pixel imaging remote sensor operating at 330 GHz is described. It is based on a frequency modulated continuous wave (FMCW) and aimed at detection of concealed objects for ranges up to 40 m. The system consists of 2 horn-lens antennas integrated with a homodyne transceiver. The synthesized linear FMCW signal at X-band is multiplied by a factor of 32 to generate the transmitted signal. An intermediate frequency (IF) signal obtained in the output port of the 2-nd harmonic mixer is employed for image processing. Distance measurements were made by performing data acquisition unit based on LabView interface and resulting in a range resolution about 1 cm. Examples of 2D and 3D images reconstructed with this sensor are presented.