Synthesizing Switching Controllers for Hybrid Systems by Continuous Invariant Generation

We extend a template-based approach for synthesizing switching controllers for semi-algebraic hybrid systems, in which all expressions are polynomials. This is achieved by combining a QE (quantifier elimination)-based method for generating continuous invariants with a qualitative approach for predefining templates. Our synthesis method is relatively complete with regard to a given family of predefined templates. Using qualitative analysis, we discuss heuristics to reduce the numbers of parameters appearing in the templates. To avoid too much human interaction in choosing templates as well as the high computational complexity caused by QE, we further investigate applications of the SOS (sum-of-squares) relaxation approach and the template polyhedra approach in continuous invariant generation, which are both well supported by efficient numerical solvers

Ranking Templates for Linear Loops

We present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on linear ranking templates. Linear ranking templates are parametrized, well-founded relations such that an assignment to the parameters gives rise to a ranking function. This approach generalizes existing methods and enables us to use templates for many different ranking functions with affine-linear components. We discuss templates for multiphase, piecewise, and lexicographic ranking functions. Because these ranking templates require both strict and non-strict inequalities, we use Motzkin's Transposition Theorem instead of Farkas Lemma to transform the generated $\exists\forall$-constraint into an $\exists$-constraint.Comment: TACAS 201

Reducing the number of templates for aligned-spin compact binary coalescence gravitational wave searches using metric-agnostic template nudging

Efficient multi-dimensional template placement is crucial in computationally intensive matched-filtering searches for Gravitational Waves (GWs). Here, we implement the Neighboring Cell Algorithm (NCA) to improve the detection volume of an existing Compact Binary Coalescence (CBC) template bank. This algorithm has already been successfully applied for a binary millisecond pulsar search in data from the Fermi satellite. It repositions templates from over-dense regions to under-dense regions and reduces the number of templates that would have been required by a stochastic method to achieve the same detection volume. Our method is readily generalizable to other CBC parameter spaces. Here we apply this method to the aligned--single-spin neutron-star--black-hole binary coalescence inspiral-merger-ringdown gravitational wave parameter space. We show that the template nudging algorithm can attain the equivalent effectualness of the stochastic method with 12% fewer templates

Efficient generation and optimization of stochastic template banks by a neighboring cell algorithm

Placing signal templates (grid points) as efficiently as possible to cover a multi-dimensional parameter space is crucial in computing-intensive matched-filtering searches for gravitational waves, but also in similar searches in other fields of astronomy. To generate efficient coverings of arbitrary parameter spaces, stochastic template banks have been advocated, where templates are placed at random while rejecting those too close to others. However, in this simple scheme, for each new random point its distance to every template in the existing bank is computed. This rapidly increasing number of distance computations can render the acceptance of new templates computationally prohibitive, particularly for wide parameter spaces or in large dimensions. This work presents a neighboring cell algorithm that can dramatically improve the efficiency of constructing a stochastic template bank. By dividing the parameter space into sub-volumes (cells), for an arbitrary point an efficient hashing technique is exploited to obtain the index of its enclosing cell along with the parameters of its neighboring templates. Hence only distances to these neighboring templates in the bank are computed, massively lowering the overall computing cost, as demonstrated in simple examples. Furthermore, we propose a novel method based on this technique to increase the fraction of covered parameter space solely by directed template shifts, without adding any templates. As is demonstrated in examples, this method can be highly effective..Comment: PRD accepte

Implementation of non-linear templates using a decomposition technique by a 0.5 /spl mu/m CMOS CNN universal chip

This paper demonstrates the processing capabilities of a recently designed analog programmable array processor. This new prototype, called CNNUC3, follows the cellular neural network universal machine computing paradigm. Due to its very advanced features and algorithmic capabilities, this chip has been demonstrated to be able to perform not only linear templates executions, but also to be very adequate for the implementation of non-linear templates by using a decomposition method. This paper focus on the application examples of the execution of non-linear templates with the CNNUC3 prototype. A brief description of the theoretical background is also presented in the paper

Computational Resources to Filter Gravitational Wave Data with P-approximant Templates

The prior knowledge of the gravitational waveform from compact binary systems makes matched filtering an attractive detection strategy. This detection method involves the filtering of the detector output with a set of theoretical waveforms or templates. One of the most important factors in this strategy is knowing how many templates are needed in order to reduce the loss of possible signals. In this study we calculate the number of templates and computational power needed for a one-step search for gravitational waves from inspiralling binary systems. We build on previous works by firstly expanding the post-Newtonian waveforms to 2.5-PN order and secondly, for the first time, calculating the number of templates needed when using P-approximant waveforms. The analysis is carried out for the four main first-generation interferometers, LIGO, GEO600, VIRGO and TAMA. As well as template number, we also calculate the computational cost of generating banks of templates for filtering GW data. We carry out the calculations for two initial conditions. In the first case we assume a minimum individual mass of $1 M_{\odot}$ and in the second, we assume a minimum individual mass of $5 M_{\odot}$. We find that, in general, we need more P-approximant templates to carry out a search than if we use standard PN templates. This increase varies according to the order of PN-approximation, but can be as high as a factor of 3 and is explained by the smaller span of the P-approximant templates as we go to higher masses. The promising outcome is that for 2-PN templates the increase is small and is outweighed by the known robustness of the 2-PN P-approximant templates.Comment: 17 pages, 8 figures, Submitted to Class.Quant.Gra