360,213 research outputs found
Software Engineering and Complexity in Effective Algebraic Geometry
We introduce the notion of a robust parameterized arithmetic circuit for the
evaluation of algebraic families of multivariate polynomials. Based on this
notion, we present a computation model, adapted to Scientific Computing, which
captures all known branching parsimonious symbolic algorithms in effective
Algebraic Geometry. We justify this model by arguments from Software
Engineering. Finally we exhibit a class of simple elimination problems of
effective Algebraic Geometry which require exponential time to be solved by
branching parsimonious algorithms of our computation model.Comment: 70 pages. arXiv admin note: substantial text overlap with
arXiv:1201.434
Polar Varieties, Real Equation Solving and Data-Structures: The hypersurface case
In this paper we apply for the first time a new method for multivariate
equation solving which was developed in \cite{gh1}, \cite{gh2}, \cite{gh3} for
complex root determination to the {\em real} case. Our main result concerns the
problem of finding at least one representative point for each connected
component of a real compact and smooth hypersurface. The basic algorithm of
\cite{gh1}, \cite{gh2}, \cite{gh3} yields a new method for symbolically solving
zero-dimensional polynomial equation systems over the complex numbers. One
feature of central importance of this algorithm is the use of a
problem--adapted data type represented by the data structures arithmetic
network and straight-line program (arithmetic circuit). The algorithm finds the
complex solutions of any affine zero-dimensional equation system in non-uniform
sequential time that is {\em polynomial} in the length of the input (given in
straight--line program representation) and an adequately defined {\em geometric
degree of the equation system}. Replacing the notion of geometric degree of the
given polynomial equation system by a suitably defined {\em real (or complex)
degree} of certain polar varieties associated to the input equation of the real
hypersurface under consideration, we are able to find for each connected
component of the hypersurface a representative point (this point will be given
in a suitable encoding). The input equation is supposed to be given by a
straight-line program and the (sequential time) complexity of the algorithm is
polynomial in the input length and the degree of the polar varieties mentioned
above.Comment: Late
Visualization on colour based flow vector of thermal image for movement detection during interactive session
Recently thermal imaging is exploited in applications such as motion and face detection. It has drawn attention many researchers to build such technology to improve lifestyle. This work proposed a technique to detect and identify a motion in sequence images for the application in security monitoring system or outdoor surveillance. Conventional system might cause false information with the present of shadow. Thus, methods employed in this work are Canny edge detector method, Lucas Kanade and Horn Shunck algorithms, to overcome the major problem when using thresholding method, which is only intensity or pixel magnitude is considered instead of relationships between the pixels. The results obtained could be observed in flow vector parameter and the segmentation colour based image for the time frame from 1 to 10 seconds. The visualization of both the parameters clarified the movement and changes of pixel intensity between two frames by the supportive colour segmentation, either in smooth or rough motion. Thus, this technique may contribute to others application such as biometrics, military system, and surveillance machine
A Link Quality Model for Generalised Frequency Division Multiplexing
5G systems aim to achieve extremely high data rates, low end-to-end latency
and ultra-low power consumption. Recently, there has been considerable interest
in the design of 5G physical layer waveforms. One important candidate is
Generalised Frequency Division Multiplexing (GFDM). In order to evaluate its
performance and features, system-level studies should be undertaken in a range
of scenarios. These studies, however, require highly complex computations if
they are performed using bit-level simulators. In this paper, the Mutual
Information (MI) based link quality model (PHY abstraction), which has been
regularly used to implement system-level studies for Orthogonal Frequency
Division Multiplexing (OFDM), is applied to GFDM. The performance of the GFDM
waveform using this model and the bit-level simulation performance is measured
using different channel types. Moreover, a system-level study for a GFDM based
LTE-A system in a realistic scenario, using both a bit-level simulator and this
abstraction model, has been studied and compared. The results reveal the
accuracy of this model using realistic channel data. Based on these results,
the PHY abstraction technique can be applied to evaluate the performance of
GFDM based systems in an effective manner with low complexity. The maximum
difference in the Packet Error Rate (PER) and throughput results in the
abstraction case compared to bit-level simulation does not exceed 4% whilst
offering a simulation time saving reduction of around 62,000 times.Comment: 5 pages, 8 figures, accepted in VTC- spring 201
Synthesis for Polynomial Lasso Programs
We present a method for the synthesis of polynomial lasso programs. These
programs consist of a program stem, a set of transitions, and an exit
condition, all in the form of algebraic assertions (conjunctions of polynomial
equalities). Central to this approach is the discovery of non-linear
(algebraic) loop invariants. We extend Sankaranarayanan, Sipma, and Manna's
template-based approach and prove a completeness criterion. We perform program
synthesis by generating a constraint whose solution is a synthesized program
together with a loop invariant that proves the program's correctness. This
constraint is non-linear and is passed to an SMT solver. Moreover, we can
enforce the termination of the synthesized program with the support of test
cases.Comment: Paper at VMCAI'14, including appendi
- …