62,727 research outputs found
Algebraic Change-Point Detection
Elementary techniques from operational calculus, differential algebra, and
noncommutative algebra lead to a new approach for change-point detection, which
is an important field of investigation in various areas of applied sciences and
engineering. Several successful numerical experiments are presented
Frequency Change-Point Detection in physiological Signals : an Algebraic Approach
International audienceThis paper considers the problem of change-point detection for noisy data. Estimation of signal frequency content relies on diïŹerential algebra and non-commutative algebra together with operational calculus. We adapt this approach to the study of changes that may be observed in EEG signal dynamics during epileptic seizure and in ECG signal during the occurrence of a QRS complex. The correlation with frequency change is what this idea is based on. The interest of our estimator is ïŹrstly il lustrated according to several academic examples. Then, the method is applied on real physiological signals to detect abrupt frequency changes
A delay estimation approach to change-point detection
The change-point detection problem is cast into a delay estimation. Using a local piecewise polynomial representation and some elementary algebraic manipulations, we give an explicit characterization of a change-point as a solution of a given polynomial equation. A key feature of this polynomial equation is its coefficients being composed by short time window iterated integrals of the noisy signal. The so designed change-point detector shows good robustness to various type of noises
Separation-Sensitive Collision Detection for Convex Objects
We develop a class of new kinetic data structures for collision detection
between moving convex polytopes; the performance of these structures is
sensitive to the separation of the polytopes during their motion. For two
convex polygons in the plane, let be the maximum diameter of the polygons,
and let be the minimum distance between them during their motion. Our
separation certificate changes times when the relative motion of
the two polygons is a translation along a straight line or convex curve,
for translation along an algebraic trajectory, and for
algebraic rigid motion (translation and rotation). Each certificate update is
performed in time. Variants of these data structures are also
shown that exhibit \emph{hysteresis}---after a separation certificate fails,
the new certificate cannot fail again until the objects have moved by some
constant fraction of their current separation. We can then bound the number of
events by the combinatorial size of a certain cover of the motion path by
balls.Comment: 10 pages, 8 figures; to appear in Proc. 10th Annual ACM-SIAM
Symposium on Discrete Algorithms, 1999; see also
http://www.uiuc.edu/ph/www/jeffe/pubs/kollide.html ; v2 replaces submission
with camera-ready versio
Design of teacher assistance tools in an exploratory learning environment for algebraic generalisation
The MiGen project is designing and developing an intelligent exploratory environment to support 11-14 year-old students in their learning of algebraic generalisation. Deployed within the classroom, the system also provides tools to assist teachers in monitoring students' activities and progress. This paper describes the architectural design of these Teacher Assistance tools and gives a detailed description of one such tool, focussing in particular on the research challenges faced, and the technologies and approaches chosen to implement the necessary functionalities given the context of the project
Algebraic Watchdog: Mitigating Misbehavior in Wireless Network Coding
We propose a secure scheme for wireless network coding, called the algebraic
watchdog. By enabling nodes to detect malicious behaviors probabilistically and
use overheard messages to police their downstream neighbors locally, the
algebraic watchdog delivers a secure global self-checking network. Unlike
traditional Byzantine detection protocols which are receiver-based, this
protocol gives the senders an active role in checking the node downstream. The
key idea is inspired by Marti et al.'s watchdog-pathrater, which attempts to
detect and mitigate the effects of routing misbehavior.
As an initial building block of a such system, we first focus on a two-hop
network. We present a graphical model to understand the inference process nodes
execute to police their downstream neighbors; as well as to compute, analyze,
and approximate the probabilities of misdetection and false detection. In
addition, we present an algebraic analysis of the performance using an
hypothesis testing framework that provides exact formulae for probabilities of
false detection and misdetection.
We then extend the algebraic watchdog to a more general network setting, and
propose a protocol in which we can establish trust in coded systems in a
distributed manner. We develop a graphical model to detect the presence of an
adversarial node downstream within a general multi-hop network. The structure
of the graphical model (a trellis) lends itself to well-known algorithms, such
as the Viterbi algorithm, which can compute the probabilities of misdetection
and false detection. We show analytically that as long as the min-cut is not
dominated by the Byzantine adversaries, upstream nodes can monitor downstream
neighbors and allow reliable communication with certain probability. Finally,
we present simulation results that support our analysis.Comment: 10 pages, 10 figures, Submitted to IEEE Journal on Selected Areas in
Communications (JSAC) "Advances in Military Networking and Communications
Detecting Similarity of Rational Plane Curves
A novel and deterministic algorithm is presented to detect whether two given
rational plane curves are related by means of a similarity, which is a central
question in Pattern Recognition. As a by-product it finds all such
similarities, and the particular case of equal curves yields all symmetries. A
complete theoretical description of the method is provided, and the method has
been implemented and tested in the Sage system for curves of moderate degrees.Comment: 22 page
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