Geometric contextuality from the Maclachlan-Martin Kleinian groups

There are contextual sets of multiple qubits whose commutation is parametrized thanks to the coset geometry $\mathcal{G}$ of a subgroup $H$ of the two-generator free group $G=\left\langle x,y\right\rangle$. One defines geometric contextuality from the discrepancy between the commutativity of cosets on $\mathcal{G}$ and that of quantum observables.It is shown in this paper that Kleinian subgroups $K=\left\langle f,g\right\rangle$ that are non-compact, arithmetic, and generated by two elliptic isometries $f$ and $g$ (the Martin-Maclachlan classification), are appropriate contextuality filters. Standard contextual geometries such as some thin generalized polygons (starting with Mermin's $3 \times 3$ grid) belong to this frame. The Bianchi groups $PSL(2,O\_d)$, $d \in \{1,3\}$ defined over the imaginary quadratic field $O\_d=\mathbb{Q}(\sqrt{-d})$ play a special role

Combining Low-dimensional Wavelet Features and Support Vector Machine for Arrhythmia Beat Classification

Automatic feature extraction and classification are two main tasks in abnormal ECG beat recognition. Feature extraction is an important prerequisite prior to classification since it provides the classifier with input features, and the performance of classifier depends significantly on the quality of these features. This study develops an effective method to extract low-dimensional ECG beat feature vectors. It employs wavelet multi-resolution analysis to extract time-frequency domain features and then applies principle component analysis to reduce the dimension of the feature vector. In classification, 12-element feature vectors characterizing six types of beats are used as inputs for one-versus-one support vector machine, which is conducted in form of 10-fold cross validation with beat-based and record-based training schemes. Tested upon a total of 107049 beats from MIT-BIH arrhythmia database, our method has achieved average sensitivity, specificity and accuracy of 99.09%, 99.82% and 99.70%, respectively, using the beat-based training scheme, and 44.40%, 88.88% and 81.47%, respectively, using the record-based training scheme

Activity Recognition based on a Magnitude-Orientation Stream Network

The temporal component of videos provides an important clue for activity recognition, as a number of activities can be reliably recognized based on the motion information. In view of that, this work proposes a novel temporal stream for two-stream convolutional networks based on images computed from the optical flow magnitude and orientation, named Magnitude-Orientation Stream (MOS), to learn the motion in a better and richer manner. Our method applies simple nonlinear transformations on the vertical and horizontal components of the optical flow to generate input images for the temporal stream. Experimental results, carried on two well-known datasets (HMDB51 and UCF101), demonstrate that using our proposed temporal stream as input to existing neural network architectures can improve their performance for activity recognition. Results demonstrate that our temporal stream provides complementary information able to improve the classical two-stream methods, indicating the suitability of our approach to be used as a temporal video representation.Comment: 8 pages, SIBGRAPI 201