Some Supplementaries to The Counting Semantics for Abstract Argumentation

Dung's abstract argumentation framework consists of a set of interacting arguments and a series of semantics for evaluating them. Those semantics partition the powerset of the set of arguments into two classes: extensions and non-extensions. In order to reason with a specific semantics, one needs to take a credulous or skeptical approach, i.e. an argument is eventually accepted, if it is accepted in one or all extensions, respectively. In our previous work \cite{ref-pu2015counting}, we have proposed a novel semantics, called \emph{counting semantics}, which allows for a more fine-grained assessment to arguments by counting the number of their respective attackers and defenders based on argument graph and argument game. In this paper, we continue our previous work by presenting some supplementaries about how to choose the damaging factor for the counting semantics, and what relationships with some existing approaches, such as Dung's classical semantics, generic gradual valuations. Lastly, an axiomatic perspective on the ranking semantics induced by our counting semantics are presented.Comment: 8 pages, 3 figures, ICTAI 201

Multi-set canonical correlation analysis for 3D abnormal gait behaviour recognition based on virtual sample generation

Small sample dataset and two-dimensional (2D) approach are challenges to vision-based abnormal gait behaviour recognition (AGBR). The lack of three-dimensional (3D) structure of the human body causes 2D based methods to be limited in abnormal gait virtual sample generation (VSG). In this paper, 3D AGBR based on VSG and multi-set canonical correlation analysis (3D-AGRBMCCA) is proposed. First, the unstructured point cloud data of gait are obtained by using a structured light sensor. A 3D parametric body model is then deformed to fit the point cloud data, both in shape and posture. The features of point cloud data are then converted to a high-level structured representation of the body. The parametric body model is used for VSG based on the estimated body pose and shape data. Symmetry virtual samples, pose-perturbation virtual samples and various body-shape virtual samples with multi-views are generated to extend the training samples. The spatial-temporal features of the abnormal gait behaviour from different views, body pose and shape parameters are then extracted by convolutional neural network based Long Short-Term Memory model network. These are projected onto a uniform pattern space using deep learning based multi-set canonical correlation analysis. Experiments on four publicly available datasets show the proposed system performs well under various conditions

Gait recognition and understanding based on hierarchical temporal memory using 3D gait semantic folding

Gait recognition and understanding systems have shown a wide-ranging application prospect. However, their use of unstructured data from image and video has affected their performance, e.g., they are easily influenced by multi-views, occlusion, clothes, and object carrying conditions. This paper addresses these problems using a realistic 3-dimensional (3D) human structural data and sequential pattern learning framework with top-down attention modulating mechanism based on Hierarchical Temporal Memory (HTM). First, an accurate 2-dimensional (2D) to 3D human body pose and shape semantic parameters estimation method is proposed, which exploits the advantages of an instance-level body parsing model and a virtual dressing method. Second, by using gait semantic folding, the estimated body parameters are encoded using a sparse 2D matrix to construct the structural gait semantic image. In order to achieve time-based gait recognition, an HTM Network is constructed to obtain the sequence-level gait sparse distribution representations (SL-GSDRs). A top-down attention mechanism is introduced to deal with various conditions including multi-views by refining the SL-GSDRs, according to prior knowledge. The proposed gait learning model not only aids gait recognition tasks to overcome the difficulties in real application scenarios but also provides the structured gait semantic images for visual cognition. Experimental analyses on CMU MoBo, CASIA B, TUM-IITKGP, and KY4D datasets show a significant performance gain in terms of accuracy and robustness

Harnack Inequalities for SDEs with Multiplicative Noise and Non-regular Drift

The log-Harnack inequality and Harnack inequality with powers for semigroups associated to SDEs with non-degenerate diffusion coefficient and non-regular time-dependent drift coefficient are established, based on the recent papers \cite{Flandoli, Zhang11}. We consider two cases in this work: (1) the drift fulfills the LPS-type integrability, and (2) the drift is uniformly H\"older continuous with respect to the spatial variable. Finally, by using explicit heat kernel estimates for the stable process with drift, the Harnack inequality for the stochastic differential equation driven by symmetric stable process is also proved.Comment: All comments are welcom