Path-factors involving paths of order seven and nine

In this paper, we show the following two theorems (here $c_{i}(G-X)$ is the number of components $C$ of $G-X$ with $|V(C)|=i$): (i)~If a graph $G$ satisfies $c_{1}(G-X)+\frac{1}{3}c_{3}(G-X)+\frac{1}{3}c_{5}(G-X)\leq \frac{2}{3}|X|$ for all $X\subseteq V(G)$, then $G$ has a $\{P_{2},P_{7}\}$-factor. (ii)~If a graph $G$ satisfies $c_{1}(G-X)+c_{3}(G-X)+\frac{2}{3}c_{5}(G-X)+\frac{1}{3}c_{7}(G-X)\leq \frac{2}{3}|X|$ for all $X\subseteq V(G)$, then $G$ has a $\{P_{2},P_{9}\}$-factor.Comment: 29 pages, 4 figure

An explicit computation of p-stabilized vectors

In this paper, we give a method to compute p-stabilized vectors in the space of parahori-fixed vectors for connected reductive groups over p-adic fields. The application to the global setting is also discussed. In particular, we give an explicit p-stabilized form of a Saito-Kurokawa lift.Comment: 21 page

Context Based Visual Content Verification

In this paper the intermediary visual content verification method based on multi-level co-occurrences is studied. The co-occurrence statistics are in general used to determine relational properties between objects based on information collected from data. As such these measures are heavily subject to relative number of occurrences and give only limited amount of accuracy when predicting objects in real world. In order to improve the accuracy of this method in the verification task, we include the context information such as location, type of environment etc. In order to train our model we provide new annotated dataset the Advanced Attribute VOC (AAVOC) that contains additional properties of the image. We show that the usage of context greatly improve the accuracy of verification with up to 16% improvement.Comment: 6 pages, 6 Figures, Published in Proceedings of the Information and Digital Technology Conference, 201