Accurate assessment of the breast cancer deterioration degree plays a crucial role in making medical plan, and the important basis for degree assessment is the number of mitoses in a given area of the pathological image. We utilized deep multi-scale fused fully convolutional neural network (MFF-CNN) combing with conditional random felid (CRF) to detect mitoses in hematoxylin and eosin stained histology image. Analyze the characteristics of mitotic detection ----scale invariance and sparsity, as well as the difficulties ---- small amount of data , inconsistent image staining and sample class unbalanced. Based on this, mitotic detection model is designed. In this paper, a tissue-based staining equalization method is used, and to establish an effective training sample set, we select training samples by using CNN. A mitotic detection model fusing multi-level and multi-scale features and context information was designed, and the corresponding training strategy was made to reduce over-fitting. As preliminarily validated on the public 2014 ICPR MITOSIS data, our method achieves a better performance in term of detection accuracy than ever recorded for this dataset.

Graphs are largely used in computer science to model relations, or associations, among entities the compose complex systems. More recently, they found a broad field of application in bioinformatics and medical informatics supporting modelling, analysis of many systems. The applications span from representing interactions among molecules within cells, to model the functions of the brains. In order to support research, algorithms from graph theory that are able to extract knowledge from network should be coupled to efficient visualisation techniques. Although the importance of such topic, we retain that many challenges should be faced in the futures, such as automated pathway and network layout to better match biologists’ needs, the developing of a standard able to give more and better choices to represent nodes, edges finally, the developing of automated mechanism able to improve the network navigation methods that help users manage large and complex networks with the goal to improve the usability.

Let G be a finite group. The prime graph Γ(G) of G is defined as follows: The set of vertices of Γ(G) is the set of prime divisors of |G| and two distinct vertices p and p' are connected in Γ(G), whenever G has an element of order pp'. A non-abelian simple group P is called recognizable by prime graph if for any finite group G with Γ(G)=Γ(P), G has a composition factor isomorphic to P. In [4] proved finite simple groups ²D_n(q), where n ≠ 4k are quasirecognizable by prime graph. Now in this paper we discuss the quasirecognizability by prime graph of the simple groups ²D_2k(q), where k ≥ 9 and q is a prime power less than 10⁵.

It is one of very important and basic problem in compute vision field that recovering depth information of objects from two-dimensional images. In view of the shortcomings of existing methods of depth estimation, a novel approach based on SIFT (the Scale Invariant Feature Transform) is presented in this paper. The approach can estimate the depths of objects in two images which are captured by an un-calibrated ordinary monocular camera. In this approach, above all, the first image is captured. All of the camera parameters remain unchanged, and the second image is acquired after moving the camera a distance d along the optical axis. Then image segmentation and SIFT feature extraction are implemented on the two images separately, and objects in the images are matched. Lastly, an object depth can be computed by the lengths of a pair of straight line segments. In order to ensure that the best appropriate a pair of straight line segments are chose and reduce the computation, the theory of convex hull and the knowledge of triangle similarity are employed. The experimental results show our approach is effective and practical.

The problem of quantifying the vulnerability of graphs has received much attention nowadays, especially in the field of computer or communication networks. In a communication network, the vulnerability measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. If we think of a graph as modeling a network, the average lower 2-domination number of a graph is a measure of the graph vulnerability and it is defined by ${\gamma }_{2av}\left(G\right)=\frac{1}{\left|V\left(G\right)\right|}{\sum }_{v\in V\left(G\right)}{\gamma }_{2v}\left(G\right)$, where the lower 2-domination number, denoted by ${\gamma }_{2v}\left(G\right)$, of the graph G relative to v is the minimum cardinality of 2-domination set in G that contains the vertex v. In this paper, the average lower 2-domination number of wheels and some related networks namely gear graph, friendship graph, helm graph and sun flower graph are calculated. Then, we offer an algorithm for computing the 2-domination number and the average lower 2-domination number of any graph G.