Joint-tree model and the maximum genus of graphs

The vertex v of a graph G is called a 1-critical-vertex for the maximum genus of the graph, or for simplicity called 1-critical-vertex, if G-v is a connected graph and {\deg}M(G - v) = {\deg}M(G) - 1. In this paper, through the joint-tree model, we obtained some types of 1-critical-vertex, and get the upper embeddability of the Spiral Snm

The extremal genus embedding of graphs

Let Wn be a wheel graph with n spokes. How does the genus change if adding a degree-3 vertex v, which is not in V (Wn), to the graph Wn? In this paper, through the joint-tree model we obtain that the genus of Wn+v equals 0 if the three neighbors of v are in the same face boundary of P(Wn); otherwise, {\deg}(Wn + v) = 1, where P(Wn) is the unique planar embedding of Wn. In addition, via the independent set, we provide a lower bound on the maximum genus of graphs, which may be better than both the result of D. Li & Y. Liu and the result of Z. Ouyang etc: in Europ. J. Combinatorics. Furthermore, we obtain a relation between the independence number and the maximum genus of graphs, and provide an algorithm to obtain the lower bound on the number of the distinct maximum genus embedding of the complete graph Km, which, in some sense, improves the result of Y. Caro and S. Stahl respectively

Polar Angle Detection and Image Combination Based Leukocyte Segmentation for Overlapping Cell Images

Leukocyte segmentation is one of the essential steps in an automatic leukocyte recognition system. Due to the complexity of the overlapping cell images, methods for leukocyte segmentation are still needed. In this paper, we first construct a combined image by saturation and green channels to extract the nucleus and in turn locate a cursory circular region of the leukocyte. Then the boundary of the leukocyte is represented by the polar coordinate. We determine the overlapping area by polar angle detection. Finally, another combined image is built based on the red and blue channels of the sub image covering the overlap to segment the leukocyte. The paper reports a promising segmentation for 60 microscopic cell images

Vertex Splitting and Upper Embeddable Graphs

The weak minor G of a graph G is the graph obtained from G by a sequence of edge-contraction operations on G. A weak-minor-closed family of upper embeddable graphs is a set G of upper embeddable graphs that for each graph G in G, every weak minor of G is also in G. Up to now, there are few results providing the necessary and sufficient conditions for characterizing upper embeddability of graphs. In this paper, we studied the relation between the vertex splitting operation and the upper embeddability of graphs; provided not only a necessary and sufficient condition for characterizing upper embeddability of graphs, but also a way to construct weak-minor-closed family of upper embeddable graphs from the bouquet of circles; extended a result in J: Graph Theory obtained by L. Nebesk{\P}y. In addition, the algorithm complex of determining the upper embeddability of a graph can be reduced much by the results obtained in this paper

Managing Distrust-Induced Risk with Deposit in Supply Chain Contract Decisions

This paper studies the trust issue in a two-echelon supply chain information sharing process. In a supply chain, the retailer reports the forecasted demand to the supplier. Traditionally, the supplier’s trust in the retailer’s reported information is based on the retailer’s reputation. However, this paper considers that trust is random and is also affected by the reputation and the demand gap. The supplier and retailer have been shown to have different evaluations regarding the degree of trust. Furthermore, distrust is inherently linked to perceived risk. To mitigate perceived risk, a two-stage decision process with an unpayback deposit contract is proposed. At the first stage, the supplier and the retailer negotiate the deposit contract. At the second stage, a Stackelberg game is used to determine the retailer’s reported demand and the supplier’s production quantity. We show that the deposits from the retailer’s and supplier’s perspectives are different. When the retailer’s reported demand is equal to the supplier’s forecasted demand, the retailer’s evaluation of the deposit is more than that of supplier’s. When the retailer’s reported demand is equal to the retailer’s forecasted demand, the deposit from the retailer’s perspective is at the lowest level

A stochastic dynamic programming approach-based yield management with substitution and uncertainty in semiconductor manufacturing

AbstractYield management is important and challengeable in semiconductor industry for the quality uncertainty of the final products. The total yield rate of the semiconductor manufacturing process is uncertain, each product is graded into one of several quality levels according to performance before being shipped. A product originally targeted to satisfy the demand of one product may be used to satisfy the demand of other products when it conforms to their specifications. At the same time, the products depreciate in allocation periods, which mainly results from technical progresses. This paper studies the semiconductor yield management issue of a make-to-stock system with single input, multi-products, multi-demand periods, upward substitution and periodic depreciation. The whole time horizon of the system operation process can be divided into two stages: the production stage and the allocation stage. At the first stage, the firm invests in raw materials before any actual demand is known and produces multiple types of products with random yield rates. At the second stage, products are classified into different classes by quality and allocated in numbers of periods. The production and allocation problem are modeled as a stochastic dynamic program in which the objective is to maximize the profit of the firm. We show that the PRA (parallel allocation first, then upgrade) allocation policy is the optimal allocation policy and the objective function is concave in production input. An iterative algorithm is designed to find the optimal production input and numerical experiments are used to illustrate its effectiveness

Divergent Regulation of CBF Regulon on Cold Tolerance and Plant Phenotype in Cassava Overexpressing Arabidopsis CBF3 Gene

Cassava is a tropical origin plant that is sensitive to chilling stress. In order to understand the CBF cold response pathway, a well-recognized regulatory mechanism in temperate plants, in cassava, overexpression of an Arabidopsis CBF3 gene is studied. This gene renders cassava increasingly tolerant to cold and drought stresses but is associated with retarded plant growth, leaf curling, reduced storage root yield, and reduced anthocyanin accumulation in a transcript abundance-dependent manner. Physiological analysis revealed that the transgenic cassava increased proline accumulation, reduced malondialdehyde production, and electrolyte leakage under cold stress. These transgenic lines also showed high relative water content when faced with drought. The expression of partial CBF-targeted genes in response to cold displayed temporal and spatial variations in the wild-type and transgenic plants: highly inducible in leaves and less altered in apical buds. In addition, anthocyanin accumulation was inhibited by downregulating the expression of genes involved in its biosynthesis and by interplaying between the CBF3 and the endogenous transcription factors. Thus, the heterologous CBF3 modulates the expression of stress-related genes and carries out a series of physiological adjustments under stressful conditions, showing a varied regulation pattern of CBF regulon from that of cassava CBFs