Model of Multi-branch Trees for Efficient Resource Allocation

Although exploring the principles of resource allocation is still important in many fields, little is known about appropriate methods for optimal resource allocation thus far. This is because we should consider many issues including opposing interests between many types of stakeholders. Here, we develop a new allocation method to resolve budget conflicts. To do so, we consider two points—minimizing assessment costs and satisfying allocational efficiency. In our method, an evaluator's assessment is restricted to one's own projects in one's own department, and both an executive's and mid-level executives' assessments are also restricted to each representative project in each branch or department they manage. At the same time, we develop a calculation method to integrate such assessments by using a multi-branch tree structure, where a set of leaf nodes represents projects and a set of non-leaf nodes represents either directors or executives. Our method is incentive-compatible because no director has any incentive to make fallacious assessments

Region colorings for spatial graphs (Women in Mathematics)

A Dehn p-coloring for a spatial graph diagram is an assignment of an element (color) of Zp={1, 2, ··· , P-1} to each region of the diagram. At each crossing, some coloring condition is satisfied. We give a family of spatial graph invariants and classify the vertex conditions of Dehn colorings. Some examples of spatial graphs can be distinguished by the number of Dehn colorings by selecting an appropriate vertex condition, whereas they cannot be distinguished by the number of Dehn colorings with no vertex condition. This is joint work with Kanako Oshiro (Sophia University)

Gauss diagram formulas of Vassiliev invariants of spatial 2-bouquet graphs

We introduce new formulas that are Vassiliev invariants of flat vertex isotopy classes of spatial 2-bouquet graphs, which are equivalent to 2-string links. Although any Gauss diagram formula of Vassiliev invariants of spatial 2-bouquet graphs in a 3-space has been unknown, this paper gives the first and simple example.Comment: 10 pages, 7 figures, Typos were correcte