Graphs are some one of the simplest type of objects in Mathematics. In Chapter Chapter ?? we saw how to construct kernels between graphs, that is, when the individual examples x ∈ X are graphs. In this chapter we consider the case when the input space X is itself a graph and the examples are vertices in this graph. Such a case may arise naturally in diverse contexts. We may be faced with a netw...

We prove that the only nearest neighbor jump process with local dependence on the occupation times satisfying the partially exchangeable property is the vertex reinforced jump process, under some technical conditions (Theorem 4). This result gives a counterpart to the characterization of edge reinforced random walk given by Rolles [9].

Existing novice robot programming systems are complex, which ironically makes them unsuitable for novices. We have analysed 19 reports of robot projects to inform development of an ontology of critical concepts that end user robot programming environments must include. This is a first step to simpler end user robot programming systems.

We give a characterization of a modi ed edge reinforced random walk in terms of certain partially exchangeable sequences In particu lar we obtain a characterization of edge reinforced random walk in troduced by Coppersmith and Diaconis on a edge connected graph Modifying the notion of partial exchangeability introduced by Diaco nis and Freedman in we characterize unique mixtures of reversible M...

nowadays, strategic planning was very important for every company, many companies realize the importance of strategic planning. holding companies have considered this issue. strategic planning in holding multibusinessess company differs from other single companies based on complexities. holding companies are faced with two important strategic decisions: 1) what areas and how investments should ...

We use multilinear maps to provide a solution to the long-standing problem of public-key broadcast encryption where all parameters in the system are small. In our constructions, ciphertext overhead, private key size, and public key size are all poly-logarithmic in the total number of users. The systems are fully collusion-resistant against any number of colluders. All our systems are based on a...

Enhancing Mathematical Graphical Displays in Excel through AnimationThe use of spreadsheets in teaching mathematics has increased significantly in recent years. One can implement mathematical algorithms, models, visualizations, and applications naturally and effectively through interactive spreadsheet constructions and creative graphical displays. This paper demonstrates techniques that enable ...

Despite the utilization of several earthquake resistant traditional techniques in Iranian architecture throughout the centuries, the high seismic vulnerability of Iranian vernacular constructions is obvious. One of the latest innovations in building earthquake-proof emergency dwellings, prior to introducing the modern seismic design codes, took place during the successive destructive earthqu...