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Reconfiguring a very large scale integration (VLSI) array with faults is to construct a maximum logical sub-array (target array) without faults. A large target array implies a good harvest of the corresponding reconfiguration algorithm. Thus, a tight upper bound of the harvest can be directly used to evaluate the performance of the reconfiguration algorithm. This paper presents a new approach to calculate the upper bound of the harvest for the VLSI arrays with clustered faults. The latest upper bound is successfully reduced and the proposed technique to calculate the upper bound is bound into a reconfiguration algorithm cited in this paper. Simulation results show that the upper bound is reduced up to 20% on 256 × 256 array with clustered faults, and the corresponding reconfiguration process is significantly accelerated over 30%, without loss of harvest. [ABSTRACT FROM AUTHOR]

In this paper, we study the bound on the number of isolated zeros of Abelian integrals associated with the seventh-degree hyperbolic Hamiltonian system. When the unperturbed system has a unique period annulus bounded by a heteroclinic loop, a series of results on the upper bound of the number of zeros of the related Abelian integrals are obtained. However, there are still some open problems left about the exact bound. Furthermore, we give some results for the system when the parameters in the Hamiltonian system are fixed to certain values. The main tools involve algebraic symbolic computations such as counting the zeros of semi-algebraic systems. [ABSTRACT FROM AUTHOR]

Most of us may have had the experience of forgetting some term from a physical book when the term appears in neither the table of contents nor the index. Unfortunately, we must search for it page by page. In one edition of the popular physical book "Harry Potter and the Sorcerer's Stone", for example, the term "dragon's blood" only appears on pages 81 and 175, so browsing through the whole book to find it would be inevitable. In this study, a mechanism is provided to carry out an online search on physical books. To financially support this mechanism, we can put online advertisements with different offers on these physical books. An advertisement scheduling problem (ASP) is therefore formulated to maximize the total profit. To obtain the optimal schedules, we propose a branch-and-bound algorithm equipped with an upper bound. Experimental results show that the proposed upper bound performs well and completes the search in only 4% of the execution time of an ordinary branch-and-bound algorithm. [ABSTRACT FROM AUTHOR]