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Since reversible logic has promising applications in domains like low-power design and quantum computing, it is necessary to efficiently design high-performance reversible logic circuits. In this paper, in order to reduce the number of qubits while achieving low quantum cost, the Kronecker functional decision diagram (KFDD) based reversible circuit synthesis method is improved by using two strategies. One is to generate a locally optimal reversible cascade for each of the KFDD nodes by performing transformations on the function represented by a node and using a gate library consisting of NOT, CNOT, Toffoli gates and mixed-polarity Peres gates. This strategy helps reduce the quantum cost and the number of qubits. The other is to map KFDD nodes to their locally optimal reversible cascades level by level via breadth-first traversal of the KFDD. This strategy reduces the number of qubits by using the circuit line labeled by an input variable of the KFDD as the target line of a reversible gate. Comparison results are presented in tabular and graphical forms. Compared to the existing decision diagram based reversible circuit synthesis methods, the proposed method can reduce both the quantum cost and the number of qubits in many cases. Compared to other state-of-the-art synthesis methods for reversible circuits, the proposed method can achieve much lower quantum cost but still incurs a high number of qubits for many functions. However, it can achieve the minimum number of qubits for a few irreversible functions while achieving much lower quantum cost. In addition, the proposed method is very time efficient. • Locally optimal reversible cascades are generated for the KFDD nodes. • The circuit line labeled by an input variable of the KFDD is used as the target line of a reversible gate. • The proposed reversible circuit synthesis method is very time efficient. • Both the quantum cost and the number of qubits of the circuit synthesized from a KFDD are reduced in many cases. • For a few irreversible functions, the minimum number of qubits is achieved while achieving low quantum cost. [ABSTRACT FROM AUTHOR]

In this paper, we show how to construct various extensions of Shanks transformation for functions in a vector space. They are aimed at transforming a function tending slowly to its limit when the argument tends to infinity into another function with better convergence properties. Their expressions as ratio of determinants and recursive algorithms for their implementation are given. A simplified form of one of them is derived. It allows us to obtain a convergence result for an important class of functions. An application to integrable systems is discussed. [ABSTRACT FROM AUTHOR]

• Function transformation through shape morphing by swelling hydrogel structures. • Photopolymerization of prepolymer filled in the void of swollen hydrogel structures. • Choice of prepolymer to keep water molecules inside swollen hydrogel network. • Fabrication of inversely tapered shapes for oil repellent functions. • Stress dissipation through laterally buckled line shapes of a film surface. The functions of materials are correlated with their shapes. Here, we propose a scheme of functional transformation of a polymeric film by changing the surface shape. After the preparation of straight shapes such as lines or rectangles on a substrate by conventional microfabrication methods, we transformed the shapes into laterally buckled or inversely tapered shapes. The change in surface shape induced stress dissipation or superomniphobic functions, which are difficult to obtain with straight shapes. To transform the shapes, we harnessed a method of swelling hydrogel shapes bonded to a substrate. We replicated the swollen shapes with functional materials by photopolymerization of liquid prepolymers filled within the cavities of the swollen hydrogel shapes. We investigated methods to hold water molecules within the hydrogel networks during photopolymerization by controlling the surface energy of the photocurable liquid prepolymer and removing air between the liquid prepolymer and the cavities for easy infiltration of the liquid prepolymer into the inversely tapered shapes. The proposed scheme of function transformation by using surface shape morphing can be a platform technology for developing unprecedented functions depending on shape. [ABSTRACT FROM AUTHOR]