Computing the partition function of the Ising model on a graph has been investigated from both sides of computer science and statistical physics, with producing fertile results of P cases, FPTAS/FPRAS cases, inapproximability and intractability. Recently, measurement-based quantum computing as well as quantum annealing open up another bridge between two fields by relating a tree tensor network representing a quantum graph state to a rank decomposition of the graph. This paper makes this bridge wider in both directions. An $O^*(2^{ rac{omega}{2} bw(G)})$-time algorithm is developed for the partition function on n-vertex graph G with branch decomposition of width bw(G), where O* ignores a polynomial factor in n and ω is the matrix multiplication parameter less than 2.37287. Related algorithms of $O^*(4^{rw( ilde{G})})$ time for the tree tensor network are given which are of interest in quantum computation, given rank decomposition of a subdivided graph $ ilde{G}$ with width $rw( ilde{G})$. These algorithms are parameter-exponential, i.e., O*(cp) for constant c and parameter p, and such an algorithm is not known for a more general case of computing the Tutte polynomial in terms of bw(G) (the current best time is O*(min{2n, bw(G)O(bw(G))})) with a negative result in terms of the clique-width, related to the rank-width, under ETH.

The forbidden state problem is to synthesize a control policy for preventing a Petri net from reaching any state in its forbidden set. In this paper, we address a liveness preserving version of the forbidden state problem for lossy Petri nets. During the process of keeping Petri nets out of the set of their forbidden states, a control policy does not disable a live marking. We present a method to solve the above problem based on fixed point computations. We show that for lossy Petri nets, the problem is decidable. From a practical viewpoint, the problem associated with our fixed point approach is 'state explosion. ' In order to overcome this problem, we propose a symbolic approach, which uses Boolean functions for implicitly representing the set of states. We use Boolean functions for representing reachable markings. Thus OBDDs, compact representations of Boolean functions, can reduce the time and space involved in solving the forbidden state problem described in this paper.

This paper proposes an enhanced affinity graph (EA-graph) for image segmentation. Firstly, the original image is over-segmented to obtain several sets of superpixels with different scales, and the color and texture features of the superpixels are extracted. Then, the similarity relationship between neighborhood superpixels is used to construct the local affinity graph. Meanwhile, the global affinity graph is obtained by sparse reconstruction among all superpixels. The local affinity graph and global affinity graph are superimposed to obtain an enhanced affinity graph for eliminating the influences of noise and isolated regions in the image. Finally, a bipartite graph is introduced to express the affiliation between pixels and superpixels, and segmentation is performed using a spectral clustering algorithm. Experimental results on the Berkeley segmentation database demonstrate that our method achieves significantly better performance compared to state-of-the-art algorithms.

In this study, flexible organic solar cells (OSCs) employing a solution-processed hole-transporting layer (HTL) and low temperature annealing active layer have been fabricated. Vanadium oxide (V$_{2}$O$_{5})$, poly(3,4-ethylene dioxythiophene):poly(styrene sulfonate) (PEDOT:PSS), V$_{2}$O$_{5}$/PEDOT:PSS or PEDOT:PSS/V$_{2}$O$_{5}$ is used as the HTL. Poly(3-hexythiophene) (P3HT):[6,6]-phenyl C61-butyric acid methyl ester (PCBM) is used as the active layer. HTL and active layer are all formed by a spin coating method on polyethylene terephthalate (PET) substrates. The OSC configuration has been optimized in the study to be PET/ITO/V$_{2}$O$_{5}$/PEDOT:PSS/P3HT:PCBM/LiF/Al. Based on a low annealing temperature of 90$^{circ}$C for P3HT:PCBM and parameters optimization of solution-processed V$_{2}$O$_{5}$/PEDOT:PSS, the OSC demonstrates a current density (JSC) and power conversion efficiency (PCE) of 6.08, mA/cm$^{2}$ and 1.57%, while an OSC without the HTL has PCE around 0.06%. The V$_{2}$O$_{5}$/PEDOT:PSS stacked HTL provides not only a stepwise hole-transporting energy diagram configuration but a smooth film surface for coating P3HT:PCBM active layer, which subsequently increases charge carrier transporting capability and extracts holes from the active layer to the anode.