A polynomial-time algorithm to solve the large scale of airplane refueling problem

Airplane refueling problem is a nonlinear combinatorial optimization problem with $n!$ feasible feasible solutions. Given a fleet of $n$ airplanes with mid-air refueling technique, each airplane has a specific fuel capacity and fuel consumption rate. The fleet starts to fly together to a same target and during the trip each airplane could instantaneously refuel to other airplanes and then be dropped out. The question is how to find the best refueling policy to make the last remaining airplane travels the farthest. To solve the large scale of the airplane refueling problem in polynomial-time, we propose the definition of the sequential feasible solution by employing the data structural properties of the airplane refueling problem. We prove that if an airplane refueling problem has feasible solutions, it must have sequential feasible solutions, and its optimal feasible solution must be the optimal sequential feasible solution. Then we present the sequential search algorithm which has a computational complexity that depends on the number of sequential feasible solutions referred to $Q_n$, which is proved to be upper bounded by $2^{n-2}$ as an exponential bound that lacks of applicability on larger input for worst case. Therefore we investigate the complexity behavior of the sequential search algorithm from dynamic perspective, and find out that $Q_n$ is bounded by $\frac{m^2}{n}C_n^m$ when the input $n$ is greater than $2m$. Here $m$ is a constant and $2m$ is regarded as the "inflection point" of the complexity of the sequential search algorithm from exponential-time to polynomial-time. Moreover, we build an efficient computability scheme according to which we shall predict the specific complexity of the sequential search algorithm to choose a proper algorithm considering the available running time for decision makers or users.Comment: 18 pages, 2 figure

The nn-vehicle exploration problem is NP-complete

The $n$-vehicle exploration problem (NVEP) is a combinatorial optimization problem, which tries to find an optimal permutation of a fleet to maximize the length traveled by the last vehicle. NVEP has a fractional form of objective function, and its computational complexity of general case remains open. We show that Hamiltonian Path $\leq_P$ NVEP, and prove that NVEP is NP-complete.Comment: 5 pages, 6 figure

UVL: A Unified Framework for Video Tampering Localization

With the development of deep learning technology, various forgery methods emerge endlessly. Meanwhile, methods to detect these fake videos have also achieved excellent performance on some datasets. However, these methods suffer from poor generalization to unknown videos and are inefficient for new forgery methods. To address this challenging problem, we propose UVL, a novel unified video tampering localization framework for synthesizing forgeries. Specifically, UVL extracts common features of synthetic forgeries: boundary artifacts of synthetic edges, unnatural distribution of generated pixels, and noncorrelation between the forgery region and the original. These features are widely present in different types of synthetic forgeries and help improve generalization for detecting unknown videos. Extensive experiments on three types of synthetic forgery: video inpainting, video splicing and DeepFake show that the proposed UVL achieves state-of-the-art performance on various benchmarks and outperforms existing methods by a large margin on cross-dataset

"Maps preserving the spectrum of generalized Jordan product of operators", and its "Addendum"

In the paper "Maps preserving the spectrum of generalized Jordan product of operators", we define a generalized Jordan products on standard operator algebras $A_1, A_2$ on complex Banach spaces $X_1, X_2$, respectively. This includes the usual Jordan product $A_1 \circ A_2 = A_1 A_2 + A_2 A_1$, and the triple $\{A_1,A_2,A_3\} = A_1 A_2 A_3 + A_3 A_2 A_1$. Let a map $\Phi : A_1 \to A_2$ prserving the spectra of the products $$\sigma (\Phi (A_1) \circ ... \circ \Phi (A_k)) = \sigma (A_1\circ ... \circ A_k)$$ whenever any one of $A_1, ..., A_k$ has rank at most one. It is shown in this paper that if the range of $\Phi$ contains all operators of rank at most three, then $\Phi$ must be a Jordan isomorphism multiplied by an $m$th root of unity. Similar results for maps between self-adjoint operators acting on Hilbert spaces are also obtained. After our paper "Maps preserving the spectrum of generalized Jordan product of operators" was published in Linear Algebra Appl. 432 (2010), 1049-1069, Jianlian Cui pointed out that some arguments in the proof of Theorem 3.1 are not entirely clear and accurate. Here we supply some details in the "Addendum".Comment: 1. 29 pages, the "orginal paper". 2. 5 pages, the "Addendum". 3. Replace the latex file of the "original paper" to avoid the conflict of using an old version of 'natbib' at April 23, 2010. The newer version simply does not use `natbib' at all, and nothing else is changed

Starch/microcrystalline cellulose hybrid gels as gastric-floating drug delivery systems

We report hybrid gels based on a high-amylose starch and microcrystalline cellulose with demonstrated properties for gastric-floating drug delivery purposes. The starch/cellulose gels were prepared by ionic liquid dissolution and regeneration, resulting in a continuous surface and a porous interior and a type-II crystalline structure of cellulose. These polysaccharide gels displayed satisfactory elasticity (0.88), recovery (0.26–0.36) and equilibrium swelling (1013–1369%). The hybrid gels were loaded with ranitidine hydrochloride as a model drug and subsequently, low-density starch/cellulose tablets were fabricated by vacuum-freeze-drying. In vitro tests in a simulated gastric fluid indicate that the 3:7 (wt./wt.) starch/cellulose system could maintain the buoyancy for up to 24 h with a release of 45.87% for the first 1 h and a sustained release for up to 10 h. Therefore, our results have demonstrated the excellent gastric-floating ability and sustainable drug release behavior of the starch/cellulose hybrid gels

Human genome-wide repair map of DNA damage caused by the cigarette smoke carcinogen benzo[a]pyrene

Benzo[a]pyrene (BaP) is a widespread potent carcinogen found in food, coal tar, cigarette smoke, and industrial smoke. Cigarette smoking is the leading cause of lung cancer, and the mutagenesis in smoking-associated lung cancer is determined by multiple factors, including nucleotide excision repair. We have developed a general method for genome-wide mapping of nucleotide excision repair at single-nucleotide resolution and applied it to generate repair maps of UV- and BaP-induced DNA damage in human. Results show a novel sequence specificity of BaP diol epoxide-deoxyguanosine repair. This general method can be used to study repair of all types of DNA damages that undergo nucleotide excision repair