We refine the enumeration of fusene chains of a given length with respect to the number of turns by constructing bijections between such chains and ternary words. Explicit formulas thus obtained are ...then used to compute the expected values for the whole class of bond-additive degree-based topological indices over all such chains of a given length. The results are also applicable to several other classes of chemically interesting polycyclic chains, such as, e.g., phenylene and spiro chains.
Convexity Deficit of Benzenoids Basic, Nino; Berkemer, Sarah J; Fallmann, Jorg ...
Croatica Chemica Acta,
2020, Volume:
92, Issue:
4
Journal Article, Paper
Peer reviewed
Open access
In 2012, a family of benzenoids was introduced by Cruz, Gutman, and Rada, which they called convex benzenoids. In this paper we introduce the convexity deficit, a new topological index intended for ...benzenoids and, more generally, fusenes. This index measures by how much a given fusene departs from convexity. It is defined in terms of the boundary-edges code. In particular, convex benzenoids are exactly the benzenoids having convexity deficit equal to O. Quasi-convex benzenoids form the family of non-convex benzenoids that are closest to convex, i.e., they have convexity deficit equal to 1. Finally, we investigate convexity deficit of several important families of benzenoids. Keywords: Benzenoid, fusene, convexity deficit, convex benzenoid, quasi-convex benzenoid, pseudo-convex benzenoid.
A hexagonal patch is a plane graph in which inner faces have length 6, inner vertices have degree 3, and boundary vertices have degree 2 or 3. We consider the following counting problem: given a ...sequence of twos and threes, how many hexagonal patches exist with this degree sequence along the outer face? This problem is motivated by the enumeration of benzenoid hydrocarbons and fullerenes in computational chemistry. We give the first polynomial time algorithm for this problem. We show that it can be reduced to counting maximum independent sets in circle graphs, and give a simple and fast algorithm for this problem. It is also shown how to subsequently generate hexagonal patches.
It is shown that a geometrically planar fusene is uniquely determined by its boundary edge code. Surprisingly, the same conclusion is not true in general but holds for geometrically planar and ...non-planar fusenes with at most 25 hexagons, except for two particular cases. In addition, it is proved that two fusenes with the same boundary edge code have the same number of hexagons.
A hexagonal patch is a plane graph in which inner faces have length 6, inner vertices have degree 3, and boundary vertices have degree 2 or 3. We consider the following counting problem: given a ...sequence of twos and threes, how many hexagonal patches exist with this degree sequence along the outer face? This problem is motivated by the enumeration of benzenoid hydrocarbons and fullerenes in computational chemistry. We give the first polynomial time algorithm for this problem. We show that it can be reduced to counting maximum independent sets in circle graphs, and give a simple and fast algorithm for this problem.
Detail-Revealing Deep Video Super-Resolution Xin Tao; Hongyun Gao; Renjie Liao ...
2017 IEEE International Conference on Computer Vision (ICCV),
2017-Oct.
Conference Proceeding
Open access
Previous CNN-based video super-resolution approaches need to align multiple frames to the reference. In this paper, we show that proper frame alignment and motion compensation is crucial for ...achieving high quality results. We accordingly propose a "sub-pixel motion compensation" (SPMC) layer in a CNN framework. Analysis and experiments show the suitability of this layer in video SR. The final end-to-end, scalable CNN framework effectively incorporates the SPMC layer and fuses multiple frames to reveal image details. Our implementation can generate visually and quantitatively high-quality results, superior to current state-of-the-arts, without the need of parameter tuning.
How can we find a general way to choose the most suitable samples for training a classifier? Even with very limited prior information? Active learning, which can be regarded as an iterative ...optimization procedure, plays a key role to construct a refined training set to improve the classification performance in a variety of applications, such as text analysis, image recognition, social network modeling, etc. Although combining representativeness and informativeness of samples has been proven promising for active sampling, state-of-the-art methods perform well under certain data structures. Then can we find a way to fuse the two active sampling criteria without any assumption on data? This paper proposes a general active learning framework that effectively fuses the two criteria. Inspired by a two-sample discrepancy problem, triple measures are elaborately designed to guarantee that the query samples not only possess the representativeness of the unlabeled data but also reveal the diversity of the labeled data. Any appropriate similarity measure can be employed to construct the triple measures. Meanwhile, an uncertain measure is leveraged to generate the informativeness criterion, which can be carried out in different ways. Rooted in this framework, a practical active learning algorithm is proposed, which exploits a radial basis function together with the estimated probabilities to construct the triple measures and a modified best-versus-second-best strategy to construct the uncertain measure, respectively. Experimental results on benchmark datasets demonstrate that our algorithm consistently achieves superior performance over the state-of-the-art active learning algorithms.
Zusammenfassung
Die amyotrophe Lateralsklerose (ALS) ist eine rasch progrediente Degeneration sowohl des ersten als auch des zweiten motorischen Neurons. Klinische Charakteristika sind ...fortschreitende, sich kontinuierlich über den Körper ausbreitende Paresen und Atrophien der Extremitätenmuskulatur. Die Genetik der ALS ist in den letzten 5 Jahren komplexer geworden. Neben den häufigen SOD1-Mutationen kamen die seltener auftretenden Mutationen in den Genen für TDP-43 und FUS hinzu, sowie vor Kurzem das
C9ORF72
-Gen, das in Deutschland mittlerweile noch vor dem
SOD1
-Gen (24 vs. 13 % in unserem Krankengut) die häufigste Mutation bei der ALS ist. Daneben gibt es noch weniger häufige genetische Veränderungen, die eher von pathogenetischem Interesse sind. Interessant ist auch, dass in den letzten Jahren die phänotypische Vielfalt zugenommen hat.
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