We provide an improved implementation of Schmitzer's sparse multi-scale algorithm for discrete optimal transport on grids. We report roughly 2-4 times faster runtimes on the DOTmark benchmark. The source code is open source and publicly available.
Antioxidants remove free radicals and inhibit the oxidation of oxygen-sensitive substances, which are of great significance in disease prevention and food preservative. Therefore, it is of great significance to establish a convenient, efficient and universal method for screening and evaluating antioxidant activity. In this study, Nitrogen-doped Graphene (N-G) with high conductivity and Chitosan (CS) with good film forming and stability were used as electrode substrate materials. And a ds-DNA/N-G@CS/GCE electrochemical biosensor for rapid evaluation of antioxidant activity was constructed by assembling ds-DNA and taking advantage of the signal difference between pre- and post-damage ds-DNA loading in Ru(NH3)6 3+ probe solution. N-G@CS with good electro-catalysis and high capacitance significantly improved the response signal of the sensor. At the same time, Square Wave Voltammetry (SWV) was used to optimize the conditions affecting the evaluation results of biosensors. The results showed that under the Fenton solution system with pH 7.0 and the ratio of Fe2+ to OH− 1:4, the biosensor has a high oxidation ds-DNA damage within 30 min The system can inhibit the damage of ds-DNA by adding antioxidants. Under optimized experimental conditions, composite yogurt and plain yogurt with weak antioxidant activity difference were evaluated by the constructed biosensor, and compared with L-ascorbic acid, the activity order was L-ascorbic acid > composite yogurt > plain yogurt. The results were consistent with the results of hydroxyl radical scavenging and ABTS+ radical scavenging experiments, and there was no significant difference between the three methods. This study not only provides a convenient and efficient method for the evaluation of antioxidant activity, but also provides strategies and technical support for the development of low-cost, highly sensitive and universal portable activity evaluation techniques.
This paper deals with circulant matrices. It is shown that a circulant matrix can be multiplied by a vector in time O(n log(n)) in a ring with roots of unity without making use of an FFT algorithm. With our algorithm we achieve a speedup of a factor of about 2.25 for the multiplication of two polynomials with integer coefficients compared to multiplication by an FFT algorithm. Moreover this paper discusses multiplication of large integers as further application.
We describe SMS, our submission to the exact treedepth track of PACE 2020. SMS computes the treedepth of a graph by branching on the small minimal separators of the graph.
In this paper, we consider differential approximability of the traveling salesman problem (TSP). We show that TSP is $3/4$-differential approximable, which improves the currently best known bound $3/4 -O(1/n)$ due to Escoffier and Monnot in 2008, where $n$ denotes the number of vertices in the given graph.
Answering a question of Abbasi-Zadeh, Bansal, Guruganesh, Nikolov, Schwartz and Singh (2018), we prove the existence of a slowed-down sticky Brownian motion whose induced rounding for MAXCUT attains the Goemans--Williamson approximation ratio. This is an especially simple particular case of the general rounding framework of Krivine diffusions that we investigate elsewhere.
We give an exact $O(nk^2)$ algorithm for finding the densest k subgraph in outerplanar graphs. We extend this to an exact $O(nk^2 8^b)$ algorithm for finding the densest k subgraph in b-outerplanar graphs. Finally, we hypothesize that Baker's PTAS technique will not work for the densest k subgraph problem in planar graphs.
We prove that a connected planar graph with $n$ vertices and $n+μ$ edges has a vertex separator of size $O( \sqrtμ + 1)$, and this separator can be computed in linear time.
We provide a simple method for improving the performance of the recently introduced learned Bloom filters, by showing that they perform better when the learned function is sandwiched between two Bloom filters.
In a permutation sequence built by means of sub permutations the transition between successive permutations are subject to a set of n(n - 1)/2 rules that group into n - 1 matrices with a high degree of regularity. By means of these rules the sequence can be produced in O(3n!) time and O(n^3) space.
We propose a \textit{purely combinatorial algorithm} for \mkvc{} in bipartite graphs, achieving approximation ratio~0.7. The only combinatorial algorithms currently known until now for this problem are the natural greedy algorithm, that achieves ratio 0.632, and an easy~$2/3$-approximation algorithm presented in \cite{DBLP:journals/corr/BonnetEPS14}.
State of the art maximum clique algorithms use a greedy graph colouring as a bound. We show that greedy graph colouring can be misleading, which has implications for parallel branch and bound.
In this paper, we apply results on number systems based on continued fraction expansions to modular arithmetic. We provide two new algorithms in order to compute modular multiplication and modular division. The presented algorithms are based on the Euclidean algorithm and are of quadratic complexity.
The Inverse 3-SAT problem is known to be coNP Complete. This article shows a new interesting way to solve directly the problem by using closure under resolution and partial assignment properties. An algorithm is proposed which lets solve the (co)Inverse 3-SAT problem.