Searcharxiv⌕ Search

arXiv subjects

Dan Chen

Publications and source records attributed to Dan Chen.

27 records · Page 2Linked to original sources
arXiv2020

Finite-size scaling of geometric renormalization flows in complex networks

Recently, the concept of geometric renormalization group provides a good approach for studying the structural symmetry and functional invariance of complex networks. Along this line, we systematically investigate the finite-size scaling of structural and dynamical observables in geometric renormalization flows of synthetic and real evolutionary networks. Our results show that these observables can be well characterized by a certain scaling function. Specifically, we show that the critical exponent implied by the scaling function is independent of these observables but only depends on the small-world properties of the network, namely, all networks located in the small-world phase have a uniform scaling exponent, while those located in the non-small-world phase and in their critical regions have another uniform scaling. More importantly, we perform extensive experiments on real evolutionary networks with small-world characteristics, and our results show that these observables also have uniform scaling in their geometric renormalization flows. Therefore, in a sense this exponent can be used as an effective measure for classifying universal small-world and non-small-world network models.

physics.soc-ph↗
arXiv2019

Improving the soil water module of the Decision Support System for Agrotechnology Transfer cropping system model for subsurface irrigation

Ensuring that crops use water and nutrients efficiently is an important strategy for increasing the profitability of farming and reducing the environmental load from agriculture. Subsurface irrigation can be an alternative to surface irrigation as a means of losing less irrigation water, but the application timing and amount are often difficult to determine. Well-defined soil and crop models are useful for assisting decision support, but most of the models developed to date have been for surface irrigation. The present study examines whether the Decision Support System for Agrotechnology Transfer (DSSAT, version 4.5) cropping system model is applicable for the production of processing tomatoes with subsurface irrigation, and it revises the soil module to simulate irrigation schemes with subsurface irrigation. Five farmed fields in California, USA, are used to test the performance of the model. The original DSSAT model fails to produce fruit yield by overestimating the water deficiency. The soil water module is then revised by introducing the movement of soil moisture due to a vertical soil moisture gradient. Moreover, an external parameter optimization system is constructed to minimize the error between the simulation and observations. The revised module reduces the errors in the soil moisture profile at each field compared to those by the original DSSAT model. The average soil moisture error decreases from 0.065m^3/m^3 to 0.029m^3/m^3. The yields estimated by the modified model are in a reasonable range from 80 to 150 ton/ha, which is commonly observed under well-managed conditions. The present results show that although further testing is required for yield prediction, the present modification to the original DSSAT model improves the precision of the soil moisture profile under subsurface irrigation and can be used for decision support for efficient producting of processing tomatoes.

q-bio.QM↗
arXiv2019

Weighted infinitesimal unitary bialgebras on rooted forests and weighted cocycles

In this paper, we define a new coproduct on the space of decorated planar rooted forests to equip it with a weighted infinitesimal unitary bialgebraic structure. We introduce the concept of $Ω$-cocycle infinitesimal bialgebras of weight $λ$ and then prove that the space of decorated planar rooted forests $H_{\mathrm{RT}}(X,Ω)$, together with a set of grafting operations $\{ B^+_ω\mid ω\in Ω\}$, is the free $Ω$-cocycle infinitesimal unitary bialgebra of weight $λ$ on a set $X$, involving a weighted version of a Hochschild 1-cocycle condition. As an application, we equip a free cocycle infinitesimal unitary bialgebraic structure on the undecorated planar rooted forests, which is the object studied in the well-known (noncommutative) Connes-Kreimer Hopf algebra. Finally, we construct a new pre-Lie algebraic structure on decorated planar rooted forests.

math.RA↗
arXiv2014

Evaluation of heat extraction through sapphire fibers for the GW observatory KAGRA

Currently, the Japanese gravitational wave laser interferometer KAGRA is under construction in the Kamioka mine. As one main feature, it will employ sapphire mirrors operated at a temperature of 20K to reduce the impact from thermal noise. To reduce seismic noise, the mirrors will also be suspended from multi-stage pendulums. Thus the heat load deposited in the mirrors by absorption of the circulating laser light as well as heat load from thermal radiation will need to be extracted through the last suspension stage. This stage will consist of four thin sapphire fibers with larger heads necessary to connect the fibers to both the mirror and the upper stage. In this paper, we discuss heat conductivity measurements on different fiber candidates. While all fibers had a diameter of 1.6mm, different surface treatments and approaches to attach the heads were analyzed. Our measurements show that fibers fulfilling the basic KAGRA heat conductivity requirement of $κ\geq $5000W/m/K at 20K are technologically feasible.

astro-ph.IM↗
arXiv2013

Approximating Majority Depth

We consider the problem of approximating the majority depth (Liu and Singh, 1993) of a point q with respect to an n-point set, S, by random sampling. At the heart of this problem is a data structures question: How can we preprocess a set of n lines so that we can quickly test whether a randomly selected vertex in the arrangement of these lines is above or below the median level. We describe a Monte-Carlo data structure for this problem that can be constructed in O(nlog n) time, can answer queries O((log n)^{4/3}) expected time, and answers correctly with high probability.

cs.CG↗
arXiv2009

Memoryless Routing in Convex Subdivisions: Random Walks are Optimal

A memoryless routing algorithm is one in which the decision about the next edge on the route to a vertex t for a packet currently located at vertex v is made based only on the coordinates of v, t, and the neighbourhood, N(v), of v. The current paper explores the limitations of such algorithms by showing that, for any (randomized) memoryless routing algorithm A, there exists a convex subdivision on which A takes Omega(n^2) expected time to route a message between some pair of vertices. Since this lower bound is matched by a random walk, this result implies that the geometric information available in convex subdivisions is not helpful for this class of routing algorithms. The current paper also shows the existence of triangulations for which the Random-Compass algorithm proposed by Bose etal (2002,2004) requires 2^{Ω(n)} time to route between some pair of vertices.

cs.CG↗
arXiv2009

A Branch and Cut Algorithm for the Halfspace Depth Problem

The concept of \emph{data depth} in non-parametric multivariate descriptive statistics is the generalization of the univariate rank method to multivariate data. \emph{Halfspace depth} is a measure of data depth. Given a set $S$ of points and a point $p$, the halfspace depth (or rank) of $p$ is defined as the minimum number of points of $S$ contained in any closed halfspace with $p$ on its boundary. Computing halfspace depth is NP-hard, and it is equivalent to the Maximum Feasible Subsystem problem. In this paper a mixed integer program is formulated with the big-$M$ method for the halfspace depth problem. We suggest a branch and cut algorithm for these integer programs. In this algorithm, Chinneck's heuristic algorithm is used to find an upper bound and a related technique based on sensitivity analysis is used for branching. Irreducible Infeasible Subsystem (IIS) hitting set cuts are applied. We also suggest a binary search algorithm which may be more numerically stable. The algorithms are implemented with the BCP framework from the \textbf{COIN-OR} project.

cs.CG↗
arXiv2007

A Branch and Cut Algorithm for the Halfspace Depth Problem

The concept of data depth in non-parametric multivariate descriptive statistics is the generalization of the univariate rank method to multivariate data. Halfspace depth is a measure of data depth. Given a set S of points and a point p, the halfspace depth (or rank) k of p is defined as the minimum number of points of S contained in any closed halfspace with p on its boundary. Computing halfspace depth is NP-hard, and it is equivalent to the Maximum Feasible Subsystem problem. In this thesis a mixed integer program is formulated with the big-M method for the halfspace depth problem. We suggest a branch and cut algorithm. In this algorithm, Chinneck's heuristic algorithm is used to find an upper bound and a related technique based on sensitivity analysis is used for branching. Irreducible Infeasible Subsystem (IIS) hitting set cuts are applied. We also suggest a binary search algorithm which may be more stable numerically. The algorithms are implemented with the BCP framework from the COIN-OR project.

cs.CG↗