On the performance of the ICP algorithm

We present upper and lower bounds for the number of iterations performed by the Iterative Closest Point (ICP) algorithm. This algorithm has been proposed by Besl and McKay as a successful heuristic for matching of point sets in d-space under translation, but so far it seems not to have been rigorously analyzed. We consider two standard measures of resemblance that the algorithm attempts to optimize: The RMS (root mean squared distance) and the (one-sided) Hausdorff distance. We show that in both cases the number of iterations performed by the algorithm is polynomial in the number of input points. In particular, this bound is quadratic in the one-dimensional problem, under the RMS measure, for which we present a lower bound construction of Ω(nlogn) iterations, where n is the overall size of the input. Under the Hausdorff measure, this bound is only O(n) for input point sets whose spread is polynomial in n, and this is tight in the worst case.We also present several structural geometric properties of the algorithm under both measures. For the RMS measure, we show that at each iteration of the algorithm the cost function monotonically and strictly decreases along the vector Δt of the relative translation. As a result, we conclude that the polygonal path π, obtained by concatenating all the relative translations that are computed during the execution of the algorithm, does not intersect itself. In particular, in the one-dimensional problem all the relative translations of the ICP algorithm are in the same (left or right) direction. For the Hausdorff measure, some of these properties continue to hold (such as monotonicity in one dimension), whereas others do not.     

Finding more perfect matchings in leapfrog fullerenes

We use some recent results on the existence of long cycles in leapfrog fullerenes to establish new exponential lower bounds on the number of perfect matchings in such graphs. The new bounds are expressed in terms of Fibonacci numbers.     

q-Weighted log-concavity and q-product theorem on the normality of posets

We show that q-weighted log-concavity and the strict normalized matching property are preserved under the q-direct product over weighted posets. As consequences, two classes of weighted posets including the finite linear lattices are strictly q-weighted log-concave and strictly normal.     

Minimally non-Pfaffian graphs

We consider the question of characterizing Pfaffian graphs. We exhibit an infinite family of non-Pfaffian graphs minimal with respect to the matching minor relation. This is in sharp contrast with the bipartite case, as Little [C.H.C. Little, A characterization of convertible (0,1)-matrices, J. Combin. Theory Ser. B 18 (1975) 187–208] proved that every bipartite non-Pfaffian graph contains a matching minor isomorphic to K_3,3. We relax the notion of a matching minor and conjecture that there are only finitely many (perhaps as few as two) non-Pfaffian graphs minimal with respect to this notion.We define Pfaffian factor-critical graphs and study them in the second part of the paper. They seem to be of interest as the number of near perfect matchings in a Pfaffian factor-critical graph can be computed in polynomial time. We give a polynomial time recognition algorithm for this class of graphs and characterize non-Pfaffian factor-critical graphs in terms of forbidden central subgraphs.     

Estimating the covariance matrix and the generalized variance under a symmetric loss

For estimating the power of a generalized variance under a multivariate normal distribution with unknown means, the inadmissibility of the best affine equivariant estimator relative to the symmetric loss is shown, and a class of improved estimators is given. The problem of estimating the covariance matrix is also discussed.     

FTRLIM: Distributed Instance Matching Framework for Large-Scale Knowledge Graph Fusion

Instance matching is a key task in knowledge graph fusion, and it is critical to improving the efficiency of instance matching, given the increasing scale of knowledge graphs. Blocking algorithms selecting candidate instance pairs for comparison is one of the effective methods to achieve the goal. In this paper, we propose a novel blocking algorithm named MultiObJ, which constructs indexes for instances based on the Ordered Joint of Multiple Objects’ features to limit the number of candidate instance pairs. Based on MultiObJ, we further propose a distributed framework named Follow-the-Regular-Leader Instance Matching (FTRLIM), which matches instances between large-scale knowledge graphs with approximately linear time complexity. FTRLIM has participated in OAEI 2019 and achieved the best matching quality with significantly efficiency. In this research, we construct three data collections based on a real-world large-scale knowledge graph. Experiment results on the constructed data collections and two real-world datasets indicate that MultiObJ and FTRLIM outperform other state-of-the-art methods.     

Temperature dependent narrow-band terahertz pulse generation in periodically poled crystals via difference frequency generation

Femtosecond optical pulse is used to generate narrow-band terahertz pulses depending on a quasi-phase-matched condition in periodically poled lithium niobate (PPLN) and stoichiometric lithium tantalate (PPSLT) crystals by difference frequency generation. The origin of narrow-band THz generation proved that the two frequency components of the fs pulse contribute to the frequency mixing. By cryogenic cooling, the absorption of THz waves in the crystal is significantly reduced which results in efficient THz generation. Simultaneously generated forward and backward THz pulses were 1.38 and 0.65 THz with as narrow as the bandwidth of 32 GHz in the PPSLT sample. Temperature dependence of the generated THz waveforms had good agreement with the simulation result using one dimensional plane-wave propagation model.     

基于溴钨灯和LED积分球光源的可调谐光谱分布及光谱匹配

采用溴钨灯和恒流驱动的LED混合作为积分球内部光源,提出了模拟退火算法作为光谱匹配算法,研究了光谱分布可调谐积分球光源的光谱匹配技术.仿真实验表明,该混合光源完全能够定量地模拟CIE-D65和等能光谱分布,且在辐射功率优于LED模拟结果的前提下,LED的数量分别减少79.8％和82.9％,平均相对误差分别减小10％和4...     

Recoupling in solid state NMR using γ prepared states and phase matching

The paper describes two-dimensional solid state NMR experiments that use powdered dephased antiphase coherence (γ preparation) to encode chemical shifts in the indirect dimension. Both components of this chemical shift encoded gamma-prepared states can be refocused into inphase coherence by a recoupling element. This helps to achieve sensitivity enhancement in 2D NMR experiments by quadrature detection. The powder dependence of the gamma-prepared states allows for manipulating them by suitable insertion of delays in the recoupling periods. This helps to design experiments that suppress diagonal peaks in 2D spectra, leading to improved resolution. We describe some new phase modulated heteronuclear and homonuclear recoupling pulse sequences that simplify the implementation of the described experiments based on γ prepared states. Recoupling in the heteronuclear spin system is achieved by matching the difference in the amplitude of the sine/cosine modulated phase on the two rf-channels to the spinning frequency while maintaining the same power on the two rf-channels.