This work proposes the data augmentation by molecular rotation, with consideration that the protein-ligand binding events are rotation-variant. As a proof-of-concept, known active (i. e., 1-labeled) ligands to human β-secretase 1 (BACE-1) are rotated for the generation of 0-labeled data, and the rotation-dependent prediction accuracy of 3D graph convolutional network (3DGCN) is investigated after data augmentation. The data augmentation makes the orientation-recognizing ability of 3DGCN improved significantly in the classification task for BACE-1/ligand binding. Furthermore, the data-augmented 3DGCN has a capability for predicting active ligands from a candidate dataset, via improved performance of orientation recognition, which would be applied to virtual drug screening and discovery. 相似文献
Let be a directed graph. A transitive fraternal augmentation of is a directed graph with the same vertex set, including all the arcs of and such that for any vertices x,y,z,
1.
if and then or (fraternity);
2.
if and then (transitivity).
In this paper, we explore some generalization of the transitive fraternal augmentations for directed graphs and its applications. In particular, we show that the 2-coloring number col2(G)≤O(∇1(G)∇0(G)2), where ∇k(G) (k≥0) denotes the greatest reduced average density with depth k of a graph G; we give a constructive proof that ∇k(G) bounds the distance (k+1)-coloring number colk+1(G) with a function f(∇k(G)). On the other hand, ∇k(G)≤(col2k+1(G))2k+1. We also show that an inductive generalization of transitive fraternal augmentations can be used to study nonrepetitive colorings of graphs. 相似文献
This paper discusses practical Bayesian estimation of stochastic volatility models based on OU processes with marginal Gamma
laws. Estimation is based on a parameterization which is derived from the Rosiński representation, and has the advantage of
being a non-centered parameterization. The parameterization is based on a marked point process, living on the positive real
line, with uniformly distributed marks. We define a Markov chain Monte Carlo (MCMC) scheme which enables multiple updates
of the latent point process, and generalizes single updating algorithm used earlier. At each MCMC draw more than one point
is added or deleted from the latent point process. This is particularly useful for high intensity processes. Furthermore,
the article deals with superposition models, where it discuss how the identifiability problem inherent in the superposition
model may be avoided by the use of a Markov prior. Finally, applications to simulated data as well as exchange rate data are
discussed. 相似文献
The paper presents results related to a theorem of Szigeti on covering symmetric skew-supermodular set functions by hypergraphs. We prove the following generalization using a variation of Schrijver’s supermodular colouring theorem: if p1 and p2 are skew-supermodular functions with the same maximum value, then it is possible to find in polynomial time a hypergraph of minimum total size that covers both p1 and p2. We also give some applications concerning the connectivity augmentation of hypergraphs. 相似文献
For semiparametric survival models with interval-censored data and a cure fraction, it is often difficult to derive nonparametric maximum likelihood estimation due to the challenge in maximizing the complex likelihood function. In this article, we propose a computationally efficient EM algorithm, facilitated by a gamma-Poisson data augmentation, for maximum likelihood estimation in a class of generalized odds rate mixture cure (GORMC) models with interval-censored data. The gamma-Poisson data augmentation greatly simplifies the EM estimation and enhances the convergence speed of the EM algorithm. The empirical properties of the proposed method are examined through extensive simulation studies and compared with numerical maximum likelihood estimates. An R package “GORCure” is developed to implement the proposed method and its use is illustrated by an application to the Aerobic Center Longitudinal Study dataset. Supplementary material for this article is available online. 相似文献
Quantile regression provides an attractive tool to the analysis of censored responses, because the conditional quantile functions are often of direct interest in regression analysis, and moreover, the quantiles are often identifiable while the conditional mean functions are not. Existing methods of estimation for censored quantiles are mostly limited to singly left- or right-censored data, with some attempts made to extend the methods to doubly censored data. In this article, we propose a new and unified approach, based on a variation of the data augmentation algorithm, to censored quantile regression estimation. The proposed method adapts easily to different forms of censoring including doubly censored and interval censored data, and somewhat surprisingly, the resulting estimates improve on the performance of the best known estimators with singly censored data. Supplementary material for this article is available online. 相似文献
LetZG be the integral group ring of a groupG and I(G) its augmentation ideal. For a free groupF andR a normal subgroup ofF, the intersectionIn+1 (F) ∩In+1 (R) is determined for alln≥ 1. The subgroupsF ∩ (1+ZFI (R) I (F) I (S)) ANDF ∩ (1 + I (R)I3 (F)) of F are identified whenR and S are arbitrary subgroups ofF. 相似文献
Let be a nilpotent Lie algebra, over a field of characteristic zero, and its universal enveloping algebra. In this paper we study: (1) the prime ideal structure of related to finitely generated -modules , and in particular the set of associated primes for such (note that now is equal to the set of annihilator primes for ); (2) the problem of nontriviality for the modules when is a (maximal) prime of , and in particular when is the augmentation ideal of . We define the support of , as a natural generalization of the same notion from commutative theory, and show that it is the object of primary interest when dealing with (2). We also introduce and study the reduced localization and the reduced support, which enables to better understand the set . We prove the following generalization of a stability result given by W. Casselman and M. S. Osborne in the case when , as in the theorem, are abelian. We also present some of its interesting consequences.
Theorem.Let be a finite-dimensional Lie algebra over a field of characteristic zero, and an ideal of ; denote by the universal enveloping algebra of . Let be a -module which is finitely generated as an -module. Then every annihilator prime of , when is regarded as a -module, is -stable for the adjoint action of on .
We discuss efficient Bayesian estimation of dynamic covariance matrices in multivariate time series through a factor stochastic volatility model. In particular, we propose two interweaving strategies to substantially accelerate convergence and mixing of standard MCMC approaches. Similar to marginal data augmentation techniques, the proposed acceleration procedures exploit nonidentifiability issues which frequently arise in factor models. Our new interweaving strategies are easy to implement and come at almost no extra computational cost; nevertheless, they can boost estimation efficiency by several orders of magnitude as is shown in extensive simulation studies. To conclude, the application of our algorithm to a 26-dimensional exchange rate dataset illustrates the superior performance of the new approach for real-world data. Supplementary materials for this article are available online. 相似文献