We propose a DC (Difference of two Convex functions) formulation approach for sparse optimization problems having a cardinality or rank constraint. With the largest-
k
norm, an exact DC ...representation of the cardinality constraint is provided. We then transform the cardinality-constrained problem into a penalty function form and derive exact penalty parameter values for some optimization problems, especially for quadratic minimization problems which often appear in practice. A DC Algorithm (DCA) is presented, where the dual step at each iteration can be efficiently carried out due to the accessible subgradient of the largest-
k
norm. Furthermore, we can solve each DCA subproblem in linear time via a soft thresholding operation if there are no additional constraints. The framework is extended to the rank-constrained problem as well as the cardinality- and the rank-minimization problems. Numerical experiments demonstrate the efficiency of the proposed DCA in comparison with existing methods which have other penalty terms.
In this paper, we propose a new method for a class of difference-of-convex (DC) optimization problems, whose objective is the sum of a smooth function and a possibly non-prox-friendly DC function. ...The method sequentially solves subproblems constructed from a quadratic approximation of the smooth function and a linear majorization of the concave part of the DC function. We allow the subproblem to be solved inexactly, and propose a new inexact rule to characterize the inexactness of the approximate solution. For several classical algorithms applied to the subproblem, we derive practical termination criteria so as to obtain solutions satisfying the inexact rule. We also present some convergence results for our method, including the global subsequential convergence and a non-asymptotic complexity analysis. Finally, numerical experiments are conducted to illustrate the efficiency of our method.
Extracellular vesicles (EVs) have attracted much attention as potential diagnostic biomarkers for human diseases. Although both plasma and serum are utilized as a source of blood EVs, it remains ...unclear whether, how and to what extent the choice of plasma and serum affects the experimental results. To address this issue, in this study, we performed comprehensive characterization of EV fractions derived from plasma and serum, and investigated the differences between these blood EVs. We demonstrated by nanoparticle tracking analysis that EV fractions derived from serum contain more particles than those from plasma of mice. Proteomic analysis demonstrated that platelet-associated proteins are selectively enriched in serum EV fractions from both mice and humans. A literature review of proteomic data of human blood EVs reported by other groups further confirmed that selective enrichment of platelet-associated proteins is commonly observed in serum EVs, and confers different proteome profiles to plasma EVs. Our data provide experimental evidence that EV fractions derived from serum generally contain additional EVs that are released from platelets, which may qualitatively and quantitatively alter EV profiles when using serum as a source of blood EVs.
•We study modularity density maximization for community detection in networks.•Column generation algorithm is accelerated using several techniques.•Computational experiments demonstrate the ...effectiveness of our proposed method.•Computational complexity of modularity density maximization is also analyzed.
Community detection is a fundamental network-analysis primitive with a variety of applications in diverse domains. Although the modularity introduced by Newman and Girvan (2004) has widely been used as a quality function for community detection, it has some drawbacks. The modularity density introduced by Li et al. (2008) is known to be an effective alternative to the modularity, which mitigates one of the drawbacks called the resolution limit. A large body of work has been devoted to designing exact and heuristic methods for modularity density maximization, without any computational complexity analysis. In this study, we investigate modularity density maximization from both algorithmic and computational complexity aspects. Specifically, we first accelerate column generation for the modularity density maximization problem. To this end, we point out that the auxiliary problem appearing in column generation can be viewed as a dense subgraph discovery problem. Then we employ a well-known strategy for dense subgraph discovery, called the greedy peeling, for approximately solving the auxiliary problem. Moreover, we reformulate the auxiliary problem to a sequence of 0–1 linear programming problems, enabling us to compute its optimal value more efficiently and to get more diverse columns. Computational experiments using a variety of real-world networks demonstrate the effectiveness of our proposed algorithm. Finally, we show the NP-hardness of a slight variant of the modularity density maximization problem, where the output partition has to have two or more clusters, as well as showing the NP-hardness of the auxiliary problem in column generation.
A new Levenberg–Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM method have been proposed, their main differences ...being in the choice of a damping parameter. In this paper, we propose a new rule for updating the parameter so as to achieve both global and local convergence even under the presence of a convex constraint set. The key to our results is a new perspective of the LM method from majorization-minimization methods. Specifically, we show that if the damping parameter is set in a specific way, the objective function of the standard subproblem in LM methods becomes an upper bound on the original objective function under certain standard assumptions. Our method solves a sequence of the subproblems approximately using an (accelerated) projected gradient method. It finds an
ε
-stationary point after
O
(
ε
-
2
)
computation and achieves local quadratic convergence for zero-residual problems under a local error bound condition. Numerical results on compressed sensing and matrix factorization show that our method converges faster in many cases than existing methods.
Excitotoxicity is well known in the neuronal death in the brain and is also linked to neuronal damages in the retina. Recent accumulating evidence show that microglia greatly affect excitotoxicity in ...the brain, but their roles in retina have received only limited attention. Here, we report that retinal excitotoxicity is mediated by microglia. To this end, we employed three discrete methods, that is, pharmacological inhibition of microglia by minocycline, pharmacological ablation by an antagonist for colony stimulating factor 1 receptor (PLX5622), and genetic ablation of microglia using Iba1‐tTA::DTAtetO/tetO mice. Intravitreal injection of NMDA increased the number of apoptotic retinal ganglion cells (RGCs) followed by reduction in the number of RGCs. Although microglia did not respond to NMDA directly, they became reactive earlier than RGC damages. Inhibition or ablation of microglia protected RGCs against NMDA. We found up‐regulation of proinflammatory cytokine genes including Il1b, Il6 and Tnfa, among which Tnfa was selectively blocked by minocycline. PLX5622 also suppressed Tnfa expression. Tumor necrosis factor α (TNFα) signals were restricted in microglia at very early followed by spreading into other cell types. TNFα up‐regulation in microglia and other cells were significantly attenuated by minocycline and PLX5622, suggesting a central role of microglia for TNFα induction. Both inhibition of TNFα and knockdown of TNF receptor type 1 by siRNA protected RGCs against NMDA. Taken together, our data demonstrate that a phenotypic change of microglia into a neurotoxic one is a critical event for the NMDA‐induced degeneration of RGCs, suggesting an importance of non‐cell‐autonomous mechanism in the retinal neuronal excitotoxicity.
Main Points
Microglia have a critical role for the N‐methyl‐d‐aspartate (NMDA)‐induced neuronal damages in the retina, although they do not respond to NMDA directly. For such microglia‐mediated noncell‐autonomous mechanisms, TNFα has a central role.
Variable clustering is important for explanatory analysis. However, only few dedicated methods for variable clustering with the Gaussian graphical model have been proposed. Even more severe, small ...insignificant partial correlations due to noise can dramatically change the clustering result when evaluating for example with the Bayesian information criteria (BIC). In this work, we try to address this issue by proposing a Bayesian model that accounts for negligible small, but not necessarily zero, partial correlations. Based on our model, we propose to evaluate a variable clustering result using the marginal likelihood. To address the intractable calculation of the marginal likelihood, we propose two solutions: one based on a variational approximation and another based on MCMC. Experiments on simulated data show that the proposed method is similarly accurate as BIC in the no noise setting, but considerably more accurate when there are noisy partial correlations. Furthermore, on real data the proposed method provides clustering results that are intuitively sensible, which is not always the case when using BIC or its extensions.
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