Many high dimensional sparse learning problems are formulated as nonconvex optimization. A popular approach to solve these nonconvex optimization problems is through convex relaxations such as linear and semidefinite programming. In this paper, we study the statistical limits of convex relaxations. Particularly, we consider two problems: Mean estimation for sparse principal submatrix and edge p...

We consider the problems of finding a maximum clique in a graph and finding a maximum-edge biclique in a bipartite graph. Both problems are NP-hard. We write both problems as matrix-rank minimization and then relax them using the nuclear norm. This technique, which may be regarded as a generalization of compressive sensing, has recently been shown to be an effective way to solve rank optimizati...

In this paper, we present a novel approach based on the random walk process for finding meaningful representations of a graph model. Our approach leverages the transient behavior of many short random walks with novel initialization mechanisms to generate model discriminative features. These features are able to capture a more comprehensive structural signature of the underlying graph model. The...

We demonstrate some lower bounds for parameterized problems via parameterized classes corresponding to the classical AC. Among others, we derive such a lower bound for all fptapproximations of the parameterized clique problem and for a parameterized halting problem, which recently turned out to link problems of computational complexity, descriptive complexity, and proof theory. To show the firs...

Identification and characterization of gene regulatory binding motifs is one of the fundamental tasks toward systematically understanding the molecular mechanisms of transcriptional regulation. Recently, the problem has been abstracted as the challenge planted (l,d)-motif problem. Previous studies have developed numerous methods to solve the problem. But most of them need to specify the length ...

Phytoremediation offers an ecologically and economically attractive remediation technique for soils contaminated with polycyclic aromatic hydrocarbons (PAHs). In addition to the choice of plant species, agronomic practices may affect the efficiency of PAH phytoremediation. Inorganic nutrient amendments may stimulate plant and microbial growth, and clipping aboveground biomass might stimulate ro...

BACKGROUND Forest resources supply a wide range of environmental services like mitigation of increasing levels of atmospheric carbon dioxide (CO2). As climate is changing, forest managers have added pressure to obtain forest resources by following stand management alternatives that are biologically sustainable and economically profitable. The goal of this study is to project the effect of typic...

methyl bromide for use in strawberry production. By year’s end, many of the pessimistic predictions about the California strawberry industry’s future had not come to pass. Consumer costs had not increased to cover expected higher production costs (e.g., Carpenter et al. 2000; Norman 2005), nor had production substantially moved to Mexico, which, per Montreal Protocol rules, initially was grante...

we start this article by rebuilding higher operads of weak higher transformations, and correct those in cite{cambat}. as in cite{cambat} we propose an operadic approach for weak higher $n$-transformations, for each $ninmathbb{n}$, where such weak higher $n$-transformations are seen as algebras for specific contractible higher operads. the last chapter of this article asserts that, up to precise...

THE following observations, though inconclusive, are recorded because they seem to have some relevance to the question of a virus as part causal factor in rheumatism. I. A case of multiple arthritis of some duration, with deformities and X-ray rarefaction (sedimentation rate unknown), developed a very acute exacerbation in one knee-joint. Fluid from this joint was sent to the author for examina...