Let M be a real r × c matrix, and let k positive integer. In the column subset selection problem (CSSP), we need to minimize quantity ‖ − S A , where can an arbitrary runs over all submatrices of . This its applications in numerical linear algebra are being discussed for several decades, but algorithmic complexity remained open issue. We show that CSSP is NP-complete.

We prove that the class NP has Co-NP-immune sets and the class Co-NP has NP-immune sets relative to a random oracle.

We prove that the class NP has Co-NP-immune sets relative to a random oracle. Moreover, we prove that, relative to a random oracle, there are L 2 P and NP-set L 1 L such that L 1 is Co-NP-immune and L n L 1 is NP-immune. The second theorem implies the theorem in 4] that Co-NP has NP-immune sets relative to a random oracle.

The P=?NP problem is philosophically solved by showing P is equal to NP in the random access with unit multiply (MRAM) model. It is shown that the MRAM model empirically best models computation hardness. The P=?NP problem is shown to be a scientific rather than a mathematical problem. The assumptions involved in the current definition of the P?=NP problem as a problem involving non deterministi...

In this paper we prove that the relations P = NP and P 6= NP relativise to the deterministic / non-deterministic artificial recurrent neural net (ARNN ) with real weights (informally considered as oracles in [1] and [2]). Although, in the nineties, a dozen of papers were written on the ARNN model, some introducing computation via neural nets with real weights and some introducing non-determinis...

We will provide a formalization of the use of real weights in analog recurrent neural networks as a restricted class of oracles, closely related to physical oracles, and prove that the famous P = NP problem relativizes with respect to deterministic and nonderterministic analog recurrent neural networks with real weights working in polynomial time. As a direct consequence, these devices have res...

In many binary classification applications, such as disease diagnosis and spam detection, practitioners commonly face the need to limit type I error (i.e., the conditional probability of misclassifying a class 0 observation as class 1) so that it remains below a desired threshold. To address this need, the Neyman-Pearson (NP) classification paradigm is a natural choice; it minimizes type II err...

background: para-nonylphenol (p-np) is able to induce malformations in male reproductive system. objective: the aim of this study was to investigate the preventing role of vitamin e (vit.e) on sperm parameters and reproductive hormones in developing rats. materials and methods: pregnant rats were divided into 4 groups: control p-np vit.e and p-np+vit.e. treatments were performed on day 7 of ges...

background: human breast milk is the most important food for infants and one of the main roads to exposure to toxic substances. in this study, nonylphenol (np) levels in human milk samples collected from turkish mothers (n=100) were determined, and the factors including mothers’ demographics, eating habits, obstetric histories, and usage of cleaning and cosmetic products were examined. methods:...