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...