FPT-algorithms for some problems related to integer programming

In this paper, we present FPT-algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems' formulations are near square. The parameter is the maximum absolute value of rank minors of the corresponding matrices. Additionally, we present FPT-algorithms with respect to the same parameter for the problems, when the matrices have no singular rank sub-matrices.Comment: arXiv admin note: text overlap with arXiv:1710.00321 From author: some minor corrections has been don

Value of information in the binary case and confusion matrix

The simplest Bayesian system used to illustrate ideas of probability theory is a coin and a boolean utility function. To illustrate ideas of hypothesis testing, estimation or optimal control, one needs to use at least two coins and a confusion matrix accounting for the utilities of four possible outcomes. Here we use such a system to illustrate the main ideas of Stratonovich’s value of information (VoI) theory in the context of a financial time-series forecast. We demonstrate how VoI can provide a theoretical upper bound on the accuracy of the forecasts facilitating the analysis and optimization of models

Quantum Informational Dark Energy: Dark energy from forgetting

We suggest that dark energy has a quantum informational origin. Landauer's principle associated with the erasure of quantum information at a cosmic horizon implies the non-zero vacuum energy having effective negative pressure. Assuming the holographic principle, the minimum free energy condition, and the Gibbons-Hawking temperature for the cosmic event horizon we obtain the holographic dark energy with the parameter $d\simeq 1$, which is consistent with the current observational data. It is also shown that both the entanglement energy and the horizon energy can be related to Landauer's principle.Comment: revtex,8 pages, 2 figures more detailed arguments adde

Bounds for the solution set of linear complementarity problems

AbstractWe give here bounds for the feasible domain and the solution norm of Linear Complementarity Problems (LCP). These bounds are motivated by formulating the LCP as a global quadratic optimization problem and are characterized by the eigenstructure of the corresponding matrix. We prove boundedness of the feasible domain when the quadratic problem is concave, and give easily computable bounds for the solution norm for the convex case. We also obtain lower and upper bounds for the solution norm of the general nonconvex problem