We show that on an n = 24m+ 8k-dimensional even unimodular lattice, if the shortest vector length is ≥ 2m, then as the number of vectors of length 2m decreases, the secrecy gain increases. We will also prove a similar result on general unimodular lattices. Furthermore, assuming the conjecture by Belfiore and Solé, we will calculate the difference between inverses of secrecy gains as the number ...

We study the problem k-SET SPLITTING in fixed parameter complexity. We show that the problem can be solved in time O∗(2.6494k), improving on the best currently known running time of O∗(8k). This is done by showing that a non-trivial instance must have a small minimal SET COVER, and using this to reduce the problem to a series of small instances of MAX SAT. We also give a linear kernel containin...

We present the first fixed-parameter algorithm for constructing a tree-child phylogenetic network that displays an arbitrary number of binary input trees and has minimum reticulations among all such networks. The uses recently introduced framework cherry picking sequences runs in $$O((8k)^k \mathrm {poly}(n, t))$$ time, where n is leaves every tree, t trees, k reticulation constructed network. ...

This paper aims to show that Li-Fi now reached a state, where it can be considered reliable wireless communication solution for future technologies. Currently, the Internet accessed using Wi-Fi, but has its limitations too. It is sufficient current services insufficient with IoT and cloud-based services. In upcoming decade, hard drives will obsolete everything on cloud. Modern Web applications ...

This work is devoted to the study of the existence of at least one (non-zero) solution to a problem involving the discrete p-Laplacian. As a special case, we derive an existence theorem for a second-order discrete problem, depending on a positive real parameter a, whose prototype is given by Duðk 1Þ 1⁄4 af ðk;uðkÞÞ; 8k 2 Z1⁄21; T ; uð0Þ 1⁄4 uðT þ 1Þ 1⁄4 0: ( Our approach is based on variational...

The excess of a graph G is defined as the minimum number of edges that must be deleted from G in order to get a forest. We prove that every graph with excess at most k has chromatic number at most 1 2(3+ √ 1 + 8k) and that this bound is tight. Moreover, we prove that the oriented chromatic number of any graph with excess k is at most k+3, except for graphs having excess 1 and containing a direc...

We present the Period{Luminosity relation from 290 Cepheids toward the LMC and 597 Cepheids towards the SMC respectively obtained from the monitoring of 1.134.000 and 504.000 stars over 150 nights using the two 4k 8k CCD camera of the Eros2 microlensing project. A slope break of the Period{Luminosity relation has been observed for SMC fundamental mode Cepheids with periods smaller than 2 days. ...

Nitrogen-vacancy centers in diamond are widely studied both as a testbed for solid state quantum optics and for their applications in quantum information processing and magnetometry. Here we demonstrate coupling of the nitrogen-vacancy centers to gap plasmons in metal nano-slits. We use diamond samples where nitrogen-vacancy centers are implanted tens of nanometers under the surface. Silver nan...

Smooth circle actions are constructed on odd-dimensional homotopy spheres that do not bound spin manifolds. Examples are given in every dimension for which exotic spheres of the described type exist. A result of H. B. Lawson and S.-T. Yau [15] implies that homotopy spheres not bounding spin manifolds do not admit effective smooth S3 or S03 actions. On the other hand, G. Bredon has shown that ev...