Inflation is known to be generically eternal to the future: the false vacuum is thermalized in some regions of space, while inflation continues in other regions. Here, we address the question of whether inflation can also be eternal to the past. We argue that such a steady-state picture is impossible and, therefore, that inflation must have had a beginning. First, it is shown that the old infla...

In the field of privacy preserving protocols, Private Set Intersection (PSI) plays an important role. In most cases, PSI allows two parties to securely determine intersection their private input sets, and no other information. this paper, employing a Bloom filter, we propose Multiparty Cardinality (MPSI-CA), where number participants in is not limited two. The secur...

We investigate the condition for eternal inflation to take place in the noncommutative spacetime. We find that the possibility for eternal inflation’s happening is greatly suppressed in this case. If eternal inflation can not happen in the low energy region where the noncommutativity is very weak (the UV region), it will never happen along the whole inflationary history. Based on these conclusi...

The status of exponential scalar potentials in supergravity is reviewed, and updated. One version of N=8 D=4 supergravity with a positive exponential potential, obtainable from a ‘non-compactification’ of M-theory, is shown to have an accelerating cosmological solution that realizes ‘eternal quintessence’.

M-commerce is a major application domain for mobile devices, enabling users to perform commercial transactions wherever they go. However, these applications require a high level of security. In this paper, we identify the special characteristics of m-commerce and reflect on some important security issues.

We define and study the following two-player game on a graph G. Let k ∈ N∗. A set of k guards is occupying some vertices of G while one spy is standing at some node. At each turn, first the spy may move along at most s edges, where s ∈ N∗ is his speed. Then, each guard may move along one edge. The spy and the guards may occupy the same vertices. The spy has to escape the surveillance of the gua...

The concepts of secure sets and security number in graphs were introduced first by Brigham et al. in 2007 as a generalization of the concept of alliances in graphs. Defensive alliances are related to the defense of a single vertex. But, in a general realistic settings, alliances should be formed so that any attack on the entire alliance or any subset of the alliance can be defended. In this sen...

In the Spy game, a spy is placed first at some vertex of a graph G. Then, k > 0 guards are also occupying some vertices of G. At each turn, the spy moves at speed s ≥ 2, i.e., along at most s edges and then, each guard moves at speed 1. The spy and any number of guards may occupy the same vertex. The goal of the guards is to control the spy at distance d ≥ 0, i.e., to ensure that, at every turn...