Moduli and multi-field inflation

Moduli with flat or run-away classical potentials are generic in theories based on supersymmetry and extra dimensions. They mix between themselves and with matter fields in kinetic terms and in the nonperturbative superpotentials. As the result, interesting structure appears in the scalar potential which helps to stabilise and trap moduli and leads to multi-field inflation. The new and attractive feature of multi-inflationary setup are isocurvature perturbations which can modify in an interesting way the final spectrum of primordial fluctuations resulting from inflation.Comment: 8 pages, 5 figures, based on talks given at CTP Symposium on Supersymmetry at LHC (Cairo, March 11-14 2007) and String Phenomenology 2007 (Frascati, June 4-8 2007

Coverage and Connectivity in Three-Dimensional Networks

Most wireless terrestrial networks are designed based on the assumption that the nodes are deployed on a two-dimensional (2D) plane. However, this 2D assumption is not valid in underwater, atmospheric, or space communications. In fact, recent interest in underwater acoustic ad hoc and sensor networks hints at the need to understand how to design networks in 3D. Unfortunately, the design of 3D networks is surprisingly more difficult than the design of 2D networks. For example, proofs of Kelvin's conjecture and Kepler's conjecture required centuries of research to achieve breakthroughs, whereas their 2D counterparts are trivial to solve. In this paper, we consider the coverage and connectivity issues of 3D networks, where the goal is to find a node placement strategy with 100% sensing coverage of a 3D space, while minimizing the number of nodes required for surveillance. Our results indicate that the use of the Voronoi tessellation of 3D space to create truncated octahedral cells results in the best strategy. In this truncated octahedron placement strategy, the transmission range must be at least 1.7889 times the sensing range in order to maintain connectivity among nodes. If the transmission range is between 1.4142 and 1.7889 times the sensing range, then a hexagonal prism placement strategy or a rhombic dodecahedron placement strategy should be used. Although the required number of nodes in the hexagonal prism and the rhombic dodecahedron placement strategies is the same, this number is 43.25% higher than the number of nodes required by the truncated octahedron placement strategy. We verify by simulation that our placement strategies indeed guarantee ubiquitous coverage. We believe that our approach and our results presented in this paper could be used for extending the processes of 2D network design to 3D networks.Comment: To appear in ACM Mobicom 200

Praca człowieka w wersji dyscyplinarnej oraz zintegrowanej i globalnej

The 50th anniversary of the labour pedagogy work encourages a more general reflection on the present and future of our work. In this reflection, the co-founders of the sub-disciplines highlight the significant scientific achievements, but also express their concerns for the future. Therefore, a focus on the complex of pedagogy of work is presented and proposed – of course, treated disciplinarily, but in an integrated and global context. In other words, it is about the labour pedagogy in multi-problem, multi-aspect and humanities-oriented dimensions.Jubileusz 50-lecia pedagogiki pracy skłania do ogólniejszych refleksji nad teraźniejszością i przyszłością naszego dzieła. W owej refleksji współtwórcy danej subdyscypliny podkreślają znaczący dorobek naukowy, ale także wyrażają zaniepokojenie w kontekście przyszłości. Stąd przedstawiono i zaproponowano ‘ukłon’ w kierunku kompleksu nauk o pracy - oczywiście traktowanych dyscyplinarnie, jednak w sposób zintegrowany oraz globalny. Chodzi oczywiście o nauki o pracy w wymiarach wieloproblemowych, wieloaspektowych i nasyconych humanistycznie

Matrix measures and random walks

In this paper we study the connection between matrix measures and random walks with a tridiagonal block transition matrix. We derive sufficient conditions such that the blocks of the n-step transition matrix of the Markov chain can be represented as integrals with respect to a matrix valued spectral measure. Several stochastic properties of the processes are characterized by means of this matrix measure. In many cases this measure is supported in the interval [-1, 1]. The results are illustrated by several examples including random walks on a grid and the embedded chain of a queuing system. --Markov chain,block tridiagonal transition matrix,spectral measure,matrix measure,quasi birth and death processes,canonical moments

Secure Data Transmission in Mobile Ad Hoc Networks

The vision of nomadic computing with its ubiquitous access has stimulated much interest in the Mobile Ad Hoc Networking (MANET) technology. However, its proliferation strongly depends on the availability of security provisions, among other factors. In the open, collaborative MANET environment practically any node can maliciously or selfishly disrupt and deny communication of other nodes. In this paper, we present and evaluate the Secure Message Transmission (SMT) protocol, which safeguards the data transmission against arbitrary malicious behavior of other nodes. SMT is a lightweight, yet very effective, protocol that can operate solely in an end-to-end manner. It exploits the redundancy of multipath routing and adapts its operation to remain efficient and effective even in highly adverse environments. SMT is capable of delivering up to 250% more data messages than a protocol that does not secure the data transmission. Moreover, SMT outperforms an alternative single-path protocol, a secure data forwarding protocol we term Secure Single Path (SSP) protocol. SMT imposes up to 68% less routing overhead than SSP, delivers up to 22% more data packets and achieves end-to-end delays that are up to 94% lower than those of SSP. Thus, SMT is better suited to support QoS for real-time communications in the ad hoc networking environment. The security of data transmission is achieved without restrictive assumptions on the network nodes' trust and network membership, without the use of intrusion detection schemes, and at the expense of moderate multi-path transmission overhead only