Distributed Deterministic Broadcasting in Uniform-Power Ad Hoc Wireless Networks

Development of many futuristic technologies, such as MANET, VANET, iThings, nano-devices, depend on efficient distributed communication protocols in multi-hop ad hoc networks. A vast majority of research in this area focus on design heuristic protocols, and analyze their performance by simulations on networks generated randomly or obtained in practical measurements of some (usually small-size) wireless networks. %some library. Moreover, they often assume access to truly random sources, which is often not reasonable in case of wireless devices. In this work we use a formal framework to study the problem of broadcasting and its time complexity in any two dimensional Euclidean wireless network with uniform transmission powers. For the analysis, we consider two popular models of ad hoc networks based on the Signal-to-Interference-and-Noise Ratio (SINR): one with opportunistic links, and the other with randomly disturbed SINR. In the former model, we show that one of our algorithms accomplishes broadcasting in $O(D\log^2 n)$ rounds, where $n$ is the number of nodes and $D$ is the diameter of the network. If nodes know a priori the granularity $g$ of the network, i.e., the inverse of the maximum transmission range over the minimum distance between any two stations, a modification of this algorithm accomplishes broadcasting in $O(D\log g)$ rounds. Finally, we modify both algorithms to make them efficient in the latter model with randomly disturbed SINR, with only logarithmic growth of performance. Ours are the first provably efficient and well-scalable, under the two models, distributed deterministic solutions for the broadcast task.Comment: arXiv admin note: substantial text overlap with arXiv:1207.673

Comparison of Structural Development and Biochemical Accumulation of Waxy and Non-waxy Wheat Caryopses

This study was conducted to compare structural development and biochemical accumulation of waxy and non-waxy wheat (NW) caryopses. The caryopses’ microstructure of the waxy wheat (WW) and NW cultivars at different developmental stages were observed under light, fluorescence, and scanning electron microscope. The results were as follows: Compared with NW,WWhad a shorter maturation duration, which was reflected in several following characteristics. Programmed cell death of the pericarp began earlier, and the chlorophyll-containing layer in the pericarp was smaller. Vacuoles in chalazal cells accumulated more tannins at different developmental stages. Starch granules and protein bodies in the endosperm showed a higher accumulation level in developing caryopses, and aleurone cells were larger in size with larger numbers of aleurone grains. An analysis of the element content indicated that the mineral elements Mg, P, K, and Ca exhibited a higher content, while the heavy elements Cr, Cd, and Pb exhibited a lower content in the aleurone layer

Enhancing Approximations for Regular Reachability Analysis

This paper introduces two mechanisms for computing over-approximations of sets of reachable states, with the aim of ensuring termination of state-space exploration. The first mechanism consists in over-approximating the automata representing reachable sets by merging some of their states with respect to simple syntactic criteria, or a combination of such criteria. The second approximation mechanism consists in manipulating an auxiliary automaton when applying a transducer representing the transition relation to an automaton encoding the initial states. In addition, for the second mechanism we propose a new approach to refine the approximations depending on a property of interest. The proposals are evaluated on examples of mutual exclusion protocols

Rendezvous of Distance-aware Mobile Agents in Unknown Graphs

We study the problem of rendezvous of two mobile agents starting at distinct locations in an unknown graph. The agents have distinct labels and walk in synchronous steps. However the graph is unlabelled and the agents have no means of marking the nodes of the graph and cannot communicate with or see each other until they meet at a node. When the graph is very large we want the time to rendezvous to be independent of the graph size and to depend only on the initial distance between the agents and some local parameters such as the degree of the vertices, and the size of the agent's label. It is well known that even for simple graphs of degree $\Delta$, the rendezvous time can be exponential in $\Delta$ in the worst case. In this paper, we introduce a new version of the rendezvous problem where the agents are equipped with a device that measures its distance to the other agent after every step. We show that these \emph{distance-aware} agents are able to rendezvous in any unknown graph, in time polynomial in all the local parameters such the degree of the nodes, the initial distance $D$ and the size of the smaller of the two agent labels $l = \min(l_1, l_2)$. Our algorithm has a time complexity of $O(\Delta(D+\log{l}))$ and we show an almost matching lower bound of $\Omega(\Delta(D+\log{l}/\log{\Delta}))$ on the time complexity of any rendezvous algorithm in our scenario. Further, this lower bound extends existing lower bounds for the general rendezvous problem without distance awareness

Analytic Methods in Nonperturbative QCD

Recently developed analytic methods in the framework of the Field Correlator Method are reviewed in this series of four lectures and results of calculations are compared to lattice data and experiment. Recent lattice data demonstrating the Casimir scaling of static quark interaction strongly support the FCM and leave very little space for all other theoretical models, e.g. instanton gas/liquid model. Results of calculations for mesons, baryons, quark-gluon plasma and phase transition temperature demonstrate that new analytic methods are a powerful tool of nonperturbative QCD along with lattice simulations.Comment: LaTeX, 34 pages; Lectures given at the 13th Indian-Summer School "Understanding the Structure of Hadrons", August 28 - September 1, 2000, Prague, Czech Republi

Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting in Muonium

We calculate three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with the first order electron and muon polarization loop insertions in graphs with two exchanged photons. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm squared contribution was obtained a long time ago. Here we calculate the single-logarithmic and nonlogarithmic contributions. We previously calculated the three-loop radiative-recoil corrections generated by two-loop polarization insertions in the exchanged photons. The current paper therefore concludes calculation of all three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by diagrams with closed fermion loop insertions in the exchanged photons. The new results obtained here improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from experimental data on the muonium hyperfine splitting.Comment: 27 pages, 6 figures, 7 table

Rendezvous of Heterogeneous Mobile Agents in Edge-weighted Networks

We introduce a variant of the deterministic rendezvous problem for a pair of heterogeneous agents operating in an undirected graph, which differ in the time they require to traverse particular edges of the graph. Each agent knows the complete topology of the graph and the initial positions of both agents. The agent also knows its own traversal times for all of the edges of the graph, but is unaware of the corresponding traversal times for the other agent. The goal of the agents is to meet on an edge or a node of the graph. In this scenario, we study the time required by the agents to meet, compared to the meeting time $T_{OPT}$ in the offline scenario in which the agents have complete knowledge about each others speed characteristics. When no additional assumptions are made, we show that rendezvous in our model can be achieved after time $O(n T_{OPT})$ in a $n$-node graph, and that such time is essentially in some cases the best possible. However, we prove that the rendezvous time can be reduced to $\Theta (T_{OPT})$ when the agents are allowed to exchange $\Theta(n)$ bits of information at the start of the rendezvous process. We then show that under some natural assumption about the traversal times of edges, the hardness of the heterogeneous rendezvous problem can be substantially decreased, both in terms of time required for rendezvous without communication, and the communication complexity of achieving rendezvous in time $\Theta (T_{OPT})$