Strong Robustness of Randomized Rumor Spreading Protocols

Randomized rumor spreading is a classical protocol to disseminate information across a network. At SODA 2008, a quasirandom version of this protocol was proposed and competitive bounds for its run-time were proven. This prompts the question: to what extent does the quasirandom protocol inherit the second principal advantage of randomized rumor spreading, namely robustness against transmission failures? In this paper, we present a result precise up to $(1 \pm o(1))$ factors. We limit ourselves to the network in which every two vertices are connected by a direct link. Run-times accurate to their leading constants are unknown for all other non-trivial networks. We show that if each transmission reaches its destination with a probability of $p \in (0,1]$, after (1+\e)(\frac{1}{\log_2(1+p)}\log_2n+\frac{1}{p}\ln n) rounds the quasirandom protocol has informed all $n$ nodes in the network with probability at least 1-n^{-p\e/40}. Note that this is faster than the intuitively natural $1/p$ factor increase over the run-time of approximately $\log_2 n + \ln n$ for the non-corrupted case. We also provide a corresponding lower bound for the classical model. This demonstrates that the quasirandom model is at least as robust as the fully random model despite the greatly reduced degree of independent randomness.Comment: Accepted for publication in "Discrete Applied Mathematics". A short version appeared in the proceedings of the 20th International Symposium on Algorithms and Computation (ISAAC 2009). Minor typos fixed in the second version. Proofs of Lemma 11 and Theorem 12 fixed in the third version. Proof of Lemma 8 fixed in the fourth versio

Testing the validity of the compulsory schooling law instrument

Changes in compulsory schooling laws have been proposed as an instrument for the endogenous choice of schooling. It has been argued that raising minimum schooling exogenously increases the educational attainment of a subset of pupils without directly affecting later life outcomes such as income or health. Using the method of Huber and Mellace (2015) and data from the Survey of Health, Ageing and Retirement in Europe, we jointly test random instrument assignment, weak monotonicity of education in the instrument, and the instrument exclusion restriction. The satisfaction of these restrictions permits identifying the local average treatment effect of education on those choosing more schooling as a reaction to the law change. Our results do not point to the invalidity of the schooling law instrument, though we acknowledge that even asymptotically, testing cannot detect all possible violations of instrument validity

Signal calibration for an electrical impedance mammography system

Electrical Impedance Tomography (EIT) technology has been applied clinically since the 1980s. Numerous papers have addressed a variety of systematic error sources and indicated different calibration methods. The Sussex Mk4 Electrical Impedance Mammography (EIM) system has been developed for the investigation of early stage breast lesions. Investigations have shown that the system performance is subjected to a number of systematic errors: frequencies-dependant noise level due to both internal and external sources; stray capacitance within both PCB tracks and cable connections; and artefacts generated by patient movement during scanning etc. This paper reports upon several traditional and novel calibration methods utilized to reduce some of these errors in the acquired signals before image reconstruction. Techniques used include frequency spectrum analysis, filtering, phase calibration and other means of noise reduction. Results of both before and after calibration are presented and analyzed. The conclusion is reached that the signal quality of the Sussex Mk4 EIM system is such that the system is, post-calibrated, capable of producing images for the diagnosis of breast cancer

Perspectives on the Missiological Legacy of Martin Luther and the Protestant Reformation

Upon the occasion of the 500th anniversary Martin Luther’s publication of his 95 theses, this composite article brings together five perspectives on the missiological legacy of the reformer and the subsequent Protestant Reformation. The blend of voices makes clear that Luther and the subsequent Protestant Reformation do not have a simple missiological legacy but rather various legacies: theological, ecclesiological, political, and practical; some of which co-exist, and even collide, in the same ecclesiastical community. The scandalous legacy of a splintered and splintering church remains. Yet, demonstrations of mutual recognition, reciprocal respect, and genuine fellowship can be found in certain missiological circles

What if electricity from wood costs two-euro cents / kWh and produces high quality charcoal?

Among the renewable energy sources to generate electricity, the combustion or gasification of biomass could play an extremely important role in the future. A major reason for its importance is the independence between the time of availability of the energy source and power generation. However, to maintain their importance in the long run, correspondingly low levelized cost of electricity (LCOE) are necessary; the technology used must also be able to operate profitably without subsidized renewable energy feed-in tariffs. The aim of this work is to reduce the LCOE of biomass combined heat and power-plants with a gasification reactor –wood gasification plants in particular – by utilizing or increasing the value of the gasification residue and a favorable input material. Essentially, the gasification residue is refined into a higher quality product so that the charcoal has the properties of an activated carbon (AC). Furthermore, waste wood (untreated pallets and packaging wood) should be treated in such a way that the resulting fractions can be processed in an existing reactor with the floating fixed-bed gasification (FFBG) technology. Therefore, a Functionalization Unit (Green Carbon Unit (GCU)) and treatment processes for waste wood are to be developed. Please click Additional Files below to see the full abstract

Optimal Token Allocations in Solitaire Knock \u27M Down

In the game Knock ’m Down, tokens are placed in N bins. At each step of the game, a bin is chosen at random according to a fixed probability distribution. If a token remains in that bin, it is removed. When all the tokens have been removed, the player is done. In the solitaire version of this game, the goal is to minimize the expected number of moves needed to remove all the tokens. Here we present necessary conditions on the number of tokens needed for each bin in an optimal solution, leading to an asymptotic solution. MR Subject Classifications: primary: 91A6