Conserving Local Magnetic Helicity in Numerical Simulations

Magnetic helicity is robustly conserved in systems with large magnetic Reynolds numbers, including most systems of astrophysical interest. This plays a major role in suppressing the kinematic large scale dynamo and driving the large scale dynamo through the magnetic helicity flux. Numerical simulations of astrophysical systems typically lack sufficient resolution to enforce global magnetic helicity over several dynamical times. Errors in the internal distribution of magnetic helicity are equally serious and possibly larger. Here we propose an algorithm for enforcing strict local conservation of magnetic helicity in the Coulomb gauge in numerical simulations.Comment: Comments are welcom

Classical and quantum partition bound and detector inefficiency

We study randomized and quantum efficiency lower bounds in communication complexity. These arise from the study of zero-communication protocols in which players are allowed to abort. Our scenario is inspired by the physics setup of Bell experiments, where two players share a predefined entangled state but are not allowed to communicate. Each is given a measurement as input, which they perform on their share of the system. The outcomes of the measurements should follow a distribution predicted by quantum mechanics; however, in practice, the detectors may fail to produce an output in some of the runs. The efficiency of the experiment is the probability that the experiment succeeds (neither of the detectors fails). When the players share a quantum state, this gives rise to a new bound on quantum communication complexity (eff*) that subsumes the factorization norm. When players share randomness instead of a quantum state, the efficiency bound (eff), coincides with the partition bound of Jain and Klauck. This is one of the strongest lower bounds known for randomized communication complexity, which subsumes all the known combinatorial and algebraic methods including the rectangle (corruption) bound, the factorization norm, and discrepancy. The lower bound is formulated as a convex optimization problem. In practice, the dual form is more feasible to use, and we show that it amounts to constructing an explicit Bell inequality (for eff) or Tsirelson inequality (for eff*). We give an example of a quantum distribution where the violation can be exponentially bigger than the previously studied class of normalized Bell inequalities. For one-way communication, we show that the quantum one-way partition bound is tight for classical communication with shared entanglement up to arbitrarily small error.Comment: 21 pages, extended versio

Inter-arrival times of message propagation on directed networks

One of the challenges in fighting cybercrime is to understand the dynamics of message propagation on botnets, networks of infected computers used to send viruses, unsolicited commercial emails (SPAM) or denial of service attacks. We map this problem to the propagation of multiple random walkers on directed networks and we evaluate the inter-arrival time distribution between successive walkers arriving at a target. We show that the temporal organization of this process, which models information propagation on unstructured peer to peer networks, has the same features as SPAM arriving to a single user. We study the behavior of the message inter-arrival time distribution on three different network topologies using two different rules for sending messages. In all networks the propagation is not a pure Poisson process. It shows universal features on Poissonian networks and a more complex behavior on scale free networks. Results open the possibility to indirectly learn about the process of sending messages on networks with unknown topologies, by studying inter-arrival times at any node of the network.Comment: 9 pages, 12 figure

Discovery of a proto-white dwarf with a massive unseen companion

We report the discovery of SDSS~J022932.28+713002.7, a nascent extremely low-mass (ELM) white dwarf (WD) orbiting a massive ($> 1\,M_\odot$ at 2$\sigma$ confidence) companion with a period of 36 hours. We use a combination of spectroscopy, including data from the ongoing SDSS-V survey, and photometry to measure the stellar parameters for the primary pre-ELM white dwarf. The lightcurve of the primary WD exhibits ellipsoidal variation, which we combine with radial velocity data and $\tt{PHOEBE}$ binary simulations to estimate the mass of the invisible companion. We find that the primary WD has mass $M_1$ = $0.18^{+0.02}_{-0.02}$ M$_\odot$ and the unseen secondary has mass $M_2$ = $1.19^{+0.21}_{-0.14}$ M$_\odot$. The mass of the companion suggests that it is most likely a near-Chandrasekhar mass white dwarf or a neutron star. It is likely that the system recently went through a Roche lobe overflow from the visible primary onto the invisible secondary. The dynamical configuration of the binary is consistent with the theoretical evolutionary tracks for such objects, and the primary is currently in its contraction phase. The measured orbital period puts this system on a stable evolutionary path which, within a few Gyrs, will lead to a contracted ELM white dwarf orbiting a massive compact companion.Comment: 21 Pages, 8 Figure

Non-locality and Communication Complexity

Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. In this review we study the information counterpart of computing. The abstract form of the distributed computing setting is called communication complexity. It studies the amount of information, in terms of bits or in our case qubits, that two spatially separated computing devices need to exchange in order to perform some computational task. Surprisingly, quantum mechanics can be used to obtain dramatic advantages for such tasks. We review the area of quantum communication complexity, and show how it connects the foundational physics questions regarding non-locality with those of communication complexity studied in theoretical computer science. The first examples exhibiting the advantage of the use of qubits in distributed information-processing tasks were based on non-locality tests. However, by now the field has produced strong and interesting quantum protocols and algorithms of its own that demonstrate that entanglement, although it cannot be used to replace communication, can be used to reduce the communication exponentially. In turn, these new advances yield a new outlook on the foundations of physics, and could even yield new proposals for experiments that test the foundations of physics.Comment: Survey paper, 63 pages LaTeX. A reformatted version will appear in Reviews of Modern Physic

Sublinear Algorithms for Approximating String Compressibility

We raise the question of approximating the compressibility of a string with respect to a fixed compression scheme, in sublinear time. We study this question in detail for two popular lossless compression schemes: run-length encoding (RLE) and a variant of Lempel-Ziv (LZ77), and present sublinear algorithms for approximating compressibility with respect to both schemes. We also give several lower bounds that show that our algorithms for both schemes cannot be improved significantly. Our investigation of LZ77 yields results whose interest goes beyond the initial questions we set out to study. In particular, we prove combinatorial structural lemmas that relate the compressibility of a string with respect to LZ77 to the number of distinct short substrings contained in it (its ℓth subword complexity , for small ℓ). In addition, we show that approximating the compressibility with respect to LZ77 is related to approximating the support size of a distribution.National Science Foundation (U.S.) (Award CCF-1065125)National Science Foundation (U.S.) (Award CCF-0728645)Marie Curie International Reintegration Grant PIRG03-GA-2008-231077Israel Science Foundation (Grant 1147/09)Israel Science Foundation (Grant 1675/09

Politische Dimensionen von Militärübungen und Manövern – ein Projektbericht

Die virtuellen Kriege und Operationen, die in Militärübungen gespielt und geprobt werden, können entweder der Abschreckung dienen oder aber Angriffe vorbereiten bzw. zur Maskierung tatsächlicher Angriffe dienen. Für Beobachter ist es vielfach nicht offensichtlich, um welche Art von Militärübung es sich handelt. Die Ergebnisse eines vierjährigen internationalen Projektes zu politischen Dimensionen von Militärübungen richten das Schlaglicht insbesondere auf Missverständnisse und deren ungewollte politische Auswirkungen, die im Extremfall unbeabsichtigt zum Krieg führen können

Genome Erosion in a Nitrogen-Fixing Vertically Transmitted Endosymbiotic Multicellular Cyanobacterium

Background: An ancient cyanobacterial incorporation into a eukaryotic organism led to the evolution of plastids (chloroplasts) and subsequently to the origin of the plant kingdom. The underlying mechanism and the identities of the partners in this monophyletic event remain elusive. Methodology/Principal Findings: To shed light on this evolutionary process, we sequenced the genome of a cyanobacterium residing extracellularly in an endosymbiosis with a plant, the water-fern Azolla filiculoides Lam. This symbiosis was selected as it has characters which make it unique among extant cyanobacterial plant symbioses: the cyanobacterium lacks autonomous growth and is vertically transmitted between plant generations. Our results reveal features of evolutionary significance. The genome is in an eroding state, evidenced by a large proportion of pseudogenes (31.2%) and a high frequency of transposable elements (,600) scattered throughout the genome. Pseudogenization is found in genes such as the replication initiator dnaA and DNA repair genes, considered essential to free-living cyanobacteria. For some functional categories of genes pseudogenes are more prevalent than functional genes. Loss of function is apparent even within the ‘core’ gene categories of bacteria, such as genes involved in glycolysis and nutrient uptake. In contrast, serving as a critical source of nitrogen for the host, genes related to metabolic processes such as cell differentiation and nitrogen-fixation are well preserved. Conclusions/Significance: This is the first finding of genome degradation in a plant symbiont and phenotypically complex cyanobacterium and one of only a few extracellular endosymbionts described showing signs of reductive genome evolution. Our findings suggest an ongoing selective streamlining of this cyanobacterial genome which has resulted in an organism devoted to nitrogen fixation and devoid of autonomous growth. The cyanobacterial symbiont of Azolla can thus be considered at the initial phase of a transition from free-living organism to a nitrogen-fixing plant entity, a transition process which may mimic what drove the evolution of chloroplasts from a cyanobacterial ancestor