Multifractality of the Feigenbaum attractor and fractional derivatives

It is shown that fractional derivatives of the (integrated) invariant measure of the Feigenbaum map at the onset of chaos have power-law tails in their cumulative distributions, whose exponents can be related to the spectrum of singularities $f(\alpha)$. This is a new way of characterizing multifractality in dynamical systems, so far applied only to multifractal random functions (Frisch and Matsumoto (J. Stat. Phys. 108:1181, 2002)). The relation between the thermodynamic approach (Vul, Sinai and Khanin (Russian Math. Surveys 39:1, 1984)) and that based on singularities of the invariant measures is also examined. The theory for fractional derivatives is developed from a heuristic point view and tested by very accurate simulations.Comment: 20 pages, 5 figures, J.Stat.Phys. in pres

How Puppet Masters Create Genocide: A Study in the State-Sponsored Killings in Rwanda and Cambodia

This paper calls on the United States to assess where its true interests lie in evaluating genocide and mass killings. Through an examination of the social and political factors which were paramount in bringing about the atrocities in Cambodia in the late 1970s and Rwanda in the mid-1990s, the U.S. is urged to take heed of the tried-and-true methods used by ruthless regimes throughout history in bringing about the destruction of their own citizenry. Consideration of the psychological imperatives necessary for ordinary men or women to depart from the standard boundaries of civilized society and butcher their neighbors and countrymen is worthwhile in understanding how individuals permit, if not facilitate, genocide in their own backyards. Many believe that genocides are inevitable and caused by ancient ethnic or religious strife. Governments understand these tensions and use them to exploit their own people and gain political leverage. Genocide does not occur over night. Bringing about the conditions necessary to permit such a grave injustice is cultivated over many years, often decades. When governments enact laws and issue directives, no matter the content, the legitimacy of such edicts cannot be overlooked by the average citizen, especially the ill-educated and impoverished. By looking at the legislation and government programs enacted prior to mass-murder, clear and systematic evidence of intent cannot be overlooked. The goal of this article is to spread awareness of the methods and techniques employed leading up to genocide so that the freedom-loving nations of the world may act proactively and prevent tragedies before needless blood is spilled

Fluctuating dynamics at the quasiperiodic onset of chaos, Tsallis q-statistics and Mori's q-phase thermodynamics

We analyze the fluctuating dynamics at the golden-mean transition to chaos in the critical circle map and find that trajectories within the critical attractor consist of infinite sets of power laws mixed together. We elucidate this structure assisted by known renormalization group (RG) results. Next we proceed to weigh the new findings against Tsallis' entropic and Mori's thermodynamic theoretical schemes and observe behavior to a large extent richer than previously reported. We find that the sensitivity to initial conditions has the form of families of intertwined q-exponentials, of which we determine the q-indexes and the generalized Lyapunov coefficient spectra. Further, the dynamics within the critical attractor is found to consist of not one but a collection of Mori's q-phase transitions with a hierarchical structure. The value of Mori's `thermodynamic field' variable q at each transition corresponds to the same special value for the entropic index q. We discuss the relationship between the two formalisms and indicate the usefulness of the methods involved to determine the universal trajectory scaling function and/or the ocurrence and characterization of dynamical phase transitions.Comment: Resubmitted to Physical Review E. The title has been changed slightly and the abstract has been extended. There is a new subsection following the conclusions that explains the role and usefulness of the q-statistics in the problem studied. Other minor changes througout the tex

Develop and test fuel cell powered on-site integrated total energy system

Test results are presented for a 24 cell, two sq ft (4kW) stack. This stack is a precursor to a 25kW stack that is a key milestone. Results are discussed in terms of cell performance, electrolyte management, thermal management, and reactant gas manifolding. The results obtained in preliminary testing of a 50kW methanol processing subsystem are discussed. Subcontracting activities involving application analysis for fuel cell on site integrated energy systems are updated

Numerical stability of mass transfer driven by Roche lobe overflow in close binaries

Numerical computation of the time evolution of the mass transfer rate in a close binary can be and, in particular, has been a computational challenge. Using a simple physical model to calculate the mass transfer rate, we show that for a simple explicit iteration scheme the mass transfer rate is numerically unstable unless the time steps are sufficiently small. In general, more sophisticated explicit algorithms do not provide any significant improvement since this instability is a direct result of time discretization. For a typical binary evolution, computation of the mass transfer rate as a smooth function of time limits the maximum tolerable time step and thereby sets the minimum total computational effort required for an evolutionary computation. By methods of ``Controlling Chaos'' it can be shown that a specific implicit iteration scheme, based on Newton's method, is the most promising solution for the problem.Comment: 6 pages, LaTeX, two eps figures, Astronomy and Astrophysics, accepte

An Algorithmic Argument for Nonadaptive Query Complexity Lower Bounds on Advised Quantum Computation

This paper employs a powerful argument, called an algorithmic argument, to prove lower bounds of the quantum query complexity of a multiple-block ordered search problem in which, given a block number i, we are to find a location of a target keyword in an ordered list of the i-th block. Apart from much studied polynomial and adversary methods for quantum query complexity lower bounds, our argument shows that the multiple-block ordered search needs a large number of nonadaptive oracle queries on a black-box model of quantum computation that is also supplemented with advice. Our argument is also applied to the notions of computational complexity theory: quantum truth-table reducibility and quantum truth-table autoreducibility.Comment: 16 pages. An extended abstract will appear in the Proceedings of the 29th International Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science, Springer-Verlag, Prague, August 22-27, 200

Distribution of repetitions of ancestors in genealogical trees

We calculate the probability distribution of repetitions of ancestors in a genealogical tree for simple neutral models of a closed population with sexual reproduction and non-overlapping generations. Each ancestor at generation g in the past has a weight w which is (up to a normalization) the number of times this ancestor appears in the genealogical tree of an individual at present. The distribution P_g(w) of these weights reaches a stationary shape P_\infty(w) for large g, i.e. for a large number of generations back in the past. For small w, P_\infty(w) is a power law with a non-trivial exponent which can be computed exactly using a standard procedure of the renormalization group approach. Some extensions of the model are discussed and the effect of these variants on the shape of P_\infty(w) are analysed.Comment: 20 pages, 5 figures included, to appear in Physica

Chaos properties and localization in Lorentz lattice gases

The thermodynamic formalism of Ruelle, Sinai, and Bowen, in which chaotic properties of dynamical systems are expressed in terms of a free energy-type function - called the topological pressure - is applied to a Lorentz Lattice Gas, as typical for diffusive systems with static disorder. In the limit of large system sizes, the mechanism and effects of localization on large clusters of scatterers in the calculation of the topological pressure are elucidated and supported by strong numerical evidence. Moreover it clarifies and illustrates a previous theoretical analysis [Appert et al. J. Stat. Phys. 87, chao-dyn/9607019] of this localization phenomenon.Comment: 32 pages, 19 Postscript figures, submitted to PR

Stochastics theory of log-periodic patterns

We introduce an analytical model based on birth-death clustering processes to help understanding the empirical log-periodic corrections to power-law scaling and the finite-time singularity as reported in several domains including rupture, earthquakes, world population and financial systems. In our stochastics theory log-periodicities are a consequence of transient clusters induced by an entropy-like term that may reflect the amount of cooperative information carried by the state of a large system of different species. The clustering completion rates for the system are assumed to be given by a simple linear death process. The singularity at t_{o} is derived in terms of birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge

Submodular Maximization Meets Streaming: Matchings, Matroids, and More

We study the problem of finding a maximum matching in a graph given by an input stream listing its edges in some arbitrary order, where the quantity to be maximized is given by a monotone submodular function on subsets of edges. This problem, which we call maximum submodular-function matching (MSM), is a natural generalization of maximum weight matching (MWM), which is in turn a generalization of maximum cardinality matching (MCM). We give two incomparable algorithms for this problem with space usage falling in the semi-streaming range---they store only $O(n)$ edges, using $O(n\log n)$ working memory---that achieve approximation ratios of $7.75$ in a single pass and $(3+\epsilon)$ in $O(\epsilon^{-3})$ passes respectively. The operations of these algorithms mimic those of Zelke's and McGregor's respective algorithms for MWM; the novelty lies in the analysis for the MSM setting. In fact we identify a general framework for MWM algorithms that allows this kind of adaptation to the broader setting of MSM. In the sequel, we give generalizations of these results where the maximization is over "independent sets" in a very general sense. This generalization captures hypermatchings in hypergraphs as well as independence in the intersection of multiple matroids.Comment: 18 page