A rigorous and efficient asymptotic test for power-law cross-correlation

Podobnik and Stanley recently proposed a novel framework, Detrended Cross-Correlation Analysis, for the analysis of power-law cross-correlation between two time-series, a phenomenon which occurs widely in physical, geophysical, financial and numerous additional applications. While highly promising in these important application domains, to date no rigorous or efficient statistical test has been proposed which uses the information provided by DCCA across time-scales for the presence of this power-law cross-correlation. In this paper we fill this gap by proposing a method based on DCCA for testing the hypothesis of power-law cross-correlation; the method synthesizes the information generated by DCCA across time-scales and returns conservative but practically relevant p-values for the null hypothesis of zero correlation, which may be efficiently calculated in software. Thus our proposals generate confidence estimates for a DCCA analysis in a fully probabilistic fashion

Exact Solution of the Multi-Allelic Diffusion Model

We give an exact solution to the Kolmogorov equation describing genetic drift for an arbitrary number of alleles at a given locus. This is achieved by finding a change of variable which makes the equation separable, and therefore reduces the problem with an arbitrary number of alleles to the solution of a set of equations that are essentially no more complicated than that found in the two-allele case. The same change of variable also renders the Kolmogorov equation with the effect of mutations added separable, as long as the mutation matrix has equal entries in each row. Thus this case can also be solved exactly for an arbitrary number of alleles. The general solution, which is in the form of a probability distribution, is in agreement with the previously known results--which were for the cases of two and three alleles only. Results are also given for a wide range of other quantities of interest, such as the probabilities of extinction of various numbers of alleles, mean times to these extinctions, and the means and variances of the allele frequencies. To aid dissemination, these results are presented in two stages: first of all they are given without derivations and too much mathematical detail, and then subsequently derivations and a more technical discussion are provided.Comment: 56 pages. 15 figures. Requires Elsevier document clas

Spatial fluctuations of a surviving particle in the trapping reaction

We consider the trapping reaction, $A+B\to B$, where $A$ and $B$ particles have a diffusive dynamics characterized by diffusion constants $D_A$ and $D_B$. The interaction with $B$ particles can be formally incorporated in an effective dynamics for one $A$ particle as was recently shown by Bray {\it et al}. [Phys. Rev. E {\bf 67}, 060102 (2003)]. We use this method to compute, in space dimension $d=1$, the asymptotic behaviour of the spatial fluctuation, $^{1/2}$, for a surviving $A$ particle in the perturbative regime, $D_A/D_B\ll 1$, for the case of an initially uniform distribution of $B$ particles. We show that, for $t\gg 1$, $^{1/2} \propto t^{\phi}$ with $\phi=1/4$. By contrast, the fluctuations of paths constrained to return to their starting point at time $t$ grow with the larger exponent 1/3. Numerical tests are consistent with these predictions.Comment: 10 pages, 5 figure

Representing older people: towards meaningful images of the user in design scenarios

Designing for older people requires the consideration of a range of difficult and sometimes highly personal design problems. Issues such as fear, loneliness, dependency, and physical decline may be difficult to observe or discuss in interviews. Pastiche scenarios and pastiche personae are techniques that employ characters to create a space for the discussion of new technological developments and as a means to explore user experience. This paper argues that the use of such characters can help to overcome restrictive notions of older people by disrupting designers' prior assumptions. In this paper, we reflect on our experiences using pastiche techniques in two separate technology design projects that sought to address the needs of older people. In the first case pastiche scenarios were developed by the designers of the system and used as discussion documents with users. In the second case, pastiche personae were used by groups of users themselves to generate scenarios which were scribed for later use by the design team. We explore how the use of fictional characters and settings can generate new ideas and undermine rhetorical devices within scenarios that attempt to fit characters to the technology, rather than vice versa. To assist in future development of pastiche techniques in designing for older people, we provide an array of fictional older characters drawn from literary and popular culture.</p

Plio-Quaternary exhumation history of the central Nepalese Himalaya: 1. Apatite and zircon fission track and apatite [U-Th]/He analyses

New apatite and zircon fission track and (U-Th)/He analyses serve to document the bedrock cooling history of the central Nepalese Himalaya near the Annapurna Range. We have obtained 82 apatite fission track (AFT), 7 zircon fission track (ZFT), and 7 apatite (U-Th)/He (AHe) ages from samples collected along the Marsyandi drainage, including eight vertical relief profiles from ridges on either side of the river averaging more than 2 km in elevation range. In addition, three profiles were sampled along ridge crests that also lie ∼2 km above the adjacent valleys, and a transect of >20 valley bottom samples spans from the Lesser Himalaya across the Greater Himalaya and into the Tethyan strata. As a consequence, these data provide one of the more comprehensive low-temperature thermochronologic studies within the Himalaya. Conversely, the youthfulness of this orogen is pushing the limits of these dating techniques. AFT ages range from >3.8 to 0 Ma, ZFT ages from 1.9 to 0.8 Ma, and AHe ages from 0.9 to 0.3 Ma. Most ridges have maximum ages of 1.3–0.8 Ma at 2 km above the valley bottom. Only one ridge crest (in the south central zone of the field area) yielded significantly older ZFT and AFT ages of ∼2 Ma; we infer that a splay of the Main Central Thrust separates this ridge from the rest of the Greater Himalaya. ZFT and AFT ages from a vertical transect along this ridge indicate exhumation rates of ∼1.5 km Myr−1 (r2 > 0.7) from ∼2 to 0.6–0.8 Ma, whereas AHe ages indicate a faster exhumation rate of ∼2.6 km Myr−1 (r2 = 0.9) over the last 0.8 Myr. Exhumation rates calculated for six of the remaining seven vertical profiles ranged from 1.5 to 12 km Myr−1 (all with low r2 values of <0.6) for the time period from ∼1.2 to 0.3 Ma, with no discernible patterns in south to north exhumation rates evident. The absence of a trend in exhumation rates, despite a strong spatial gradient in rainfall, argues against a correlation of long-term exhumation rates with modern patterns of rainfall. AFT ages in the Tethyan strata are, on average, older than in the Greater Himalaya and may be a response to a drier climate, slip on the South Tibetan Detachment, or a gentler dip of the underlying thrust ramp. These data are further evaluated with thermokinematic modeling in the companion paper by Whipp et al

Nonequilibrium Stationary States and Phase Transitions in Directed Ising Models

We study the nonequilibrium properties of directed Ising models with non conserved dynamics, in which each spin is influenced by only a subset of its nearest neighbours. We treat the following models: (i) the one-dimensional chain; (ii) the two-dimensional square lattice; (iii) the two-dimensional triangular lattice; (iv) the three-dimensional cubic lattice. We raise and answer the question: (a) Under what conditions is the stationary state described by the equilibrium Boltzmann-Gibbs distribution? We show that for models (i), (ii), and (iii), in which each spin "sees" only half of its neighbours, there is a unique set of transition rates, namely with exponential dependence in the local field, for which this is the case. For model (iv), we find that any rates satisfying the constraints required for the stationary measure to be Gibbsian should satisfy detailed balance, ruling out the possibility of directed dynamics. We finally show that directed models on lattices of coordination number $z\ge8$ with exponential rates cannot accommodate a Gibbsian stationary state. We conjecture that this property extends to any form of the rates. We are thus led to the conclusion that directed models with Gibbsian stationary states only exist in dimension one and two. We then raise the question: (b) Do directed Ising models, augmented by Glauber dynamics, exhibit a phase transition to a ferromagnetic state? For the models considered above, the answers are open problems, to the exception of the simple cases (i) and (ii). For Cayley trees, where each spin sees only the spins further from the root, we show that there is a phase transition provided the branching ratio, $q$, satisfies $q \ge 3$