Efficient Evaluation of Multidimensional Time-Varying Density Forecasts

We propose two simple evaluation methods for time varying density forecasts of continuous higher dimensional random variables. Both methods are based on the probability integral transformation for unidimensional forecasts. The first method tests multinormal densities and relies on the rotation of the coordinate system. The advantage of the second method is not only its applicability to any continuous distribution but also the evaluation of the forecast accuracy in specific regions of its domain as defined by the user’s interest. We show that the latter property is particularly useful for evaluating a multidimensional generalization of the Value at Risk. In simulations and in an empirical study, we examine the performance of both tests.

Genetic Algorithm Search for Predictive Patterns in Multidimensional Time Series

Based on an algorithm for pattern matching in character strings, we implement a pattern matching machine that searches for occurrences of patterns in multidimensional time series. Before the search process takes place, time series are encoded in user-designed alphabets. The patterns, on the other hand, are formulated as regular expressions that are composed of letters from these alphabets and operators. Furthermore, we develop a genetic algorithm to breed patterns that maximize a user-defined fitness function. In an application to financial data, we show that patterns bred to predict high exchange rates volatility in training samples retain statistically significant predictive power in validation samples.

The top-down mechanism for body-mass-abundance scaling

Scaling relationships between mean body masses and abundances of species in multitrophic communities continue to be a subject of intense research and debate. The top-down mechanism explored in this paper explains the frequently observed inverse linear relationship between body mass and abundance (i.e., constant biomass) in terms of a balancing of resource biomasses by behaviorally and evolutionarily adapting foragers, and the evolutionary response of resources to this foraging pressure. The mechanism is tested using an allometric, multitrophic community model with a complex food web structure. It is a statistical model describing the evolutionary and population dynamics of tens to hundreds of species in a uniform way. Particularities of the model are the detailed representation of the evolution and interaction of trophic traits to reproduce topological food web patterns, prey switching behavior modeled after experimental observations, and the evolutionary adaptation of attack rates. Model structure and design are discussed. For model states comparable to natural communities, we find that (1) the body-mass-abundance scaling does not depend on the allometric scaling exponent of physiological rates in the form expected from the energetic equivalence rule or other bottom-up theories; (2) the scaling exponent of abundance as a function of body mass is approximately -1, independent of the allometric exponent for physiological rates assumed; (3) removal of top-down control destroys this pattern, and energetic equivalence is recovered. We conclude that the top-down mechanism is active in the model, and that it is a viable alternative to bottom-up mechanisms for controlling body-mass-abundance relations in natural communities.

From the UV to the static-field limit: rates and scaling laws of intense-field ionization of helium

We present high-accuracy calculations of ionization rates of helium at UV (195 nm) wavelengths. The data are obtained from full-dimensionality integrations of the helium-laser time-dependent Schrödinger equation. Comparison is made with our previously obtained data at 390 nm and 780 nm. We show that scaling laws introduced by Parker et al extend unmodified from the near-infrared limit into the UV limit. Static-field ionization rates of helium are also obtained, again from time-dependent full-dimensionality integrations of the helium Schrödinger equation. We compare the static-field ionization results with those of Scrinzi et al and Themelis et al, who also treat the full-dimensional helium atom, but with time-independent methods. Good agreement is obtained.

Multipliers of multidimensional Fourier algebras

Let $G$ be a locally compact $\sigma$-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra $A^n(G)$ of $G$. We characterise the completely bounded multidimensional multipliers associated with $A^n(G)$ in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all $n$-dimensional completely bounded multipliers into the space of all Schur multipliers on $G^{n+1}$ with respect to the (left) Haar measure. We show that in the case $G$ is amenable the space of completely bounded multidimensional multipliers coincides with the multidimensional Fourier-Stieltjes algebra of $G$ introduced by Ylinen. We extend some well-known results for abelian groups to the multidimensional setting.

Scaling of Superdomain Bands in Ferroelectric Dots

Bundles of 90° stripe domains have been observed to form into distinct groups, or bands, in mesoscale BaTiO3 single crystal dots. Vector piezoresponse force microscopy (PFM) shows that each band region, when considered as a single entity, possesses a resolved polarization that lies approximately along the pseudocubic direction; antiparallel alignment of this resultant polarization in adjacent bands means that these regions can be considered as 180° “superdomains.” For dots with sidewall dimensions below ~2 microns, Landau–Kittel like scaling in the width of these superdomains was observed, strongly suggesting that they form in response to lateral depolarizing fields. In larger dot structures, scaling laws break down. We have rationalized these observations by considering changes in the driving force for the adoption of equilibrium superdomain periodicities implied by Landau–Kittel-free energy models; we conclude that the formation of ordered bands of superdomains is a uniquely meso/nanoscale phenomenon. We also note that the superdomain bands found by PFM imaging in air contrast with the quadrant arrangements seen previously by Schilling et al. (Nano Lett., 9, 3359 (2009)) through transmission electron microscopy imaging in vacuum. The importance of the exact nature of the boundary conditions in determining the domain patterns that spontaneously form in nanostructures is therefore clearly implied.

A comparative analysis of multidimensional features of objects resembling sets of graphs

In the present paper, we introduce a notion of a style representing abstract, complex objects having characteristics that can be represented as structured objects. Furthermore, we provide some mathematical properties of such styles. As a main result, we present a novel approach to perform a meaningful comparative analysis of such styles by defining and using graph-theoretic measures. We compare two styles by comparing the underlying feature sets representing sets of graph structurally. To determine the structural similarity between the underlying graphs, we use graph similarity measures that are computationally efficient. More precisely, in order to compare styles, we map each feature set to a so-called median graph and compare the resulting median graphs. As an application, we perform an experimental study to compare special styles representing sets of undirected graphs and present numerical results thereof. (C) 2007 Elsevier Inc. All rights reserved.

Scaling of Food-Web Properties with Diversity and Complexity Across Ecosystems

Trophic scaling models describe how topological food-web properties such as the number of predator prey links scale with species richness of the community. Early models predicted that either the link density (i.e. the number of links per species) or the connectance (i.e. the linkage probability between any pair of species) is constant across communities. More recent analyses, however, suggest that both these scaling models have to be rejected, and we discuss several hypotheses that aim to explain the scale dependence of these complexity parameters. Based on a recent, highly resolved food-web compilation, we analysed the scaling behaviour of 16 topological parameters and found significant power law scaling relationships with diversity (i.e. species richness) and complexity (i.e. connectance) for most of them. These results illustrate the lack of universal constants in food-web ecology as a function of diversity or complexity. Nonetheless, our power law scaling relationships suggest that fundamental processes determine food-web topology, and subsequent analyses demonstrated that ecosystem-specific differences in these relationships were of minor importance. As such, these newly described scaling relationships provide robust and testable cornerstones for future structural food-web models.

Scaling in the time-dependent failure of a fiber bundle with local load sharing

We study the scaling behaviors of a time-dependent fiber-bundle model with local load sharing. Upon approaching the complete failure of the bundle, the breaking rate of fibers diverges according to r(t)proportional to(T-f-t)(-xi) where T-f is the lifetime of the bundle and xi approximate to 1.0 is a universal scaling exponent. The average lifetime of the bundle [T-f] scales with the system size as N-delta, where delta depends on the distribution of individual fiber as well as the breakdown rule. [S1063-651X(99)13902-3].

Is Human Development Multidimensional?

Stiglitz's Commission on the Measurement of Economic Performance and Social Progress (CMEPSP) argued that well-being is multidimensional and identified eight distinct dimensions. Conventional linear techniques confirm that a large number of dimensions are needed to describe development. In contrast, a new non-linear technique that we introduce from chaos theory shows that a smaller number of dimensions are needed to span the development space. From the analysis, variables representing the Health, Education, Inequality and Individual Rights areas of life quality would provide a broad picture of development, whereas income per capita adds little extra information.

GAIN SCALING RELATIONSHIPS FOR NE-LIKE GE SLAB TARGETS

The gain coefficient of the strongest 3p --> 3s, J = 2 --> 1 lasing transition at 23.6 nm in the Ne-like Ge collisional excitation scheme has been measured, using the fundamental wavelength from a Nd:glass laser (1.06-mu-m), for a range of incident intensities on massive stripe targets up to 2.2 cm in length. From a threshold incident laser intensity of approximately 6 x 10(12) W/cm2, the gain coefficient rises to approximately 4.5 cm-1 for an irradiation intensity of approximately 2.5 x 10(13) W/cm2, tending towards still higher gain coefficients at higher incident intensities. For targets of maximum length, a gain-length product gL almost-equal-to 10 was reached with a resultant output power at 23.6 nm estimated to be at the approximately kW level. The beam divergence decreased with length to a minimum of approximately 7 mrad but no significant trend in beam pointing with plasma length was observed. From the trend in the gain coefficient, it appears that for a fixed energy laser irradiating a approximately 100-mu-m wide slab targets, an incident intensity of I(i) approximately 1.2 x 10(13) W/cm2 represents an optimum working level, assuming that plasma length is not limited by refractive effects. In addition to the usual valence electron excited 3p --> 3s transitions, the gain coefficient for the core excited 1s(2)2s2p(6)3d --> 1s(2)2s2p(6)3p transition at 19.9 nm has been measured to be approximately 1.5 cm-1 for an incident irradiance of approximately 2.5 x 10(13) W/cm2.

Measurements of fast electron scaling generated by petawatt laser systems

Fast electron energy spectra have been measured for a range of intensities between 10(18) and 10(21) W cm(-2) and for different target materials using electron spectrometers. Several experimental campaigns were conducted on petawatt laser facilities at the Rutherford Appleton Laboratory and Osaka University, where the pulse duration was varied from 0.5 to 5 ps relevant to upcoming fast ignition integral experiments. The incident angle was also changed from normal incidence to 40 degrees in p-polarized. The results confirm a reduction from the ponderomotive potential energy on fast electrons at the higher intensities under the wide range of different irradiation conditions.