Hammerstein model identification algorithm using Bezier-Bernstein approximation

A new identification algorithm is introduced for the Hammerstein model consisting of a nonlinear static function followed by a linear dynamical model. The nonlinear static function is characterised by using the Bezier-Bernstein approximation. The identification method is based on a hybrid scheme including the applications of the inverse of de Casteljau's algorithm, the least squares algorithm and the Gauss-Newton algorithm subject to constraints. The related work and the extension of the proposed algorithm to multi-input multi-output systems are discussed. Numerical examples including systems with some hard nonlinearities are used to illustrate the efficacy of the proposed approach through comparisons with other approaches.

Model selection approaches for non-linear system identification: a review

The identification of non-linear systems using only observed finite datasets has become a mature research area over the last two decades. A class of linear-in-the-parameter models with universal approximation capabilities have been intensively studied and widely used due to the availability of many linear-learning algorithms and their inherent convergence conditions. This article presents a systematic overview of basic research on model selection approaches for linear-in-the-parameter models. One of the fundamental problems in non-linear system identification is to find the minimal model with the best model generalisation performance from observational data only. The important concepts in achieving good model generalisation used in various non-linear system-identification algorithms are first reviewed, including Bayesian parameter regularisation and models selective criteria based on the cross validation and experimental design. A significant advance in machine learning has been the development of the support vector machine as a means for identifying kernel models based on the structural risk minimisation principle. The developments on the convex optimisation-based model construction algorithms including the support vector regression algorithms are outlined. Input selection algorithms and on-line system identification algorithms are also included in this review. Finally, some industrial applications of non-linear models are discussed.

Generalized matching networks and their properties

In this paper, we introduce two kinds of graphs: the generalized matching networks (GMNs) and the recursive generalized matching networks (RGMNs). The former generalize the hypercube-like networks (HLNs), while the latter include the generalized cubes and the star graphs. We prove that a GMN on a family of k-connected building graphs is -connected. We then prove that a GMN on a family of Hamiltonian-connected building graphs having at least three vertices each is Hamiltonian-connected. Our conclusions generalize some previously known results.

Enantiospecific adsorption of alanine on the chiral Cu{531} surface

We have studied enantiospecific differences in the adsorption of (S)- and (R)-alanine on Cu{531}R using low-energy electron diffraction (LEED), X-ray photoelectron spectroscopy, and near edge X-ray absorption fine structure (NEXAFS) spectroscopy. At saturation coverage, alanine adsorbs as alaninate forming a p(1 4) superstructure. LEED shows a significantly higher degree of long-range order for the S than for the R enantiomer. Also carbon K-edge NEXAFS spectra show differences between (S)- and (R)-alanine in the variations of the ð resonance when the linear polarization vector is rotated within the surface plane. This indicates differences in the local adsorption geometries of the molecules, most likely caused by the interaction between the methyl group and the metal surface and/or intermolecular hydrogen bonds. Comparison with model calculations and additional information from LEED and photoelectron spectroscopy suggest that both enantiomers of alaninate adsorb in two different orientations associated with triangular adsorption sites on {110} and {311} microfacets of the Cu{531} surface. The experimental data are ambiguous as to the exact difference between the local geometries of the two enantiomers. In one of two models that fit the data equally well, significantly more (R)-alaninate molecules are adsorbed on {110} sites than on {311} sites whereas for (S)-alaninate the numbers are equal. The enantiospecific differences found in these experiments are much more pronounced than those reported from other ultrahigh vacuum techniques applied to similar systems.

Comparing tube models for predicting the linear rheology of branched polymer melts

The hierarchical and "bob" (or branch-on-branch) models are tube-based computational models recently developed for predicting the linear rheology of general mixtures of polydisperse branched polymers. These two models are based on a similar tube-theory framework but differ in their numerical implementation and details of relaxation mechanisms. We present a detailed overview of the similarities and differences of these models and examine the effects of these differences on the predictions of the linear viscoelastic properties of a set of representative branched polymer samples in order to give a general picture of the performance of these models. Our analysis confirms that the hierarchical and bob models quantitatively predict the linear rheology of a wide range of branched polymer melts but also indicate that there is still no unique solution to cover all types of branched polymers without case-by-case adjustment of parameters such as the dilution exponent alpha and the factor p(2) which defines the hopping distance of a branch point relative to the tube diameter. An updated version of the hierarchical model, which shows improved computational efficiency and refined relaxation mechanisms, is introduced and used in these analyses.

Integration of chaos theory and mathematical models in building simulation: Part I: Literature review

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasingly complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I) reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develops conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to building simulation scientists, initiates a dialogue and builds bridges between scientists and engineers, and stimulates future research about a wide range of issues on building environmental systems.

Integration of chaos theory and mathematical models in building simulation: Part II: Conceptual frameworks

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasing complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I), published in the previous issue, reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develop conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to (1) building simulation scientists and designers (2) initiating a dialogue between scientists and engineers, and (3) stimulating future research on a wide range of issues involved in designing and managing building environmental systems.

Differences in glucose-dependent insulinotropic polypeptide hormone and hepatic lipase in subjects of southern and northern Europe: implications for postprandial lipaemia

The aim was to determine in 32 healthy young men from northern and southern Europe whether differences in the secretion of insulin and glucose-dependent insulinotropic polypeptide (GIP) might explain these findings through the actions of these hormones on lipoprotein lipase. In a randomized, single-blind, crossover study the effects of 2 test meals of identical macronutrient composition but different saturated fatty acid (SFA) and monounsaturated fatty acid (MUFA) contents were investigated on postprandial GIP, insulin, the ratio of incremental triacylglycerol to apolipoprotein B-48 (a marker of chylomicron size), and the activity of postheparin lipases. Fasting and postprandial GIP concentrations and postheparin hepatic lipase (HL) activities were higher in the southern Europeans (P<0.001 and P<0.02, respectively). Lipoprotein lipase activity after the SFA-rich meal was higher in the northern Europeans (P<0.01). HL activity 9 h after the SFA-rich meal and the area under the curve (AUC) for the postprandial insulin response correlated with the AUC for the postprandial GIP response (r=0.44 (P<0.04) and r=0.46 (P<0.05), respectively). There were no significant differences in chylomicron size between the 2 groups for either meal, but when the groups were combined there was a difference in chylomicron size between the SFA- and MUFA-rich meals (P<0.05), which could be due to the formation of larger chylomicrons after the MUFA-rich meal. The significantly higher GIP and insulin responses and HL activities in southern Europeans may provide an explanation for a previous report of attenuated postprandial triacylglycerol and apolipoprotein B-48 responses in them.

Why are autism spectrum conditions more prevalent in males?

Autism Spectrum Conditions (ASC) are much more common in males, a bias that may offer clues to the etiology of this condition. Although the cause of this bias remains a mystery, we argue that it occurs because ASC is an extreme manifestation of the male brain. The extreme male brain (EMB) theory, first proposed in 1997, is an extension of the Empathizing-Systemizing (E-S) theory of typical sex differences that proposes that females on average have a stronger drive to empathize while males on average have a stronger drive to systemize. In this first major update since 2005, we describe some of the evidence relating to the EMB theory of ASC and consider how typical sex differences in brain structure may be relevant to ASC. One possible biological mechanism to account for the male bias is the effect of fetal testosterone (fT). We also consider alternative biological theories, the X and Y chromosome theories, and the reduced autosomal penetrance theory. None of these theories has yet been fully confirmed or refuted, though the weight of evidence in favor of the fT theory is growing from converging sources (longitudinal amniocentesis studies from pregnancy to age 10 years old, current hormone studies, and genetic association studies of SNPs in the sex steroid pathways). Ultimately, as these theories are not mutually exclusive and ASC is multi-factorial, they may help explain the male prevalence of ASC.

The Dirichlet-to-Neumann map for the elliptic sine Gordon

We analyse the Dirichlet problem for the elliptic sine Gordon equation in the upper half plane. We express the solution $q(x,y)$ in terms of a Riemann-Hilbert problem whose jump matrix is uniquely defined by a certain function $b(\la)$, $\la\in\R$, explicitly expressed in terms of the given Dirichlet data $g_0(x)=q(x,0)$ and the unknown Neumann boundary value $g_1(x)=q_y(x,0)$, where $g_0(x)$ and $g_1(x)$ are related via the global relation $\{b(\la)=0$, $\la\geq 0\}$. Furthermore, we show that the latter relation can be used to characterise the Dirichlet to Neumann map, i.e. to express $g_1(x)$ in terms of $g_0(x)$. It appears that this provides the first case that such a map is explicitly characterised for a nonlinear integrable {\em elliptic} PDE, as opposed to an {\em evolution} PDE.

Observational tracking of the 2D structure of coronal mass ejections between the sun and 1 AU

The Solar TErrestrial RElations Observatory (STEREO) provides high cadence and high resolution images of the structure and morphology of coronal mass ejections (CMEs) in the inner heliosphere. CME directions and propagation speeds have often been estimated through the use of time-elongation maps obtained from the STEREO Heliospheric Imager (HI) data. Many of these CMEs have been identified by citizen scientists working within the SolarStormWatch project ( www.solarstormwatch.com ) as they work towards providing robust real-time identification of Earth-directed CMEs. The wide field of view of HI allows scientists to directly observe the two-dimensional (2D) structures, while the relative simplicity of time-elongation analysis means that it can be easily applied to many such events, thereby enabling a much deeper understanding of how CMEs evolve between the Sun and the Earth. For events with certain orientations, both the rear and front edges of the CME can be monitored at varying heliocentric distances (R) between the Sun and 1 AU. Here we take four example events with measurable position angle widths and identified by the citizen scientists. These events were chosen for the clarity of their structure within the HI cameras and their long track lengths in the time-elongation maps. We show a linear dependency with R for the growth of the radial width (W) and the 2D aspect ratio (χ) of these CMEs, which are measured out to ≈ 0.7 AU. We estimated the radial width from a linear best fit for the average of the four CMEs. We obtained the relationships W=0.14R+0.04 for the width and χ=2.5R+0.86 for the aspect ratio (W and R in units of AU).

The asymptotic behavior of densities related to the supremum of a stable process

If X is a stable process of index α∈(0, 2) whose Lévy measure has density cx−α−1 on (0, ∞), and S1=sup0Xt, it is known that P(S1>x)∽Aα−1x−α as x→∞ and P(S1≤x)∽Bα−1ρ−1xαρ as x↓0. [Here ρ=P(X1>0) and A and B are known constants.] It is also known that S1 has a continuous density, m say. The main point of this note is to show that m(x)∽Ax−(α+1) as x→∞ and m(x)∽Bxαρ−1 as x↓0. Similar results are obtained for related densities.