Weak constraints in four-dimensional variational data assimilation

The formulation of four-dimensional variational data assimilation allows the incorporation of constraints into the cost function which need only be weakly satisfied. In this paper we investigate the value of imposing conservation properties as weak constraints. Using the example of the two-body problem of celestial mechanics we compare weak constraints based on conservation laws with a constraint on the background state.We show how the imposition of conservation-based weak constraints changes the nature of the gradient equation. Assimilation experiments demonstrate how this can add extra information to the assimilation process, even when the underlying numerical model is conserving.

Perspex machine VII: The universal perspex machine

The perspex machine arose from the unification of projective geometry with the Turing machine. It uses a total arithmetic, called transreal arithmetic, that contains real arithmetic and allows division by zero. Transreal arithmetic is redefined here. The new arithmetic has both a positive and a negative infinity which lie at the extremes of the number line, and a number nullity that lies off the number line. We prove that nullity, 0/0, is a number. Hence a number may have one of four signs: negative, zero, positive, or nullity. It is, therefore, impossible to encode the sign of a number in one bit, as floating-, point arithmetic attempts to do, resulting in the difficulty of having both positive and negative zeros and NaNs. Transrational arithmetic is consistent with Cantor arithmetic. In an extension to real arithmetic, the product of zero, an infinity, or nullity with its reciprocal is nullity, not unity. This avoids the usual contradictions that follow from allowing division by zero. Transreal arithmetic has a fixed algebraic structure and does not admit options as IEEE, floating-point arithmetic does. Most significantly, nullity has a simple semantics that is related to zero. Zero means "no value" and nullity means "no information." We argue that nullity is as useful to a manufactured computer as zero is to a human computer. The perspex machine is intended to offer one solution to the mind-body problem by showing how the computable aspects of mind and. perhaps, the whole of mind relates to the geometrical aspects of body and, perhaps, the whole of body. We review some of Turing's writings and show that he held the view that his machine has spatial properties. In particular, that it has the property of being a 7D lattice of compact spaces. Thus, we read Turing as believing that his machine relates computation to geometrical bodies. We simplify the perspex machine by substituting an augmented Euclidean geometry for projective geometry. This leads to a general-linear perspex-machine which is very much easier to pro-ram than the original perspex-machine. We then show how to map the whole of perspex space into a unit cube. This allows us to construct a fractal of perspex machines with the cardinality of a real-numbered line or space. This fractal is the universal perspex machine. It can solve, in unit time, the halting problem for itself and for all perspex machines instantiated in real-numbered space, including all Turing machines. We cite an experiment that has been proposed to test the physical reality of the perspex machine's model of time, but we make no claim that the physical universe works this way or that it has the cardinality of the perspex machine. We leave it that the perspex machine provides an upper bound on the computational properties of physical things, including manufactured computers and biological organisms, that have a cardinality no greater than the real-number line.

The method of least squares used to invert an orbit problem

Six parameters uniquely describe the orbit of a body about the Sun. Given these parameters, it is possible to make predictions of the body's position by solving its equation of motion. The parameters cannot be directly measured, so they must be inferred indirectly by an inversion method which uses measurements of other quantities in combination with the equation of motion. Inverse techniques are valuable tools in many applications where only noisy, incomplete, and indirect observations are available for estimating parameter values. The methodology of the approach is introduced and the Kepler problem is used as a real-world example. (C) 2003 American Association of Physics Teachers.

Six new loci associated with body mass index highlight a neuronal influence on body weight regulation

Common variants at only two loci, FTO and MC4R, have been reproducibly associated with body mass index (BMI) in humans. To identify additional loci, we conducted meta-analysis of 15 genome-wide association studies for BMI (n > 32,000) and followed up top signals in 14 additional cohorts (n > 59,000). We strongly confirm FTO and MC4R and identify six additional loci (P < 5 x 10(-8)): TMEM18, KCTD15, GNPDA2, SH2B1, MTCH2 and NEGR1 (where a 45-kb deletion polymorphism is a candidate causal variant). Several of the likely causal genes are highly expressed or known to act in the central nervous system (CNS), emphasizing, as in rare monogenic forms of obesity, the role of the CNS in predisposition to obesity.

Planning rigid body motions using elastic curves

This paper tackles the problem of computing smooth, optimal trajectories on the Euclidean group of motions SE(3). The problem is formulated as an optimal control problem where the cost function to be minimized is equal to the integral of the classical curvature squared. This problem is analogous to the elastic problem from differential geometry and thus the resulting rigid body motions will trace elastic curves. An application of the Maximum Principle to this optimal control problem shifts the emphasis to the language of symplectic geometry and to the associated Hamiltonian formalism. This results in a system of first order differential equations that yield coordinate free necessary conditions for optimality for these curves. From these necessary conditions we identify an integrable case and these particular set of curves are solved analytically. These analytic solutions provide interpolating curves between an initial given position and orientation and a desired position and orientation that would be useful in motion planning for systems such as robotic manipulators and autonomous-oriented vehicles.

Variation in the FFAR1 gene modifies BMI, body composition and plasma lipids but not plasma insulin or Beta-cell function in overweight subjects

Background FFAR1 receptor is a long chain fatty acid G-protein coupled receptor which is expressed widely, but found in high density in the pancreas and central nervous system. It has been suggested that FFAR1 may play a role in insulin sensitivity, lipotoxicity and is associated with type 2 diabetes. Here we investigate the effect of three common SNPs of FFAR1 (rs2301151; rs16970264; rs1573611) on pancreatic function, BMI, body composition and plasma lipids. Methodology/Principal Findings For this enquiry we used the baseline RISCK data, which provides a cohort of overweight subjects at increased cardiometabolic risk with detailed phenotyping. The key findings were SNPs of the FFAR1 gene region were associated with differences in body composition and lipids, and the effects of the 3 SNPs combined were cumulative on BMI, body composition and total cholesterol. The effects on BMI and body fat were predominantly mediated by rs1573611 (1.06 kg/m2 higher (P = 0.009) BMI and 1.53% higher (P = 0.002) body fat per C allele). Differences in plasma lipids were also associated with the BMI-increasing allele of rs2301151 including higher total cholesterol (0.2 mmol/L per G allele, P = 0.01) and with the variant A allele of rs16970264 associated with lower total (0.3 mmol/L, P = 0.02) and LDL (0.2 mmol/L, P<0.05) cholesterol, but also with lower HDL-cholesterol (0.09 mmol/L, P<0.05) although the difference was not apparent when controlling for multiple testing. There were no statistically significant effects of the three SNPs on insulin sensitivity or beta cell function. However accumulated risk allele showed a lower beta cell function on increasing plasma fatty acids with a carbon chain greater than six. Conclusions/Significance Differences in body composition and lipids associated with common SNPs in the FFAR1 gene were apparently not mediated by changes in insulin sensitivity or beta-cell function.

Imitation of lateralised body movements: doing it the hard way

Two experiments examined imitation of lateralised body movement sequences presented at six viewing angles (0º, 60º, 120º, 180º, 240º, and 300º rotation relative to the participant’s body). Experiment 1 found that, when participants were instructed simply to ‘‘do what the model does’’, at all viewing angles they produced more actions using the same side of the body as the model (anatomical matches), than actions using the opposite side (anatomical non-matches). In Experiment 2 participants were instructed to produce either anatomical matches or anatomical non-matches of observed actions. When the model was viewed from behind (0º), the anatomically matching group were more accurate than the anatomically non-matching group, but the non-matching group was superior when the model faced the participant (180º and 240º). No reliable differences were observed between groups at 60º, 120º, and 300º. In combination, the results of Experiments 1 and 2 suggest that, when they are confronting a model, people choose to imitate the hard way; they attempt to match observed actions anatomically, in spite of the fact that anatomical matching is more subject to error than anatomical non-matching.

Differential effects of two fermentable carbohydrates on central appetite regulation and body composition

BACKGROUND: Obesity is rising at an alarming rate globally. Different fermentable carbohydrates have been shown to reduce obesity. The aim of the present study was to investigate if two different fermentable carbohydrates (inulin and b-glucan) exert similar effects on body composition and central appetite regulation in high fat fed mice. METHODOLOGY/PRINCIPAL FINDINGS: Thirty six C57BL/6 male mice were randomized and maintained for 8 weeks on a high fat diet containing 0% (w/w) fermentable carbohydrate, 10% (w/w) inulin or 10% (w/w) b-glucan individually. Fecal and cecal microbial changes were measured using fluorescent in situ hybridization, fecal metabolic profiling was obtained by proton nuclear magnetic resonance (1H NMR), colonic short chain fatty acids were measured by gas chromatography, body composition and hypothalamic neuronal activation were measured using magnetic resonance imaging (MRI) and manganese enhanced MRI (MEMRI), respectively, PYY (peptide YY) concentration was determined by radioimmunoassay, adipocyte cell size and number were also measured. Both inulin and b-glucan fed groups revealed significantly lower cumulative body weight gain compared with high fat controls. Energy intake was significantly lower in b-glucan than inulin fed mice, with the latter having the greatest effect on total adipose tissue content. Both groups also showed an increase in the numbers of Bifidobacterium and Lactobacillus-Enterococcus in cecal contents as well as feces. b- glucan appeared to have marked effects on suppressing MEMRI associated neuronal signals in the arcuate nucleus, ventromedial hypothalamus, paraventricular nucleus, periventricular nucleus and the nucleus of the tractus solitarius, suggesting a satiated state. CONCLUSIONS/SIGNIFICANCE: Although both fermentable carbohydrates are protective against increased body weight gain, the lower body fat content induced by inulin may be metabolically advantageous. b-glucan appears to suppress neuronal activity in the hypothalamic appetite centers. Differential effects of fermentable carbohydrates open new possibilities for nutritionally targeting appetite regulation and body composition.

Variation in genes related to hepatic lipid metabolism and changes in waist circumference and body weight.

We analysed single nucleotide polymorphisms (SNPs) tagging the genetic variability of six candidate genes (ATF6, FABP1, LPIN2, LPIN3, MLXIPL and MTTP) involved in the regulation of hepatic lipid metabolism, an important regulatory site of energy balance for associations with body mass index (BMI) and changes in weight and waist circumference. We also investigated effect modification by sex and dietary intake. Data of 6,287 individuals participating in the European prospective investigation into cancer and nutrition were included in the analyses. Data on weight and waist circumference were followed up for 6.9 ± 2.5 years. Association of 69 tagSNPs with baseline BMI and annual changes in weight as well as waist circumference were investigated using linear regression analysis. Interactions with sex, GI and intake of carbohydrates, fat as well as saturated, monounsaturated and polyunsaturated fatty acids were examined by including multiplicative SNP-covariate terms into the regression model. Neither baseline BMI nor annual weight or waist circumference changes were significantly associated with variation in the selected genes in the entire study population after correction for multiple testing. One SNP (rs1164) in LPIN2 appeared to be significantly interacting with sex (p = 0.0003) and was associated with greater annual weight gain in men (56.8 ± 23.7 g/year per allele, p = 0.02) than in women (-25.5 ± 19.8 g/year per allele, p = 0.2). With respect to gene-nutrient interaction, we could not detect any significant interactions when accounting for multiple testing. Therefore, out of our six candidate genes, LPIN2 may be considered as a candidate for further studies.

Application of complex extreme learning machine to multiclass classification problems with high dimensionality: a THz spectra classification problem

We extend extreme learning machine (ELM) classifiers to complex Reproducing Kernel Hilbert Spaces (RKHS) where the input/output variables as well as the optimization variables are complex-valued. A new family of classifiers, called complex-valued ELM (CELM) suitable for complex-valued multiple-input–multiple-output processing is introduced. In the proposed method, the associated Lagrangian is computed using induced RKHS kernels, adopting a Wirtinger calculus approach formulated as a constrained optimization problem similarly to the conventional ELM classifier formulation. When training the CELM, the Karush–Khun–Tuker (KKT) theorem is used to solve the dual optimization problem that consists of satisfying simultaneously smallest training error as well as smallest norm of output weights criteria. The proposed formulation also addresses aspects of quaternary classification within a Clifford algebra context. For 2D complex-valued inputs, user-defined complex-coupled hyper-planes divide the classifier input space into four partitions. For 3D complex-valued inputs, the formulation generates three pairs of complex-coupled hyper-planes through orthogonal projections. The six hyper-planes then divide the 3D space into eight partitions. It is shown that the CELM problem formulation is equivalent to solving six real-valued ELM tasks, which are induced by projecting the chosen complex kernel across the different user-defined coordinate planes. A classification example of powdered samples on the basis of their terahertz spectral signatures is used to demonstrate the advantages of the CELM classifiers compared to their SVM counterparts. The proposed classifiers retain the advantages of their ELM counterparts, in that they can perform multiclass classification with lower computational complexity than SVM classifiers. Furthermore, because of their ability to perform classification tasks fast, the proposed formulations are of interest to real-time applications.

Body-centric modelling, identification, and acceleration tracking control of a quadrotor UAV

This paper presents the mathematical development of a body-centric nonlinear dynamic model of a quadrotor UAV that is suitable for the development of biologically inspired navigation strategies. Analytical approximations are used to find an initial guess of the parameters of the nonlinear model, then parameter estimation methods are used to refine the model parameters using the data obtained from onboard sensors during flight. Due to the unstable nature of the quadrotor model, the identification process is performed with the system in closed-loop control of attitude angles. The obtained model parameters are validated using real unseen experimental data. Based on the identified model, a Linear-Quadratic (LQ) optimal tracker is designed to stabilize the quadrotor and facilitate its translational control by tracking body accelerations. The LQ tracker is tested on an experimental quadrotor UAV and the obtained results are a further means to validate the quality of the estimated model. The unique formulation of the control problem in the body frame makes the controller better suited for bio-inspired navigation and guidance strategies than conventional attitude or position based control systems that can be found in the existing literature.