Nonlinear Functional Form Research Articles

Distributed Reconstruction of Nonlinear Networks: An ADMM Approach

In this paper, we present a distributed algorithm for the reconstruction of large-scale nonlinear networks. In particular, we focus on the identification from time-series data of the nonlinear functional forms and associated parameters of large-scale nonlinear networks. In the previous work, a nonlinear network reconstruction problem was formulated as a nonconvex optimisation problem based on the combination of a marginal likelihood maximisation procedure with sparsity inducing priors. In this paper, we derive an iterative reweighted lasso algorithm to solve the initial nonconvex optimisation problem based on the concave-convex procedure (CCCP). Moreover, by exploiting the structure of the objective function of this algorithm, a distributed algorithm is designed. To this end, we apply the alternating direction method of multipliers (ADMM) to decompose the original problem into several subproblems. To illustrate the effectiveness of the proposed methods, we use our approach to identify a network of interconnected Kuramoto oscillators with different network sizes (500~100,000 nodes).

Spatial patterns provide support for the stress-gradient hypothesis over a range-wide aridity gradient

We examined variations in the relative importance of facilitation vs. competition, in light of the Stress-Gradient Hypothesis (SGH) by assessing plant interactions along an aridity gradient over biogeographic scales. We surveyed the relationship between a shrub species (Artemisia tridentata) and pine seedlings (Pinus monophylla) across the Great Basin and the Mojave Desert, USA, encompassing the entire range of P. monophylla. Using 69 sites we evaluated the spatial association between P. monophylla seedlings and A. tridentata shrubs, quantified with an electivity index, and implemented multiple regression analysis on the effects of macro- and micro-environmental factors: precipitation, temperature, monsoonality index, topography, substrate and litter cover. We identified annual precipitation as a main factor, which was negatively related to shrub-seedling association. Additionally, shrub-seedling association was stronger in the hot- than in the cold-desert, and was negatively related to litter cover. Effects of monsoonality, summer temperature, and bedrock type were not significant. We also considered nonlinear functional forms of a precipitation–electivity relationship, but the negative linear model proved most predictive. Our observations match SGH predictions. Studying the role of interspecific interactions in shaping species range shifts may lead to improved predictions of distribution ranges and changes in dryland vegetation under global change scenarios.

Real option value over a housing market cycle

This paper analyzes how the dynamics of house prices are affected by the option to rebuild or enlarge existing dwellings. The nonlinear functional form for option value and zoning limits provides identification of changes in option value over the cycle. For homes with high development potential, our results show that about 40% of the price increases during the boom years after the fall of the Berlin Wall were related to increased option value. In the subsequent bust about 50% of their price decline was associated with decreased option value. For dwellings with low redevelopment potential 12% of the decline in real value can be attributed to changing option value.

Expected shortfall estimation using kernel machines

In this paper we study four kernel machines for estimating expected shortfall, which are constructed through combinations of support vector quantile regression (SVQR), restricted SVQR (RSVQR), least squares support vector machine (LS-SVM) and support vector expectile regression (SVER). These kernel machines have obvious advantages such that they achieve nonlinear model but they do not require the explicit form of nonlinear mapping function. Moreover they need no assumption about the underlying probability distribution of errors. Through numerical studies on two artificial an two real data sets we show their effectiveness on the estimation performance at various confidence levels.

Demand for taxi services: new elasticity evidence

This paper investigates the factors that influence the choice of, and hence demand for taxis services, a relatively neglected mode in the urban travel task. Given the importance of positioning preferences for taxi services within the broader set of modal options, we develop a modal choice model for all available modes of transport for trips undertaken by individuals or groups of individuals in a number of market segments. A sample of recent trips in Melbourne in 2012 was used to develop segment-specific mode choice models to obtain direct (and cross) elasticities of interest for cost and service level attributes. Given the nonlinear functional form of the way attributes of interest are included in the modal choice models, a simple set of mean elasticity estimates are not behaviourally meaningful; hence a decision support system is developed to enable the calculation of mean elasticity estimates under specific future service and pricing levels. Some specific direct elasticity estimates are provided as the basis of illustrating the magnitudes of elasticity estimates under likely policy settings.

Developing a new form of the Kozeny–Carman parameter for structured porous media through lattice-Boltzmann modeling

The semi-empirical Kozeny–Carman (KC) equation is a commonly-used relationship for determining permeability as a function of porosity for granular porous materials. This model features a material-specific fitting parameter, CKC, which is generally treated as a constant coefficient. Recent studies, however, have shown that CKC is not constant and could be a varying function of porosity. We used lattice-Boltzmann (LB) modeling to calculate the absolute permeability of two simulated porous structures: periodic arrays of (a) staggered parallel infinite cylinders and (b) spheres. We then identified various functional forms of CKC, and for each form, we performed a regression analysis in order to fit the function to the permeability values determined from the LB simulations. From this analysis, we extracted optimal fitting parameters for each function that minimized the error between permeability values obtained from the KC model and the LB simulations. All linear and non-linear functional forms proposed in this work improve the predictability of the KC model. An algebraic function for CKC provided the most accurate prediction of the KC porosity–permeability relationship for the geometries examined.

Good Prediction of Gas Price between MLFF and GMDH Neural Network

Studies show neural networks have better results in predicting of financial time series in comparison to any linear or non-linear functional form to model the price movement. Neural networks have the advantage of simulating the non-linear models when little a priori knowledge of the structure of problem domains exist or the number of immeasurable input variables are great and system has a chaotic characteristics. Among different methods, MLFF neural network with back-propagation learning algorithm and GMDH neural network with genetic learning algorithms are used to predict gas price of the Henry Hob database covering 01/01/2004-13/7/2009 period. This paper uses moving average crossover inputs and the results confirms (1) the fact there is short-term dependence in gas price movements, (2) the EMA moving average has better result and also (3) by means of the GMDH neural networks, prediction accuracy in comparison to MLFF neural networks, can be improved.

Estimating the risk–return profile of new venture investments using a risk-neutral framework and ‘thick’ models

This study proposes cascade neural networks to estimate the model parameters of the Cox–Ross–Rubinstein risk-neutral approach, which, in turn, explain the risk–return profile of firms at venture capital and initial public offering (IPO)financing rounds. Combining the two methods provides better estimation accuracy than risk-adjusted valuation approaches, conventional neural networks, and linear benchmark models. The findings are persistent across in-sample and out-of-sample tests using 3926 venture capital and 1360 US IPO financing rounds between January 1989 and December 2008. More accurate estimates of the risk–return profile are due to less heterogeneous risk-free rates of return from the risk-neutral framework. Cascade neural networks nest both the linear and nonlinear functional estimation form in addition to taking account of variable interaction effects. Better estimation accuracy of the risk–return profile is desirable for investors so they can make a more informed judgement before committing capital at different stages of development and various financing rounds.

The Contribution of Public Finances to the European Growth Strategy

The objective of the paper is to point out the impact of public finances in the context of the Lisbon growth strategy. Official communications from the Commission and ECOFIN Council note that public finances can contribute to achieving the goal of higher growth and employment via three mechanisms: supporting a stable macro-economic environment, making tax and benefit systems more employment friendly, and redirecting public expenditures towards productive areas. This paper surveys the literature to investigate these channels, to quantify their impact and to identify conditions for their effectiveness. Based on empirical results in the literature, we conclude that there is substantial evidence to suggest that public finances can be considered a source of endogenous growth, but there remains considerable uncertainty regarding the size of their impact. This uncertainty emerges, among other factors, because the effectiveness of fiscal policies hinges on external conditions, such as the state of development. In addition, the link between these policy mechanisms and economic growth seems to have a non-linear functional form in the short and in the long-run.

Analysis of long-distance vacation travel demand in the United States: a multiple discrete–continuous choice framework

This study analyzes the annual vacation destination choices and related time allocation patterns of American households. More specifically, an annual vacation destination choice and time allocation model is formulated to simultaneously predict the different vacation destinations that a household visits in a year, and the time (no. of days) it allocates to each of the visited destinations. The model takes the form of a multiple discrete–continuous extreme value (MDCEV) structure. Further, a variant of the MDCEV model is proposed to reduce the prediction of unrealistically small amounts of vacation time allocation to the chosen destinations. To do so, the continuously non-linear utility functional form in the MDCEV framework is replaced with a combination of a linear and non-linear form. The empirical analysis was performed using the 1995 American Travel Survey data, with the United States divided into 210 alternative destinations. The model estimation results provide several insights into the determinants of households’ vacation destination choice and time allocation patterns. Results suggest that travel times and travel costs to the destinations, and lodging costs, leisure activity opportunities (measured by employment in the leisure industry), length of coastline, and weather conditions at the destinations influence households’ destination choices for vacations. The annual vacation destination choice model developed in this study can be incorporated into a larger national travel modeling framework for predicting the national-level, origin–destination flows for vacation travel.

Analytical Solutions to Variable Thickness and Variable Material Property Rotating Disks for a New Three-Parameter Variation Function

Analytical solutions of two different annular rotating disk problems are obtained under the assumptions of plane stress, isotropy, and small deformations. The first problem involves a homogeneous variable profile disk, whereas the second one is a functionally graded disk having a variation in elasticity modulus. For the variations of disk thickness and elasticity modulus in these problems, a new form of nonlinear function controlled by three parameters is introduced. The derivations of the closed form solutions for both type of rotating disk problems are carried out in a unified form. The closed form solutions are verified numerically by the nonlinear shooting method.

Hedonic Models with Redevelopment Options under Uncertainty

In the hedonic model, implicit market prices can be interpreted as the present values of rents per unit of each hedonic characteristic. But when rents rise, there may be substantial value associated with the option to redevelop to higher intensity per unit land value. In the presence of option value, we first demonstrate that hedonic linear regressions should include an additive nonnegative term for the value of the option. This term increases in the variance of the underlying stochastic process. If this term is omitted, then estimates of implicit market prices for desirable (undesirable) characteristics will be biased downward (upward). This prediction is supported by recent empirical studies. We further suggest that future empirical work can employ the nonlinear functional form derived from our theory.

Examining the BMI-mortality relationship using fractional polynomials

BackgroundMany previous studies estimating the relationship between body mass index (BMI) and mortality impose assumptions regarding the functional form for BMI and result in conflicting findings. This study investigated a flexible data driven modelling approach to determine the nonlinear and asymmetric functional form for BMI used to examine the relationship between mortality and obesity. This approach was then compared against other commonly used regression models.MethodsThis study used data from the National Health Interview Survey, between 1997 and 2000. Respondents were linked to the National Death Index with mortality follow-up through 2005. We estimated 5-year all-cause mortality for adults over age 18 using the logistic regression model adjusting for BMI, age and smoking status. All analyses were stratified by sex. The multivariable fractional polynomials (MFP) procedure was employed to determine the best fitting functional form for BMI and evaluated against the model that includes linear and quadratic terms for BMI and the model that groups BMI into standard weight status categories using a deviance difference test. Estimated BMI-mortality curves across models were then compared graphically.ResultsThe best fitting adjustment model contained the powers -1 and -2 for BMI. The relationship between 5-year mortality and BMI when estimated using the MFP approach exhibited a J-shaped pattern for women and a U-shaped pattern for men. A deviance difference test showed a statistically significant improvement in model fit compared to other BMI functions. We found important differences between the MFP model and other commonly used models with regard to the shape and nadir of the BMI-mortality curve and mortality estimates.ConclusionsThe MFP approach provides a robust alternative to categorization or conventional linear-quadratic models for BMI, which limit the number of curve shapes. The approach is potentially useful in estimating the relationship between the full spectrum of BMI values and other health outcomes, or costs.

NEIGHBORHOOD CONTEXT AND NONLINEAR PEER EFFECTS ON ADOLESCENT VIOLENT CRIME*

Although evidence of the strong correlation between deviant behavior and exposure to deviant peers is overwhelming, researchers have yet to investigate whether a nonlinear functional form better captures this relationship than does a linear form. Researchers also have yet to examine the extent to which peer effects vary as a function of the neighborhood context. To address these issues, we use data from the Project on Human Development in Chicago Neighborhoods (PHDCN) to examine 1) the functional form of the relationship between peer violence exposure and self-reported violent crime and 2) the extent to which the effect of exposure to violent peers on violence is ecologically structured. Estimates from logistic hierarchical models indicate that the effect of peer violence exposure on violent crime decreases at higher values of peer violence, as reflected in a nonlinear relationship (expressed in terms of log-odds). Furthermore, exposure to violent peers increases along with neighborhood disadvantage, and the effect of peer violence exposure on violent crime is attenuated as neighborhood disadvantage increases, which is reflected in a cross-level peer violence/disadvantage interaction.

Distinguishing graded and ultrasensitive signalling cascade kinetics by the shape of morphogen gradients in Drosophila

Recently, signalling gradients in cascades of two-state reaction–diffusion systems were described as a model for understanding key biochemical mechanisms that underlie development and differentiation processes in the Drosophila embryo. Diffusion-trapping at the exterior of the cell membrane triggers the mitogen-activated protein kinase (MAPK) cascade to relay an appropriate signal from the membrane to the inner part of the cytosol, whereupon another diffusion-trapping mechanism involving the nucleus reads out this signal to trigger appropriate changes in gene expression. Proposed mathematical models exhibit equilibrium distributions consistent with experimental measurements of key spatial gradients in these processes. A significant property of the formulation is that the signal is assumed to be relayed from one system to the next in a linear fashion. However, the MAPK cascade often exhibits nonlinear dose–response properties and the final remark of Berezhkovskii et al. (2009) is that this assumption remains an important property to be tested experimentally, perhaps via a new quantitative assay across multiple genetic backgrounds. In anticipation of the need to be able to sensibly interpret data from such experiments, here we provide a complementary analysis that recovers existing formulae as a special case but is also capable of handling nonlinear functional forms. Predictions of linear and nonlinear signal relays and, in particular, graded and ultrasensitive MAPK kinetics, are compared.

Generalized cointegration: a new concept with an application to health expenditure and health outcomes

We propose a new generalization of the concept of cointegration that allows for the possibility that a set of variables are involved in an unknown nonlinear relationship. Although these variables may be unit-root non-stationary, there exists a nonlinear combination of them that takes account of such non-stationarity. We then introduce an estimation technique that allows us to test for the presence of this generalized cointegration in the absence of knowledge as to the true nonlinear functional form and the full set of regressors. We outline the basic stages of the technique and discuss how the issue of unit-root non-stationarity and cointegration affects each stage of the estimation procedure. We then apply this technique to the relationship between health expenditure and health outcomes, which is an important but controversial issue. A number of studies have found very little or no relationship between the level of health expenditure and outcomes. In econometric terms, if there is such a relationship, then there should exist a cointegrating relationship between these two variables and possibly many others. The problem that arises is that we may be either unable to measure these other variables or that we do not know about them, in which case we may incorrectly find no relationship between health expenditures and outcomes. We then apply the concept of generalized cointegration; we obtain a highly significant relationship between health expenditure and health outcomes.

Recognition of good prediction of gold price between MLFF and GMDH neural network

Studies show neural networks have better results in predicting of financial time series in comparison to any linear or non-linear functional form to model the price movement. Neural networks have the advantage of simulating the non-linear models when little a priori knowledge of the structure of problem domains exist or the number of immeasurable input variables are great and system has a chaotic characteristics. Among different methods, MLFF neural network with back-propagation learning algorithm and GMDH neural network with genetic learning algorithms are used to predict gold price of the NYMEX database covering 1st January, 2002 to 13th July, 2007 period. This paper uses moving average crossover inputs and the results confirms (1) the fact that there is short-term dependence in gold price movements, (2) the EMA moving average has better result and also (3) by means of the GMDH neural networks, prediction accuracy in comparison to MLFF neural networks, can be improved. Key words: Artificial neural networks (ANN), multi layered feed forward (MLFF), group method of data handling (GMDH), simple moving average (SMA), exponential moving average (EMA), gold price.

Resistance of Concrete Masonry Walls with Membrane Catcher Systems Subjected to Blast Loading

This paper describes a methodology for analyzing the impulse pressure response of unreinforced concrete masonry walls that have been retrofitted with membranes that are not bonded to the masonry (catcher systems). Membrane catcher systems can be used to protect building occupants from secondary debris resulting from blast pressure, and the effectiveness of systems comprised of polymers, composites, geotextiles, and thin steel and aluminum sheets has been researched extensively over the past fifteen years. The methodology presented herein is based upon the large displacement response of the unreinforced masonry wall, with and without compression membrane arching, and the subsequent tension membrane resistance of the catcher system. The necessary equations are developed in the form of nonlinear resistance functions, which are then used in single-degree-of-freedom analyses to develop dynamic response predictions. The applicability of the approach is substantiated through comparison to full-scale blast test results, and demonstrations involving disparate materials and loading are made.

Kernel machine approach to testing the significance of multiple genetic markers for risk prediction.

There is growing evidence that genomic and proteomic research holds great potential for changing irrevocably the practice of medicine. The ability to identify important genomic and biological markers for risk assessment can have a great impact in public health from disease prevention, to detection, to treatment selection. However, the potentially large number of markers and the complexity in the relationship between the markers and the outcome of interest impose a grand challenge in developing accurate risk prediction models. The standard approach to identifying important markers often assesses the marginal effects of individual markers on a phenotype of interest. When multiple markers relate to the phenotype simultaneously via a complex structure, such a type of marginal analysis may not be effective. To overcome such difficulties, we employ a kernel machine Cox regression framework and propose an efficient score test to assess the overall effect of a set of markers, such as genes within a pathway or a network, on survival outcomes. The proposed test has the advantage of capturing the potentially nonlinear effects without explicitly specifying a particular nonlinear functional form. To approximate the null distribution of the score statistic, we propose a simple resampling procedure that can be easily implemented in practice. Numerical studies suggest that the test performs well with respect to both empirical size and power even when the number of variables in a gene set is not small compared to the sample size.

A Novel Approach to Pharmacodynamic Assessment of Antimicrobial Agents: New Insights to Dosing Regimen Design

Pharmacodynamic modeling has been increasingly used as a decision support tool to guide dosing regimen selection, both in the drug development and clinical settings. Killing by antimicrobial agents has been traditionally classified categorically as concentration-dependent (which would favor less fractionating regimens) or time-dependent (for which more frequent dosing is preferred). While intuitive and useful to explain empiric data, a more informative approach is necessary to provide a robust assessment of pharmacodynamic profiles in situations other than the extremes of the spectrum (e.g., agents which exhibit partial concentration-dependent killing). A quantitative approach to describe the interaction of an antimicrobial agent and a pathogen is proposed to fill this unmet need. A hypothetic antimicrobial agent with linear pharmacokinetics is used for illustrative purposes. A non-linear functional form (sigmoid Emax) of killing consisted of 3 parameters is used. Using different parameter values in conjunction with the relative growth rate of the pathogen and antimicrobial agent concentration ranges, various conventional pharmacodynamic surrogate indices (e.g., AUC/MIC, Cmax/MIC, %T>MIC) could be satisfactorily linked to outcomes. In addition, the dosing intensity represented by the average kill rate of a dosing regimen can be derived, which could be used for quantitative comparison. The relevance of our approach is further supported by experimental data from our previous investigations using a variety of gram-negative bacteria and antimicrobial agents (moxifloxacin, levofloxacin, gentamicin, amikacin and meropenem). The pharmacodynamic profiles of a wide range of antimicrobial agents can be assessed by a more flexible computational tool to support dosing selection.