Interpolation of Lipschitz functions

This paper describes a new computational approach to multivariate scattered data interpolation. It is assumed that the data is generated by a Lipschitz continuous function f. The proposed approach uses the central interpolation scheme, which produces an optimal interpolant in the worst case scenario. It provides best uniform error bounds on f, and thus translates into reliable learning of f. This paper develops a computationally efficient algorithm for evaluating the interpolant in the multivariate case. We compare the proposed method with the radial basis functions and natural neighbor interpolation, provide the details of the algorithm and illustrate it on numerical experiments. The efficiency of this method surpasses alternative interpolation methods for scattered data.

Exercise loading and cortical bone distribution at the tibial shaft

Cortical bone is not a uniform tissue, and its apparent density [cortical volumetric density (vBMD)] varies around the bone cross-section as well as along the axial length of the bone. It is not yet known, whether the varying vBMD distribution is attributable to modulation in the predominant loads affecting bone. The aim of the present study was to compare the cortical bone mass distribution through the bone cortex (radial distribution) and around the center of mass (polar distribution) among 221 premenopausal women aged 17–40 years representing athletes involved in high impact, odd impact, high magnitude, repetitive low impact, repetitive non-impact sports and leisure time physical activity (referent controls). Bone cross-sections at the tibial mid-diaphysis were assessed with pQCT. Radial and polar vBMD distributions were analyzed in three concentric cortical divisions within the cortical envelope and in four cortical sectors originating from the center of the bone cross-section. MANCOVA, including age as a covariate, revealed no significant group by division/sector interaction in either radial or polar distribution, but the mean vBMD values differed between groups (P < 0.001). The high and odd-impact groups had 1.2 to 2.6% (P < 0.05) lower cortical vBMD than referents, in all analyzed sectors/divisions. The repetitive, low-impact group had 0.4 to 1.0% lower (P < 0.05) vBMD at the mid and outer cortical regions and at the anterior sector of the tibia. The high magnitude group had 1.2% lower BMD at the lateral sector (P < 0.05). The present results generate a hypothesis that the radial and polar cortical bone vBMD distributions within the tibial mid-shaft are not modulated by exercise loading but the mean vBMD level is slightly affected.

Effects of lifetime loading history on cortical bone density and its distribution in middle-aged and older men

We have reported previously that long-term participation of weight-bearing exercise is associated with increased QCT-derived cortical bone size and strength in middle-aged and older men, but not whole bone cortical volumetric BMD. However, since bone remodeling and the distribution of loading-induced strains within cortical bone are non-uniform, the aim of this study was to examine the effects of lifetime loading history on cortical bone mass distribution and bone shape in healthy community dwelling middle-aged and older men. We used QCT to assess mid-femur and mid-tibia angular bone mass distribution around its center (polar distribution), the bone density distribution through the cortex (radial distribution), and the ratio between the maximum and minimum moments of inertia (I_max/I_min ratio) in 281 men aged 50 to 79 years. Current (> 50 years) and past (13–50 years) sport and leisure time activity was assessed by questionnaire to calculate an osteogenic index (OI) during adolescence and adulthood. All men were then categorized into a high (H) or low/non impact (L) group according to their OI scores in each period. Three contrasting groups were then formed to reflect weight-bearing impact categories during adolescence and then adulthood: H–H, H–L and L–L. For polar bone mass distribution, bone deposition in the anterolateral, medial and posterior cortices were 6–10% greater at the mid-femur and 9–24% greater at mid-tibia in men in the highest compared to lowest tertile of lifetime loading (p < 0.01– < 0.001). When comparing the influence of contrasting loading history during adolescence and adulthood, there was a graded response between the groups in the distribution of bone mass at the anterior-lateral and posterior regions of the mid-tibia (H–H > H–L > L–L). For radial bone density distribution, there were no statistically significant effects of loading at the mid-femur, but a greater lifetime OI was associated with a non-significant 10–15% greater bone density near the endocortical region of the mid-tibia. In conclusion, a greater lifetime loading history was associated with region-specific adaptations in cortical bone density.

Effects of habitual physical activity and fitness on tibial cortical bone mass structure and mass distribution in pre-pubertal boys and girl: the look study

Targeted weight-bearing activities during the pre-pubertal years can improve cortical bone mass, structure and distribution, but less is known about the influence of habitual physical activity (PA) and fitness. This study examined the effects of contrasting habitual PA and fitness levels on cortical bone density, geometry and mass distribution in pre-pubertal children. Boys (n = 241) and girls (n = 245) aged 7–9 years had a pQCT scan to measure tibial mid-shaft total, cortical and medullary area, cortical thickness, density, polar strength strain index (SSIpolar) and the mass/density distribution through the bone cortex (radial distribution divided into endo-, mid- and pericortical regions) and around the centre of mass (polar distribution). Four contrasting PA and fitness groups (inactive–unfit, inactive–fit, active–unfit, active–fit) were generated based on daily step counts (pedometer, 7-days) and fitness levels (20-m shuttle test and vertical jump) for boys and girls separately. Active-fit boys had 7.3–7.7 % greater cortical area and thickness compared to inactive–unfit boys (P < 0.05), which was largely due to a 6.4–7.8 % (P < 0.05) greater cortical mass in the posterior–lateral, medial and posterior–medial 66 % tibial regions. Cortical area was not significantly different across PA-fitness categories in girls, but active-fit girls had 6.1 % (P < 0.05) greater SSIpolar compared to inactive–fit girls, which was likely due to their 6.7 % (P < 0.05) greater total bone area. There was also a small region-specific cortical mass benefit in the posterior–medial 66 % tibia cortex in active-fit girls. Higher levels of habitual PA-fitness were associated with small regional-specific gains in 66 % tibial cortical bone mass in pre-pubertal children, particularly boys.

Effects of quenching rate on amorphous structures of Cu46Zr54 metallic glass

Metallic glass shows some superior properties different from crystalline, but the nature of amorphous structure and structural change during glass transition have not been completely understood yet. Molecular dynamics simulation provides intuitive insight into the microstructure and properties at atomistic level. Before probing into the microstructures of metallic glass with molecular dynamics (MD) simulation, it is important to obtain amorphous state first. In the current work, we reproduce the process of manufacturing metallic glass in laboratory including the melting, equilibrating and quenching procedure with molecular dynamics simulations. The structure changing at melting point and glass transition temperature are investigated with the different cooling processing. The partial radial distribution function (PRDF) is applied as a criterion to judge the final amorphous state obtained considering the quenching at different cooling rates and the effects of cooling rate on the formation of amorphous structures are further discussed.

Effects of quenching rate on amorphous structures of Cu46Zr54 metallic glass

Metallic glass shows some superior properties different from crystalline, but the nature of amorphous structure and structural change during glass transition have not been completely understood yet. Molecular dynamics simulation provides intuitive insight into the microstructure and properties at atomistic level. Before probing into the microstructures of metallic glass with molecular dynamics (MD) simulation, it is important to obtain amorphous state first. In the current work, we reproduce the process of manufacturing metallic glass in laboratory including the melting, equilibrating and quenching procedure with molecular dynamics simulations. The structure changing at melting point and glass transition temperature are investigated with the different cooling processing. The partial radial distribution function (PRDF) is applied as a criterion to judge the final amorphous state obtained considering the quenching at different cooling rates and the effects of cooling rate on the formation of amorphous structures are further discussed.

The hidden permutation model and location-based activity recognition

Permutation modeling is challenging because of the combinatorial nature of the problem. However, such modeling is often required in many real-world applications, including activity recognition where subactivities are often permuted and partially ordered. This paper introduces a novel Hidden Permutation Model (HPM) that can learn the partial ordering constraints in permuted state sequences. The HPM is parameterized as an exponential family distribution and is flexible so that it can encode constraints via different feature functions. A chain-flipping Metropolis-Hastings Markov chain Monte Carlo (MCMC) is employed for inference to overcome the O(n!) complexity. Gradient-based maximum likelihood parameter learning is presented for two cases when the permutation is known and when it is hidden. The HPM is evaluated using both simulated and real data from a location-based activity recognition domain. Experimental results indicate that the HPM performs far better than other baseline models, including the naive Bayes classifier, the HMM classifier, and Kirshner's multinomial permutation model. Our presented HPM is generic and can potentially be utilized in any problem where the modeling of permuted states from noisy data is needed.

Stochastic models of road geometry and wind condition for vehicle energy management and control

Modeling and simulation is commonly used to improve vehicle performance, to optimize vehicle system design, and to reduce vehicle development time. Vehicle performances can be affected by environmental conditions and driver behavior factors, which are often uncertain and immeasurable. To incorporate the role of environmental conditions in the modeling and simulation of vehicle systems, both real and artificial data are used. Often, real data are unavailable or inadequate for extensive investigations. Hence, it is important to be able to construct artificial environmental data whose characteristics resemble those of the real data for modeling and simulation purposes. However, to produce credible vehicle simulation results, the simulated environment must be realistic and validated using accepted practices. This paper proposes a stochastic model that is capable of creating artificial environmental factors such as road geometry and wind conditions. In addition, road geometric design principles are employed to modify the created road data, making it consistent with the real-road geometry. Two sets of real-road geometry and wind condition data are employed to propose probability models. To justify the distribution goodness of fit, Pearson's chi-square and correlation statistics have been used. Finally, the stochastic models of road geometry and wind conditions (SMRWs) are developed to produce realistic road and wind data. SMRW can be used to predict vehicle performance, energy management, and control strategies over multiple driving cycles and to assist in developing fuel-efficient vehicles.

Nature of crystalline particle assembly in ring shaped colloidal stains from concentrated dispersions

The drying of colloidal droplet suspensions is important in many realms of practical application and has sustained the interest of researchers over two decades. The arrangements of polystyrene and silica beads, both of diameter 1 μm, 10% by volume of solid deposited on normal glass (hydrophilic), and silicone (hydrophobic) surfaces evaporated from a suspension volume of 3 μL, were investigated. Doughnut shape depositions were found, imputing the influence of strong central circulation flows that resulted in three general regions. In the central region which had strong particle build-up, the top most layers of particle arrangement was confirmed to be disordered using power spectrum and radial distribution function analysis. On closer examination, this appeared more like frustrated attempts to crystallize into larger grains rather than beads arranging in a disordered fashion throughout the piling process. With an adapted micro-bulldozing operation to progressively remove layers of particles from the heap, we found that the later efforts to crystallize through lateral capillary inter-particle forces were liable to be undone once the particles contacted the disorganized particles underneath, which were formed out of the jamming of fast particles arriving at the surface. © 2014 Elsevier B.V.

Stochastic optimization models for energy management in carbonization process of carbon fiber production

Industrial producers face the task of optimizing production process in an attempt to achieve the desired quality such as mechanical properties with the lowest energy consumption. In industrial carbon fiber production, the fibers are processed in bundles containing (batches) several thousand filaments and consequently the energy optimization will be a stochastic process as it involves uncertainty, imprecision or randomness. This paper presents a stochastic optimization model to reduce energy consumption a given range of desired mechanical properties. Several processing condition sets are developed and for each set of conditions, 50 samples of fiber are analyzed for their tensile strength and modulus. The energy consumption during production of the samples is carefully monitored on the processing equipment. Then, five standard distribution functions are examined to determine those which can best describe the distribution of mechanical properties of filaments. To verify the distribution goodness of fit and correlation statistics, the Kolmogorov-Smirnov test is used. In order to estimate the selected distribution (Weibull) parameters, the maximum likelihood, least square and genetic algorithm methods are compared. An array of factors including the sample size, the confidence level, and relative error of estimated parameters are used for evaluating the tensile strength and modulus properties. The energy consumption and N2 gas cost are modeled by Convex Hull method. Finally, in order to optimize the carbon fiber production quality and its energy consumption and total cost, mixed integer linear programming is utilized. The results show that using the stochastic optimization models, we are able to predict the production quality in a given range and minimize the energy consumption of its industrial process.

Simulation of oleuropein structural conformation in vacuum, water and triolein-water systems using molecular dynamics

Oleuropein, the main phenolic compound of olive leaves, exhibits a unique blend of biological activities and has been shown to locate itself at the oil-water (O/W) interface. This behavior could influence the physico-chemical properties of dispersed systems such as emulsions. In this work, we study the effect of the microenvironment (vacuum, water, and triolein-water) on the conformational preferences of oleuropein using molecular dynamics (MD) simulations at 300K for at least 30ns. The seven torsions that describe the flexible skeleton of oleuropein were monitored together with the distance between the glucose (Glu) and hydroxytyrosol (Hyd) moieties (dglu-hyd) of the molecule. The obtained trajectories demonstrated that oleuropein adopts different conformations that depend on the environment. The preferential conformers in each system were analyzed for their molecular geometry and internal energy. In vacuum, the oleuropein preferential conformation is tight with the glucose moiety in close proximity with the hydroxytyrosol moiety. In water, oleuropein preferential conformers presented large differences in their structural properties, varying from a close like U form, and a semi-opened form, to an opened form characterized by high fluctuations in dglu-hyd values. In a triolein-water system, oleuropein tends to adopt a more open form where the glucose moiety could be approximately aligned with the hydroxytyrosol and elenolic acid moieties. Based on a calculation at the HF/6-31G* level, these flexibilities of oleuropein required energy of 19.14kcal/mol in order to adopt the conformation between water and triolein-water system. A radial distribution function (RDF) analysis showed that specific hydroxyl groups of Hyd and Glu interact with water molecules, enabling us to understand the amphiphilic character of oleuropein at the triolein-water interface. MD calculations together with interfacial tension measurements revealed that the oleuropein binding at O/W interface is an enthalpy driven mechanism.

Comparison of Two Methods for Caluculating the Partition Functions of Various Spatial Statistical Models

Likelihood computation in spatial statistics requires accurate and efficient calculation of the normalizing constant (i.e. partition function) of the Gibbs distribution of the model. Two available methods to calculate the normalizing constant by Markov chain Monte Carlo methods are compared by simulation experiments for an Ising model, a Gaussian Markov field model and a pairwise interaction point field model.

Smoothing Lipschitz functions

This paper describes a new approach to multivariate scattered data smoothing. It is assumed that the data are generated by a Lipschitz continuous function f, and include random noise to be filtered out. The proposed approach uses known, or estimated value of the Lipschitz constant of f, and forces the data to be consistent with the Lipschitz properties of f. Depending on the assumptions about the distribution of the random noise, smoothing is reduced to a standard quadratic or a linear programming problem. We discuss an efficient algorithm which eliminates the redundant inequality constraints. Numerical experiments illustrate applicability and efficiency of the method. This approach provides an efficient new tool of multivariate scattered data approximation.

A stochastic derivation of the ratio form of contest success functions

This note provides a distribution-based justification for the ratio form of contest success functions (CSFs), in which a player’s success depends positively on her effort relative to that of her opponents. I show that the inverse exponential distribution of the random shocks yields the ratio form. Extending this approach to asymmetric contests, I also derive an asymmetric ratio form of CSFs.