Natural Hierarchical Structure Research Articles

Interaction Screening for Ultrahigh-Dimensional Data

In ultrahigh-dimensional data analysis, it is extremely challenging to identify important interaction effects, and a top concern in practice is computational feasibility. For a dataset with n observations and p predictors, the augmented design matrix including all linear and order-2 terms is of size n × (p2 + 3p)/2. When p is large, say more than tens of hundreds, the number of interactions is enormous and beyond the capacity of standard machines and software tools for storage and analysis. In theory, the interaction-selection consistency is hard to achieve in high-dimensional settings. Interaction effects have heavier tails and more complex covariance structures than main effects in a random design, making theoretical analysis difficult. In this article, we propose to tackle these issues by forward-selection-based procedures called iFOR, which identify interaction effects in a greedy forward fashion while maintaining the natural hierarchical model structure. Two algorithms, iFORT and iFORM, are studied. Computationally, the iFOR procedures are designed to be simple and fast to implement. No complex optimization tools are needed, since only OLS-type calculations are involved; the iFOR algorithms avoid storing and manipulating the whole augmented matrix, so the memory and CPU requirement is minimal; the computational complexity is linear in p for sparse models, hence feasible for p ≫ n. Theoretically, we prove that they possess sure screening property for ultrahigh-dimensional settings. Numerical examples are used to demonstrate their finite sample performance. Supplementary materials for this article are available online.

Controlled deposition of magnetic particles within the 3-D template of wood: making use of the natural hierarchical structure of wood

Process of modifying wood veneer samples with metal salts to result in magnetic particle modified wood and images of the cross section of a wood sample lumen cell wall unmodified and modified with the deposition of magnetic particles.

Hierarchical-TGDR

Regularization methods that simultaneously select a small set of the most relevant features and build a classifier using the selected features have gained much attention recently in problems of classification of “omics” data. In many multi-class classification problems, which are of practical importance, the classes are naturally endowed with a hierarchical structure. However, such natural hierarchical structure is often ignored. Here, we use an existing regularization algorithm, Threshold Gradient Descent Regularization, in a hierarchical fashion, which takes advantage of natural biological structure to specifically tackle multi-class classification of microarray data. We apply this approach to one of the tasks presented by the sbv IMPROVER Diagnostic Signature Challenge: the Lung Cancer Sub-Challenge. Gene expression data from non-small cell lung carcinoma were used to classify tumors into adenocarcinoma and squamous cell carcinoma subtypes, and their clinical stages (I and II). Genetic and transcriptom...

Synchronization-Inspired Partitioning and Hierarchical Clustering

Synchronization is a powerful and inherently hierarchical concept regulating a large variety of complex processes ranging from the metabolism in a cell to opinion formation in a group of individuals. Synchronization phenomena in nature have been widely investigated and models concisely describing the dynamical synchronization process have been proposed, e.g., the well-known Extensive Kuramoto Model. We explore the potential of the Extensive Kuramoto Model for data clustering. We regard each data object as a phase oscillator and simulate the dynamical behavior of the objects over time. By interaction with similar objects, the phase of an object gradually aligns with its neighborhood, resulting in a nonlinear object movement naturally driven by the local cluster structure. We demonstrate that our framework has several attractive benefits: 1) It is suitable to detect clusters of arbitrary number, shape, and data distribution, even in difficult settings with noise points and outliers. 2) Combined with the Minimum Description Length (MDL) principle, it allows partitioning and hierarchical clustering without requiring any input parameters which are difficult to estimate. 3) Synchronization faithfully captures the natural hierarchical cluster structure of the data and MDL suggests meaningful levels of abstraction. Extensive experiments demonstrate the effectiveness and efficiency of our approach.

Place of living and health inequality: a study for elderly Italians

The aim of this study is to explore if the context matters in explaining socioeconomic inequality in the self-rated health of Italian elderly people. Our hypothesis is that health status perception is associated with existing huge imbalances among Italian areas. A multilevel approach is applied to account for the natural hierarchical structure, as individuals nested in geographical regions. Multilevel logistic regression models are performed including both individual and contextual variables, using data from 2005 Italian Health survey. We prove that individual factors (compositional effect), even representing the most important correlates of health, do not completely explain intra-regional heterogeneity, confirming the existence of an autonomous contextual effect. These territorial differences are present among both Regions and large areas, two geographical aggregations relevant in the domain of health. Moreover, for some Regions, the account for contextual factors explains variations in perceived health, leading to an overthrow of the initial situation: these Regions perform better than expected in the field of health. For other Regions, the contextual elements introduced do not catch the milieu heterogeneity. In this regard, we expect, and solicit, a major effort toward data availability, qualitatively and quantitatively, that might help in explaining residual territorial heterogeneity in health perception, a fundamental starting point for targeting specific policy interventions.

Hierarchical Composite Materials: Achieving What a Single-Phase Material Cannot

In recent years, goal-oriented composite processing techniques, making use of the Advanced Materials by Design 1 concept, have been investigated with the goal of creating materials with a desired behavior, response, or performance. When no single homogeneous material is sufficient to fulfill design requirements, fibers, particulates, precipitates, or other phases are introduced, creating composites with complex structures. In hierarchical composites, the various components in the composites are also themselves composites; 2 hence, hierarchical composites have components that span different length scales, exhibit levels of critical material responses, and in some cases have functional structural geometry. Such natural materials as bone, nacre, and wood have hierarchical structures that benefit from levels of component functionality and mechanical responses. 3 Corresponding to these natural hierarchical structures, new composite systems (e.g., bio-inspired ceramic composites and advanced metal-matrix composites) are designed to achieve what a single-phase material cannot. There will be many opportunities in the future to design composite systems with hierarchical structure impacting material properties from the nano- to the macroscale. The importance of length scales and the effect of salient properties of the different components at characteristic lengths 4 is addressed in the following papers. In the article by Tarakanova and Buehler, the structure–function relationship of spider silk is described. They consider the mechanical response of the silk at three different levels. At the lowest length scales (below 20 nm), features of the protein, such as hydrogen bonds, beta sheet crystals, and the interaction between amorphous and crystalline domains, are considered. At the next level (100 nm), a coarse-grain model of the protein networks constituting individual fibrils is subjected to four idealized loading conditions for a variety of fibril diameters. Using parameters obtained from the lower-scale simulations in the coarse-grain model, the authors demonstrate that the optimal fibril diameter is 20 nm to 80 nm, which is consistent with fibril diameters found in nature. The final level is the spider web, with the radial and spiral silk threads modeled using another coarse-grain scheme. Results from the lowest-level simulations were directly applied to model the web’s response to relevant loads at the scale of the web. The end results are two distinct multiscale models (proteinto-fibril and protein-to-web) incorporating relevant mechanical responses from the lowest length scale, linked in a bottom-up approach. The article by Dabbs and Aksay describes their recent research on processing nanoporous silica structures by liquid-crystalline L3 phase templating. The L3 phase templating technique can be used to create hierarchical structures of silica monoliths, coatings, and fibers. The silica monoliths (which have structures that resemble cancellous bone) can be tuned to have densities between 0.5 g/cm 3 and 0.8 g/cm 3 and channel diameters between 1 nm and 10 nm, simply by varying the nonpolar constituent concentration. The high void volume, void connectivity, and large surface area allow for adsorption sites, fluid infiltration, and drug incorporation while maintaining the structure and strength of the silica framework. The authors describe infiltrating photopolymers into L3 templated silica disks for optical data storage, using templated silica coating for heightened sensitivity to adsorption of targeted molecules, integrating the drug indomethacin into a thermoresponsive polymer for controlled drug release, and creating low-density, high-strength silica fibers. The L3 phase templating technique can be used to generate a variety of silica composites, thus producing application-specific hierarchical structures.

The effect of microsized roughness in nano/microsized hierarchical surfaces replicated from a lotus leaf on the activities of osteoblast-like cells (MG63)

One of the challenges in tissue engineering is the design of optimal biomedical scaffolds, which can be governed by both physical and chemical properties, such as structural properties (porosity, pore size, and tortuosity) and surface characteristics. Of these properties, we observed the effects of nano- to microsized hierarchical surface. To achieve the hierarchical surface structure on poly(ε-caprolactone) (PCL) film, we employed an electric-field-aided nano/micro-casting technique (FA-NCT) to mimic a typical natural hierarchical structure, the lotus leaf. The sizes of the microsized structures in lotus leaf replicas were controlled by employing or not employing the electric field during casting. The hierarchical surfaces showed two different roughness ranges for the microsized structure and the nanosized structure: (1) 1.7 ± 0.2 μm and 627 ± 163 nm and (2) 3.2 ± 0.3 μm and 635 ± 127 nm, respectively. To reduce the hydrophobicity in the replicated surfaces, they were coated with phlorotannin (Ph), which is derived from brown algae and has been used as a tissue regenerating material due to its hydrophilicity and various growth factors. Osteoblast-like-cells (MG63) were cultured on various surfaces. The hierarchical structure induced high cell viability compared to that of the smooth surface. Moreover, calcium deposition was enhanced when the roughness of the microsized structures in the hierarchical structure was increased. From the results, we suggest that control of the formation of micro-structure in a hierarchical structure is an important design factor along with the optimal nanostructure.

Biogenic hierarchical TiO₂/SiO₂ derived from rice husk and enhanced photocatalytic properties for dye degradation.

BackgroundRice husk, an agricultural bioresource, is utilized as a non-metallic bio-precursor to synthesize biogenic hierarchical TiO2/SiO2 (BH-TiO2/SiO2) and the products are applied to dye degradation.Methodology/Principal FindingsThe as-prepared BH-TiO2/SiO2 samples are characterized by X-ray diffraction(XRD), X-ray photoelectron spectroscopy(XPS), nitrogen-adsorption measurement, UV-vis spectroscopy and electronic paramagnetic resonance (EPR). The results show that BH-TiO2/SiO2 possesses both anatase and rutile phases with amorphous SiO2 as background, which contains mesopore structure, and nitrogen derived from original rice husk is self-doped into the lattice. Besides, the light-harvesting within the visible-light range of BH-TiO2/SiO2 has been enhanced. Moreover, the catalytic activity of BH-TiO2/SiO2 has been proven by EPR, and both the photocatalytic activity and stability of BH-TiO2/SiO2 are improved as well, which has been illustrated by cycled degradation of methylene blue dye under irradiation.Conclusions/SignificanceThis work provides a good way to combine natural hierarchical porous structure with synthetic material chemistry based on available biomass in the vast natural environment for the sustainable development of human society, and extends potentials of biomass in applications such as photocatalysts, sunlight splitting water and so forth.

Parallel and adaptive surface reconstruction based on implicit PHT-splines

We present a new surface reconstruction framework, which uses the implicit PHT-spline for shape representation and allows us to efficiently reconstruct surface models from very large sets of points. A PHT-spline is a piecewise tri-cubic polynomial over a 3D hierarchical T-mesh, the basis functions of which have good properties such as nonnegativity, compact support and partition of unity. Given a point cloud, an implicit PHT-spline surface is constructed by interpolating the Hermitian information at the basis vertices of the T-mesh, and the Hermitian information is obtained by estimating the geometric quantities on the underlying surface of the point cloud. We take full advantage of the natural hierarchical structure of PHT-splines to reconstruct surfaces adaptively, with simple error-guided local refinements that adapt to the regional geometric details of the target object. Examples show that our approach can produce high quality reconstruction surfaces very efficiently. We also present the multi-threaded algorithm of our approach and show its parallel scalability.

Cytocompatibility of bio‐inspired silicon carbide ceramics

Due to its good mechanical and biochemical properties and, also, because of its unique interconnected porosity, bio-inspired silicon carbide (bioSiC) can be considered as a promising material for biomedical applications, including controlled drug delivery devices and tissue engineering scaffolds. This innovative material is produced by molten-Si infiltration of carbon templates, obtained by controlled pyrolysis of vegetable precursors. The final SiC ceramic presents a porous-interconnected microstructure that mimics the natural hierarchical structure of bone tissue and allows the internal growth of tissue, as well as favors angiogenesis. In the present work, the in vitro cytocompatibility of the bio-inspired SiC ceramics obtained, in this case, from the tree sapelli (Entandrophragma cylindricum) was evaluated. The attachment, spreading, cytoskeleton organization, proliferation, and mineralization of the preosteoblastic cell line MC3T3-E1 were analyzed for up to 28 days of incubation by scanning electron microscopy, interferometric profilometry, confocal laser scanning microscopy, MTT assay, as well as red alizarin staining and quantification. Cells seeded onto these ceramics were able to attach, spread, and proliferate properly with the maintenance of the typical preosteoblastic morphology throughout the time of culture. A certain level of mineralization on the surface of the sapelli-based SiC ceramics is observed. These results demonstrated the cytocompatibility of this porous and hierarchical material.

Air pollution and emergency department visits for suicide attempts in vancouver, Canada.

Background:Comorbidity of depression, heart disease, and migraine has been observed in clinical practice, while ambient air pollution has been identified among different risk factors for these health conditions. Suicide attempts and ideations as the result of depression may be linked to air pollution exposure. Therefore the effects of ambient air pollution on emergency department (ED) visits for suicide attempts were investigated.Methods:Emergency visit data were collected in a hospital in Vancouver, Canada. The generalized linear mixed models technique was applied in the analysis of these data. A natural hierarchical structure of the data was used to define the clusters, with days nested in a 3-level structure (day of week, month, year). Poisson models were fitted to the clustered counts of ED visits with a single air pollutant, temperature and relative humidity. In addition, the case-crossover methodology was used with the same data for comparison. The analysis was performed by gender (all, males, females) and month (all: January–December, warm: April–September, cold: October–March).Results:Both hierarchical and case-crossover methods confirmed positive and statistically significant associations among carbon monoxide (CO), nitrogen dioxide (NO2), sulphur dioxide (SO2), and particulate matter (PM10) for all suicide attempts in the cold period. The largest increase was observed for males in the cold period for a 1-day lagged exposure to NO2, with an excess risk of 23.9% (95% CI: 7.8, 42.4) and odds ratio of 1.21 (95% CI: 1.03, 1.41). In warm months the associations were not statistically significant, and the highest positive value was obtained for ozone lagged by 1 day.Conclusion:The results indicate a potential association between air pollution and emergency department visits for suicide attempts.

Sewage flow optimization algorithm for large-scale urban sewer networks based on network community division

By considering the flow control of urban sewer networks to minimize the electricity consumption of pumping stations, a decomposition-coordination strategy for energy savings based on network community division is developed in this paper. A mathematical model characterizing the steady-state flow of urban sewer networks is first constructed, consisting of a set of algebraic equations with the structure transportation capacities captured as constraints. Since the sewer networks have no apparent natural hierarchical structure in general, it is very difficult to identify the clustered groups. A fast network division approach through calculating the betweenness of each edge is successfully applied to identify the groups and a sewer network with arbitrary configuration could be then decomposed into subnetworks. By integrating the coupling constraints of the subnetworks, the original problem is separated into N optimization subproblems in accordance with the network decomposition. Each subproblem is solved locally and the solutions to the subproblems are coordinated to form an appropriate global solution. Finally, an application to a specified large-scale sewer network is also investigated to demonstrate the validity of the proposed algorithm.

Allometric scaling laws in biology and physics

Hierarchical structures always have similar scaling laws both in biology and physics, and the scaling exponent plays an import role in sighting into the physiological properties or physical properties of the studied problems. E-infinity theory is emphasized and is predicted to be the most promising theory for natural hierarchical structures.

Structured variable selection in support vector machines

When applying the support vector machine (SVM) to high-dimensional classification problems, we often impose a sparse structure in the SVM to eliminate the influences of the irrelevant predictors. The lasso and other variable selection techniques have been successfully used in the SVM to perform automatic variable selection. In some problems, there is a natural hierarchical structure among the variables. Thus, in order to have an interpretable SVM classifier, it is important to respect the heredity principle when enforcing the sparsity in the SVM. Many variable selection methods, however, do not respect the heredity principle. In this paper we enforce both sparsity and the heredity principle in the SVM by using the so-called structured variable selection (SVS) framework originally proposed in [20]. We minimize the empirical hinge loss under a set of linear inequality constraints and a lasso-type penalty. The solution always obeys the desired heredity principle and enjoys sparsity. The new SVM classifier can be efficiently fitted, because the optimization problem is a linear program. Another contribution of this work is to present a nonparametric extension of the SVS framework, and we propose nonparametric heredity SVMs. Simulated and real data are used to illustrate the merits of the proposed method.

Approximation Capabilities of Hierarchical Fuzzy Systems

Derived from practical application in location analysis and pricing, and based on the approach of hierarchical structure analysis of continuous functions, this paper investigates the approximation capabilities of hierarchical fuzzy systems. By first introducing the concept of the natural hierarchical structure, it is proved that continuous functions with natural hierarchical structure can be naturally and effectively approximated by hierarchical fuzzy systems to overcome the curse of dimensionality in both the number of rules and parameters. Then, based on Kolmogorov's theorem, it is shown that any continuous function can be represented as a superposition of functions with the natural hierarchical structure and can then be approximated by hierarchical fuzzy systems to achieve the universal approximation property. Further, the conditions under which the hierarchical fuzzy approximation is superior to the standard fuzzy approximation in overcoming the curse of dimensionality are analyzed

Sampling from Archimedean copulas

We develop sampling algorithms for multivariate Archimedean copulas. For exchangeable copulas, where there is only one generating function, we first analyse the distribution of the copula itself, deriving a number of integral representations and a generating function representation. One of the integral representations is related, by a form of convolution, to the distribution whose Laplace transform yields the copula generating function. In the infinite-dimensional limit there is a direct connection between the distribution of the copula value and the inverse Laplace transform. Armed with these results, we present three sampling algorithms, all of which entail drawing from a one-dimensional distribution and then scaling the result to create random deviates distributed according to the copula. We implement and compare the various methods. For more general cases, in which an N-dimensional Archimedean copula is given by N−1 nested generating functions, we present algorithms in which each new variate is drawn conditional only on the value of the copula of the previously drawn variates. We also discuss the use of composite nested and exchangeable copulas for modelling random variates with a natural hierarchical structure, such as ratings and sectors for obligors in credit baskets.

Choice of units of analysis and modeling strategies in multilevel hierarchical models

Hierarchical models are common in complex surveys, psychometric applications, as well as agricultural and biomedical applications, to name but a few. The context of interest here is meta-analysis, with emphasis on the use of such an approach in the evaluation of surrogate endpoints in randomized clinical trials. The methodology rests on the ability to replicate the effect of treatment on both the true endpoint, as well as the candidate surrogate endpoint, across a number of trials. However, while a meta-analysis of clinical trials in the same indication seems the natural hierarchical structure, some authors have considered center or country as the unit, either because no meta-analytic data were available or because, even when available, they might not allow for a sufficient level of replication. This leaves us with two important, related questions. First, how sensible is it to replace one level of replication by another one? Second, what are the consequences when a truly three- or higher-level model (e.g., trial, center, patient) is replaced by a coarser two-level structure (either trial and patient or center and patient). The same or similar questions may occur in a number of different settings, as soon as interest is placed on the validity of a conclusion at a certain level of the hierarchy, such as in sociological or genetic studies. Using the framework of normally distributed endpoints, these questions will be studied, using both analytic calculation as well as Monte Carlo simulation.

Efficient particle filtering for jump markov systems. Application to time-varying autoregressions

We present an efficient particle filtering method to perform optimal estimation in jump Markov (nonlinear) systems (JMSs). Such processes consist of a mixture of heterogeneous models and possess a natural hierarchical structure. We take advantage of these specificities in order to develop a generic filtering methodology for these models. The method relies on an original and nontrivial combination of techniques that have been presented recently in the filtering literature, namely, the auxiliary particle filter and the unscented transform. This algorithm is applied to the complex problem of time-varying autoregressive estimation with an unknown time-varying model order. More precisely, we develop an attractive and original probabilistic model that relies on a flexible pole representation that easily lends itself to interpretations. We show that this problem can be formulated as a JMS and that the associated filtering problem can be efficiently addressed using the generic methodology developed in this paper. Simulations demonstrate the performance of our method compared to standard particle filtering techniques.

A novel cache distribution heuristic algorithm for a mesh of caches and its performance evaluation

The widespread use of the Internet has created two problems: document retrieval latency and network traffic. Caching of documents ‘close’ to users has helped alleviate both problems. Different caching policies have been proposed/implemented to make best use of limited available cache at each caching server. A mesh of caching servers, aided by different data diffusion algorithms and the natural hierarchical structure of the Internet topology, has increased ‘virtual’ size of cache. Yet the size of available cache is small compared to the total size of all documents served, and remains a major resource constraint. In this work, we looked at how to improve document download time, by distributing a fixed amount of total storage in a network or mesh of caches. The intuition behind our cache distribution approach is to give more storage to the caching nodes in the network, which experience more traffic, in the hope that this will reduce the average latency of document retrieval in the network. A heuristic was developed to estimate traffic at each cache of a network. From this traffic estimation, each cache then receives a corresponding percentage of the total storage capacity of the network. Through extensive simulation it is found that the proposed cache distribution algorithm can reduce latency up to 80% over prior work that includes both Harvest-type and demand-driven data diffusion algorithms. Furthermore, the best improvement was achieved in a cache range that corresponds to practical, real world cache ranges.

Information geometry on hierarchy of probability distributions

An exponential family or mixture family of probability distributions has a natural hierarchical structure. This paper gives an "orthogonal" decomposition of such a system based on information geometry. A typical example is the decomposition of stochastic dependency among a number of random variables. In general, they have a complex structure of dependencies. Pairwise dependency is easily represented by correlation, but it is more difficult to measure effects of pure triplewise or higher order interactions (dependencies) among these variables. Stochastic dependency is decomposed quantitatively into an "orthogonal" sum of pairwise, triplewise, and further higher order dependencies. This gives a new invariant decomposition of joint entropy. This problem is important for extracting intrinsic interactions in firing patterns of an ensemble of neurons and for estimating its functional connections. The orthogonal decomposition is given in a wide class of hierarchical structures including both exponential and mixture families. As an example, we decompose the dependency in a higher order Markov chain into a sum of those in various lower order Markov chains.