Messing up to clean up: Semi-randomized frequency selective space-filling curves to suppress physiological signal fluctuations in MRI.

PURPOSE: Rapid 3D steady-state sequences are widely used but are also known to be sensitive to semi-periodic physiological signal fluctuations due to, for example, cardiac pulsation, breathing, and eye/eyelids movement. This semi-periodicity results in repeating artifacts in the image whose intensity depends on the scan parameters. The purpose of this study is to design a reordering of the 2D phase encodes (within the 3D acquisition) that reduces these artifacts. METHODS: A randomized order of the phase encodes can suppress repeating artifact but may also introduce its own apparent noise, for example, in cases of slow subject movement or gradual changes in eddy currents. In a new design a semi-randomized space-filling curve is generated by scrambling the local order of the phase encodes to achieve a controlled frequency selective effect, that is, eliminating artifacts above a chosen (fluctuation) frequency threshold while leaving lower frequencies untouched, thus overcoming the limitations of a randomized order. The method was characterized in simulations and substantiated by human brain imaging at 7 T using two steady-state gradient echo variants that suffer from pulsation, either near blood vessels or near the ventricles. RESULTS: The simulations with a point source show that the maximum artifact intensity can be reduced by factors of 10-50 depending on the scan parameters. In human scanning, the new approach drastically reduced physiologically induced artifacts and was superior in this regard to both full randomization and a generalized Hilbert curve, another semi-randomized approach. CONCLUSION: The phase-encodes reordering presented here effectively removes artifacts arising from local fluctuations.

A New Transformation Technique for Reducing Information Entropy: A Case Study on Greyscale Raster Images.

This paper proposes a new string transformation technique called Move with Interleaving (MwI). Four possible ways of rearranging 2D raster images into 1D sequences of values are applied, including scan-line, left-right, strip-based, and Hilbert arrangements. Experiments on 32 benchmark greyscale raster images of various resolutions demonstrated that the proposed transformation reduces information entropy to a similar extent as the combination of the Burrows-Wheeler transform followed by the Move-To-Front or the Inversion Frequencies. The proposed transformation MwI yields the best result among all the considered transformations when the Hilbert arrangement is applied.

Radial sequences and compressed sensing in pediatric body magnetic resonance imaging.

Magnetic resonance imaging (MRI) is often an ideal imaging modality for children of any age for any anatomy and for many pathologies. MRI sequences can be prescribed to produce high-resolution images of anatomical structures, characterize tissue composition, and detect physiological states and organ function. Shortening imaging sequences in any manner possible has been a topic of research and development in MRI since its emergence. Selection of imaging sequence parameters influences more than just the appearance and signal qualities of the imaged tissues; these details along with spatial encoding and data readout steps determine the time it takes to acquire an image. As each piece of image data is acquired and encoded with spatial and temporal information it is stored in k-space. As k-space is filled, either completely or partially, a diagnostic image or physiological data can be reconstructed. Shortening the length of time required for the readout step by efficiently filling k-space using compressed sensing and radial techniques is the subject of this manuscript.

A Fast kNN Algorithm Using Multiple Space-Filling Curves.

The paper considers a time-efficient implementation of the k nearest neighbours (kNN) algorithm. A well-known approach for accelerating the kNN algorithm is to utilise dimensionality reduction methods based on the use of space-filling curves. In this paper, we take this approach further and propose an algorithm that employs multiple space-filling curves and is faster (with comparable quality) compared with the kNN algorithm, which uses kd-trees to determine the nearest neighbours. A specific method for constructing multiple Peano curves is outlined, and statements are given about the preservation of object proximity information in the course of dimensionality reduction. An experimental comparison with known kNN implementations using kd-trees was performed using test and real-life data.

Space-Filling Curve Resistor on Ultra-Thin Polyetherimide Foil for Strain Impervious Temperature Sensing.

Monitoring process parameters in the manufacture of composite structures is key to ensuring product quality and safety. Ideally, this can be done by sensors that are embedded during production and can remain as devices to monitor structural health. Extremely thin foil-based sensors weaken the finished workpiece very little. Under ideal conditions, the foil substrate bonds with the resin in the autoclaving process, as is the case when polyetherimide is used. Here, we present a temperature sensor as part of an 8 µm thick multi-sensor node foil for monitoring processing conditions during the production and structural health during the lifetime of a construction. A metallic thin film conductor was shaped in the form of a space-filling curve to suppress the influences of resistance changes due to strain, which could otherwise interfere with the measurement of the temperature. FEM simulations as well as experiments confirm that this type of sensor is completely insensitive to the direction of strain and sufficiently insensitive to the amount of strain, so that mechanical strains that can occur in the composite curing process practically do not interfere with the temperature measurement. The temperature sensor is combined with a capacitive sensor for curing monitoring based on impedance measurement and a half-bridge strain gauge sensor element. All three types are made of the same materials and are manufactured together in one process flow. This is the key to cost-effective distributed sensor arrays that can be embedded during production and remain in the workpiece, thus ensuring not only the quality of the initial product but also the operational reliability during the service life of light-weight composite constructions.

Dendritic space-filling requires a neuronal type-specific extracellular permissive signal in Drosophila.

Neurons sometimes completely fill available space in their receptive fields with evenly spaced dendrites to uniformly sample sensory or synaptic information. The mechanisms that enable neurons to sense and innervate all space in their target tissues are poorly understood. Using Drosophila somatosensory neurons as a model, we show that heparan sulfate proteoglycans (HSPGs) Dally and Syndecan on the surface of epidermal cells act as local permissive signals for the dendritic growth and maintenance of space-filling nociceptive C4da neurons, allowing them to innervate the entire skin. Using long-term time-lapse imaging with intact Drosophila larvae, we found that dendrites grow into HSPG-deficient areas but fail to stay there. HSPGs are necessary to stabilize microtubules in newly formed high-order dendrites. In contrast to C4da neurons, non-space-filling sensory neurons that develop in the same microenvironment do not rely on HSPGs for their dendritic growth. Furthermore, HSPGs do not act by transporting extracellular diffusible ligands or require leukocyte antigen-related (Lar), a receptor protein tyrosine phosphatase (RPTP) and the only known Drosophila HSPG receptor, for promoting dendritic growth of space-filling neurons. Interestingly, another RPTP, Ptp69D, promotes dendritic growth of C4da neurons in parallel to HSPGs. Together, our data reveal an HSPG-dependent pathway that specifically allows dendrites of space-filling neurons to innervate all target tissues in Drosophila.

A Method of HBase Multi-Conditional Query for Ubiquitous Sensing Applications.

Big data gathered from real systems, such as public infrastructure, healthcare, smart homes, industries, and so on, by sensor networks contain enormous value, and need to be mined deeply, which depends on a data storing and retrieving service. HBase is playing an increasingly important part in the big data environment since it provides a flexible pattern for storing extremely large amounts of unstructured data. Despite the fast-speed reading by RowKey, HBase does not natively support multi-conditional query, which is a common demand and operation in relational databases, especially for data analysis of ubiquitous sensing applications. In this paper, we introduce a method to construct a linear index by employing a Hilbert space-filling curve. As a RowKey generating schema, the proposed method maps multiple index-columns into a one-dimensional encoded sequence, and then constructs a new RowKey. We also provide a R-tree-based optimization to reduce the computational cost of encoding query conditions. Without using a secondary index mode, experimental results indicate that the proposed method has better performance in multi-conditional queries.

Adjustable Trajectory Design Based on Node Density for Mobile Sink in WSNs.

The design of movement trajectories for mobile sink plays an important role in data gathering for Wireless Sensor Networks (WSNs), as it affects the network coverage, and packet delivery ratio, as well as the network lifetime. In some scenarios, the whole network can be divided into subareas where the nodes are randomly deployed. The node densities of these subareas are quite different, which may result in a decreased packet delivery ratio and network lifetime if the movement trajectory of the mobile sink cannot adapt to these differences. To address these problems, we propose an adjustable trajectory design method based on node density for mobile sink in WSNs. The movement trajectory of the mobile sink in each subarea follows the Hilbert space-filling curve. Firstly, the trajectory is constructed based on network size. Secondly, the adjustable trajectory is established based on node density in specific subareas. Finally, the trajectories in each subarea are combined to acquire the whole network's movement trajectory for the mobile sink. In addition, an adaptable power control scheme is designed to adjust nodes' transmitting range dynamically according to the movement trajectory of the mobile sink in each subarea. The simulation results demonstrate that the proposed trajectories can adapt to network changes flexibly, thus outperform both in packet delivery ratio and in energy consumption the trajectories designed only based on the network size and the whole network node density.

Transparent metallic fractal electrodes for semiconductor devices.

Nanostructured metallic films have the potential to replace metal oxide films as transparent electrodes in optoelectronic devices. An ideal transparent electrode should possess a high, broadband, and polarization-independent transmittance. Conventional metallic gratings and grids with wavelength-scale periodicities, however, do not have all of these qualities. Furthermore, the transmission properties of a nanostructured electrode need to be assessed in the actual dielectric environment provided by a device, where a high-index semiconductor layer can reflect a substantial fraction of the incident light. Here we propose nanostructured aluminum electrodes with space-filling fractal geometries as alternatives to gratings and grids and experimentally demonstrate their superior optoelectronic performance through integration with Si photodetectors. As shown by polarization and spectrally resolved photocurrent measurements, devices with fractal electrodes exhibit both a broadband transmission and a flat polarization response that outperforms both square grids and linear gratings. Finally, we show the benefits of adding a thin silicon nitride film to the nanostructured electrodes to further reduce reflection.

Disproportional fraction of inactive components leads to the variation in metabolic scaling.

In biological systems, solitary organisms or eusocial groups, the metabolic rate often scales allometrically with systems' size, when they are inactive, and the scaling becomes nearly isometric when the systems are active. Here I propose a hypothesis attempting to offer a departing point for a general joint understanding of the difference in the scaling powers between inactive and active states. When the system is inactive, there exist inactive components, which consume less energy than the active ones, and the larger the system is, the larger the fraction of the inactive components, which leads to sublinear scaling. When the system is active, most inactive components are activated, which leads to nearly isometric scaling. I hypothesize that the disproportional fraction of the inactive components is caused by the diffusants screening in the complex transportation network. I.e., when metabolites or information diffuses in the system, due to the physical limitation of the network structure and the diffusant's physical feature, not all the components can equally receive the diffusants so that these components are inactive. Using the mammalian pulmonary system, ant colonies, and other few systems as examples, I discuss how the screening leads to the allometric and isometric metabolic scaling powers in inactive and active states respectively. It is noteworthy that there are a few exceptions, in which the metabolic rate of the system has an isometric scaling relationship with size at rest. I show that these exceptions not only do not disapprove the hypothesis, but actually support it.

Applying Convolutional Neural Networks to data on unstructured meshes with space-filling curves.

This paper presents the first classical Convolutional Neural Network (CNN) that can be applied directly to data from unstructured finite element meshes or control volume grids. CNNs have been hugely influential in the areas of image classification and image compression, both of which typically deal with data on structured grids. Unstructured meshes are frequently used to solve partial differential equations and are particularly suitable for problems that require the mesh to conform to complex geometries or for problems that require variable mesh resolution. Central to our approach are space-filling curves, which traverse the nodes or cells of a mesh tracing out a path that is as short as possible (in terms of numbers of edges) and that visits each node or cell exactly once. The space-filling curves (SFCs) are used to find an ordering of the nodes or cells that can transform multi-dimensional solutions on unstructured meshes into a one-dimensional (1D) representation, to which 1D convolutional layers can then be applied. Although developed in two dimensions, the approach is applicable to higher dimensional problems. To demonstrate the approach, the network we choose is a convolutional autoencoder (CAE), although other types of CNN could be used. The approach is tested by applying CAEs to data sets that have been reordered with a space-filling curve. Sparse layers are used at the input and output of the autoencoder, and the use of multiple SFCs is explored. We compare the accuracy of the SFC-based CAE with that of a classical CAE applied to two idealised problems on structured meshes, and then apply the approach to solutions of flow past a cylinder obtained using the finite-element method and an unstructured mesh.

Diversity-enhanced canopy space occupation and leaf functional diversity jointly promote overyielding in tropical tree communities.

Understanding the mechanisms that drive biodiversity-productivity relationships is critical for guiding forest restoration. Although complementarity among trees in the canopy space has been suggested as a key mechanism for greater productivity in mixed-species tree communities, empirical evidence remains limited. Here, we used data from a tropical tree diversity experiment to disentangle the effects of tree species richness and community functional characteristics (community-weighted mean and functional diversity of leaf traits) on canopy space filling, and how these effects are related to overyielding. We found that canopy space filling was largely explained by species identity effects rather than tree diversity effects. Communities with a high abundance of species with a conservative resource-use strategy were those with most densely packed canopies. Across monocultures and mixtures, a higher canopy space filling translated into an enhanced wood productivity. Importantly, most communities (83 %) produced more wood volume than the average of their constituent species in monoculture (i.e. most communities overyielded). Our results show that overyielding increased with leaf functional diversity and positive net biodiversity effects on canopy space filling, which mainly arose due to a high taxonomic diversity. These findings suggest that both taxonomic diversity-enhanced canopy space filling and canopy leaf diversity are important drivers for overyielding in mixed-species forests. Consequently, restoration initiatives should promote stands with functionally diverse canopies by selecting tree species with large interspecific differences in leaf nutrition, as well as leaf and branch morphology to optimize carbon capture in young forest stands.

Space filling of ß-cyclodextrin and ß-cyclodextrin derivatives by volatile hydrophobic guests.

The inclusion of volatile derivatives of benzene and cyclohexane in ß-cyclodextrin (ß-CD), hydroxypropyl-ß-CD, and hydrophilic ß-CD-thioethers was investigated by static headspace gas chromatography (HS-GC) and molecular modelling. The obtained binding constants strongly increase with the amount of space filling of the CD cavity and the salt concentration. ß-CD thioethers show a 3-10 times higher binding potential than native ß-CD.

Efficient entry point encoding and decoding algorithms on 2D Hilbert space filling curve.

The Hilbert curve is an important method for mapping high-dimensional spatial information into one-dimensional spatial information while preserving the locality in the high-dimensional space. Entry points of a Hilbert curve can be used for image compression, dimensionality reduction, corrupted image detection and many other applications. As far as we know, there is no specific algorithms developed for entry points. To address this issue, in this paper we present an efficient entry point encoding algorithm (EP-HE) and a corresponding decoding algorithm (EP-HD). These two algorithms are efficient by exploiting the m consecutive 0s in the rear part of an entry point. We further found that the outputs of these two algorithms are a certain multiple of a certain bit of s, where s is the starting state of these m levels. Therefore, the results of these m levels can be directly calculated without iteratively encoding and decoding. The experimental results show that these two algorithms outperform their counterparts in terms of processing entry points.

Investigation of Structural Energy Absorption Performance in 3D-Printed Polymer (Tough 1500 Resin) Materials with Novel Multilayer Thin-Walled Sandwich Structures Inspired by Peano Space-Filling Curves.

Inspired by Peano space-filling curves (PSCs), this study introduced the space-filling structure design concept to novel thin-walled sandwich structures and fabricated polymer samples by 3D printing technology. The crushing behaviors and energy absorption performance of the PSC multilayer thin-walled sandwich structures and the traditional serpentine space-filling curve (SSC) multilayer thin-walled sandwich structures were investigated using quasi-static compression experiments and numerical analysis. Taking the initial peak crushing force (IPF), specific energy absorption (SEA), and crushing force efficiency (CFE) as evaluation criteria, the effects of geometric parameters, including the curve order, layer height, septa thickness, and wall thickness, on energy absorption performance were comprehensively examined. The results indicated that the energy absorption capacity of the PSC structure was significantly enhanced due to its complex hierarchy. Specifically, the second-order PSC structure demonstrated a 53.2% increase in energy absorption compared to the second-order SSC structure, while the third-order PSC structure showed more than a six-fold increase in energy absorption compared to the third-order SSC structure. Furthermore, a multi-objective optimization method based on the response surface method and the NSGA-II algorithm were employed to optimize the wall thickness and layer height of the proposed novel PSC structures. The optimal solutions suggested that a reasonable wall thickness and layer height were two important factors for designing PSC structures with better energy absorption performance. The findings of this study provide an effective guide for using the space-filling concept with Peano curves for the design of a novel polymer thin-walled energy absorber with high energy absorption efficiency.

Smoothing splines approximation using Hilbert curve basis selection.

Smoothing splines have been used pervasively in nonparametric regressions. However, the computational burden of smoothing splines is significant when the sample size n is large. When the number of predictors d ≥ 2 , the computational cost for smoothing splines is at the order of O(n 3) using the standard approach. Many methods have been developed to approximate smoothing spline estimators by using q basis functions instead of n ones, resulting in a computational cost of the order O(nq 2). These methods are called the basis selection methods. Despite algorithmic benefits, most of the basis selection methods require the assumption that the sample is uniformly-distributed on a hyper-cube. These methods may have deteriorating performance when such an assumption is not met. To overcome the obstacle, we develop an efficient algorithm that is adaptive to the unknown probability density function of the predictors. Theoretically, we show the proposed estimator has the same convergence rate as the full-basis estimator when q is roughly at the order of O[n 2d/{(pr+1)(d +2)}] , where p ∈[1, 2] and r ≈ 4 are some constants depend on the type of the spline. Numerical studies on various synthetic datasets demonstrate the superior performance of the proposed estimator in comparison with mainstream competitors.

The Euler characteristic as a basis for teaching topology concepts to crystallographers.

The simple Euler polyhedral formula, expressed as an alternating count of the bounding faces, edges and vertices of any polyhedron, V - E + F = 2, is a fundamental concept in several branches of mathematics. Obviously, it is important in geometry, but it is also well known in topology, where a similar telescoping sum is known as the Euler characteristic χ of any finite space. The value of χ can also be computed for the unit polyhedra (such as the unit cell, the asymmetric unit or Dirichlet domain) which build, in a symmetric fashion, the infinite crystal lattices in all space groups. In this application χ has a modified form (χm) and value because the addends have to be weighted according to their symmetry. Although derived in geometry (in fact in crystallography), χm has an elegant topological interpretation through the concept of orbifolds. Alternatively, χm can be illustrated using the theorems of Harriot and Descartes, which predate the discovery made by Euler. Those historical theorems, which focus on angular defects of polyhedra, are beautifully expressed in the formula of de Gua de Malves. In a still more general interpretation, the theorem of Gauss-Bonnet links the Euler characteristic with the general curvature of any closed space. This article presents an overview of these interesting aspects of mathematics with Euler's formula as the leitmotif. Finally, a game is designed, allowing readers to absorb the concept of the Euler characteristic in an entertaining way.

A topological proof of the modified Euler characteristic based on the orbifold concept.

The notion of the Euler characteristic of a polyhedron or tessellation has been the subject of in-depth investigations by many authors. Two previous papers worked to explain the phenomenon of the vanishing (or zeroing) of the modified Euler characteristic of a polyhedron that underlies a periodic tessellation of a space under a crystallographic space group. The present paper formally expresses this phenomenon as a theorem about the vanishing of the Euler characteristic of certain topological spaces called topological orbifolds. In this new approach, it is explained that the theorem in question follows from the fundamental properties of the orbifold Euler characteristic. As a side effect of these considerations, a theorem due to Coxeter about the vanishing Euler characteristic of a honeycomb tessellation is re-proved in a context which frees the calculations from the assumptions made by Coxeter in his proof. The abstract mathematical concepts are visualized with down-to-earth examples motivated by concrete situations illustrating wallpaper and 3D crystallographic space groups. In a way analogous to the application of the classic Euler equation to completely bounded solids, the formula proven in this paper is applicable to such important crystallographic objects as asymmetric units and Dirichlet domains.

Design of Experiments for Matrix-Assisted Laser Desorption/Ionization of Amphiphilic Poly(Ethylene Oxide)-b-Polystyrene Block Copolymers.

Matrix-assisted laser/desorption ionization (MALDI) has become a very popular ionization technique for mass spectrometry of synthetic polymers because it allows high throughput analysis of low amounts of sample while avoiding the complexity introduced by extensive multiple charging of electrospray ionization. Yet, fundamental mechanisms underlying this ionization process are not fully understood, so development of sample preparation methods remains empirical. Reliable prediction for the optimal matrix/analyte/salt system is indeed still not possible for homopolymers and it becomes even more challenging in the case of amphiphilic block copolymers where conditions dictated by one block are not compatible with MALDI requirements of the second block. In order to perform MALDI of copolymers composed of poly (ethylene oxide) (PEO) and polystyrene (PS) blocks, it was postulated here that experimental conditions suitable for both species would also be successful for PEO-b-PS. Accordingly, designs of experiments based on Quantitative Structure Activity Relationship (QSAR) analysis were first implemented, studying the influence of 19 matrices and 26 salts on the laser fluence requested for successful MALDI. This analysis first permitted to highlight correlations between the investigated 10 descriptors of matrices and salts and the analytical response, and then to construct models that permits reliable predictions of matrix/salt couples to be used for one or the other homopolymer. Selected couples were then used for MALDI of a PEO-b-PS copolymer but no general trend was observed: experimental conditions expected to work often failed whereas ionic adducts of the copolymer were clearly detected with some matrix/salt systems that were shown to badly perform for constituting homopolymers. Overall, this rules out the working assumption stating that the MALDI behavior of chains composed of PEO and PS segments should combine the behavior of the two polymeric species. Yet, although requiring a dedicated design of experiments, MALDI of the amphiphilic PEO-b-PS copolymer was achieved for the first time.

Arithmetic proof of the multiplicity-weighted Euler characteristic for symmetrically arranged space-filling polyhedra.

The puzzling observation that the famous Euler's formula for three-dimensional polyhedra V - E + F = 2 or Euler characteristic χ = V - E + F - I = 1 (where V, E, F are the numbers of the bounding vertices, edges and faces, respectively, and I = 1 counts the single solid itself) when applied to space-filling solids, such as crystallographic asymmetric units or Dirichlet domains, are modified in such a way that they sum up to a value one unit smaller (i.e. to 1 or 0, respectively) is herewith given general validity. The proof provided in this paper for the modified Euler characteristic, χm = Vm - Em + Fm - Im = 0, is divided into two parts. First, it is demonstrated for translational lattices by using a simple argument based on parity groups of integer-indexed elements of the lattice. Next, Whitehead's theorem, about the invariance of the Euler characteristic, is used to extend the argument from the unit cell to its asymmetric unit components.