Shape-preserving Transformations Research Articles

Shape-Preserving Transformation of Electrodeposited Macroporous Microparticles for Single-Particle SERS Applications

Microparticles composed of bicontinuous and ordered macropores are important in many applications. However, rational integration of ordered macropores into a single crystalline microparticle remains a challenge. Here, we report a method to prepare three-dimensionally ordered macroporous (3DOM) Ag7O8NO3 micropyramids via selectively cementing the colloidal crystal templates via an electrochemical method and their shape-preserving transformation into 3DOM Ag micropryamids formed by Ag nanoparticles via a chemical reduction process. The interconnected macropores facilitated the transportation and enrichment of the analyte molecules into the 3DOM Ag micropyramids. The dense Ag nanoparticles on the skeletons of the 3DOM Ag micropyramids provided strong electromagnetic fields. Taken together, a 3DOM Ag micropyramid as a kind of single-particle surface-enhanced Raman scattering (SERS) sensing substrate demonstrated high SERS sensitivity and outstanding SERS signal reproducibility. We explored the application of 3DOM Ag micropyramids in SERS detection of biomolecules (e.g., adenosine, adenine, hemoglobin bovine, and lysozyme) and proved their potentials in distinguishing exosomes from tumor and non-tumor cells. The method can be extended to prepared 3DOM structures of other materials with promising applications in sensing, separation, and catalytic fields.

Nonlinear Mixed Convective Bidirectional Dynamics of Double Stratified Radiative Oldroyd-B Nanofluid Flow with Heat Source/Sink and Higher-Order Chemical Reaction

Little is known in the literature about the concept of nonuniform heat source/sink and higher-order chemical reaction for the dynamics of Oldroyd-B nanoparticles. Therefore, the present article addresses the nonuniform heat source/sink and higher-order chemical reaction features in nonlinear mixed convection bidirectional MHD dynamics of Oldroyd-B nanoparticles with thermal radiation aspects through porous space. Stratification effects for both the temperature and concentration setups are also used in the mathematical model with the significance of random movement and thermodiffusion of nanoparticles. Shape-preserving transformations have been employed to convert the transport equations into solvable forms. An innovative analytical tactic, namely, homotopy analysis method, has been adopted to find the solution of the modeled problem. Behaviors of pertinent parameters on thermal and concentration profiles have been discussed through various graphs. Inspection of heat/mass transport against appropriate varieties of pertinent parameters has been made and explained physically. Thermal profile is augmented with the higher estimations of space and temperature-dependent heat source/sink links. Concentration profile is diminished with the augmentation of higher-order chemical reaction parameter. Sherwood number is improved with the estimation of 0 ≤ β t ≤ 100 and is reduced with the growth of 0 ≤ β c ≤ 100 . Nusselt number is declined with the upgraded amounts of 0 ≤ N b ≤ 3 and 0 ≤ N t ≤ 5 .

Modality-Constrained Density Estimation via Deformable Templates

Estimation of a probability density function (pdf) from its samples, while satisfying certain shape constraints, is an important problem that lacks coverage in the literature. This article introduces a novel geometric, deformable template constrained density estimator (dtcode) for estimating pdfs constrained to have a given number of modes. Our approach explores the space of thus-constrained pdfs using the set of shape-preserving transformations: an arbitrary template from the given shape class is transformed via a shape-preserving transformation to obtain the final optimal estimate. The search for this optimal transformation, under the maximum-likelihood criterion, is performed by mapping transformations to the tangent space of a Hilbert sphere, where they are effectively linearized, and can be expressed using an orthogonal basis. This framework is first applied to (univariate) unconditional densities and then extended to conditional densities. We provide asymptotic convergence rates for dtcode, and an application of the framework to the speed distributions for different traffic flows on Californian highways.

Shape-preserving amorphous-to-crystalline transformation of CaCO3 revealed by in situ TEM

Organisms use inorganic ions and macromolecules to regulate crystallization from amorphous precursors, endowing natural biominerals with complex morphologies and enhanced properties. The mechanisms by which modifiers enable these shape-preserving transformations are poorly understood. We used in situ liquid-phase transmission electron microscopy to follow the evolution from amorphous calcium carbonate to calcite in the presence of additives. A combination of contrast analysis and infrared spectroscopy shows that Mg ions, which are widely present in seawater and biological fluids, alter the transformation pathway in a concentration-dependent manner. The ions bring excess (structural) water into the amorphous bulk so that a direct transformation is triggered by dehydration in the absence of morphological changes. Molecular dynamics simulations suggest Mg-incorporated water induces structural fluctuations, allowing transformation without the need to nucleate a separate crystal. Thus, the obtained calcite retains the original morphology of the amorphous state, biomimetically achieving the morphological control of crystals seen in biominerals.

Elastic Statistical Shape Analysis of Biological Structures with Case Studies: A Tutorial.

We describe a recent framework for statistical shape analysis of curves and show its applicability to various biological datasets. The presented methods are based on a functional representation of shape called the square-root velocity function and a closely related elastic metric. The main benefit of this approach is its invariance to reparameterization (in addition to the standard shape-preserving transformations of translation, rotation and scale), and ability to compute optimal registrations (point correspondences) across objects. Building upon the defined distance between shapes, we additionally describe tools for computing sample statistics including the mean and covariance. Based on the covariance structure, one can also explore variability in shape samples via principal component analysis. Finally, the estimated mean and covariance can be used to define Wrapped Gaussian models on the shape space, which are easy to sample from. We present multiple case studies on various biological datasets including (1) leaf outlines, (2) internal carotid arteries, (3) Diffusion Tensor Magnetic Resonance Imaging fiber tracts, (4) Glioblastoma Multiforme tumors, and (5) vertebrae in mice. We additionally provide a MATLAB package that can be used to produce the results given in this manuscript.

Shape-preserving transformation of carbonate minerals into lead halide perovskite semiconductors based on ion exchange/insertion reactions.

Biological and bio-inspired mineralization processes yield a variety of three-dimensional structures with relevance for fields such as photonics, electronics and photovoltaics. However, these processes are only compatible with specific material compositions, often carbonate salts, thereby hampering widespread applications. Here we present a strategy to convert a wide range of metal carbonate structures into lead halide perovskite semiconductors with tunable bandgaps, while preserving the 3D shape. First, we introduce lead ions by cation exchange. Second, we use carbonate as a leaving group, facilitating anion exchange with halide, which is followed rapidly by methylammonium insertion to form the perovskite. As proof of principle, pre-programmed carbonate salt shapes such as vases, coral-like forms and helices are transformed into perovskites while preserving the morphology and crystallinity of the initial micro-architectures. This approach also readily converts calcium carbonate biominerals into semiconductors, furnishing biological and programmable synthetic shapes with the performance of artificial compositions such as perovskite-based semiconductors.

Elastic Shape Analysis of Three-Dimensional Objects

Abstract Statistical analysis of shapes of 3D objects is an important problem with a wide range of applications. This analysis is difficult for many reasons, including the fact that objects differ in both geometry and topology. In this manuscript, we narrow the problem by focusing on objects with fixed topology, say objects that are diffeomorphic to unit spheres, and develop tools for analyzing their geometries. The main challenges in this problem are to register points across objects and to perform analysis while being invariant to certain shape-preserving transformations. We develop a comprehensive framework for analyzing shapes of spherical objects, i.e., objects that are embeddings of a unit sphere in ℝ, including tools for: quantifying shape differences, optimally deforming shapes into each other, summarizing shape samples, extracting principal modes of shape variability, and modeling shape variability associated with populations. An important strength of this framework is that it is elastic: it perf...

Synthetic fossilization of soft biological tissues and their shape-preserving transformation into silica or electron-conductive replicas.

Structural preservation of complex biological systems from the subcellular to whole organism level in robust forms, enabling dissection and imaging while preserving 3D context, represents an enduring grand challenge in biology. Here we report a simple immersion method for structurally preserving intact organisms via conformal stabilization within silica. This self-limiting process, which we refer to as silica bioreplication, occurs by condensation of water-soluble silicic acid proximally to biomolecular interfaces throughout the organism. Conformal nanoscopic silicification of all biomolecular features imparts structural rigidity enabling the preservation of shape and nano-to-macroscale dimensional features upon drying to form a biocomposite and further high temperature oxidative calcination to form silica replicas or reductive pyrolysis to form electrically conductive carbon replicas of complete organisms. The simplicity and generalizability of this approach should facilitate efforts in biological preservation and analysis and could enable the development of new classes of biomimetic composite materials.

Mechanically encoded cellular shapes for synthesis of anisotropic mesoporous particles.

The asymmetry that pervades molecular mechanisms of living systems increasingly informs the aims of synthetic chemistry, particularly in the development of catalysts, particles, nanomaterials, and their assemblies. For particle synthesis, overcoming viscous forces to produce complex, nonspherical shapes is particularly challenging; a problem that is continuously solved in nature when observing dynamic biological entities such as cells. Here we bridge these dynamics to synthetic chemistry and show that the intrinsic asymmetric shapes of erythrocytes can be directed, captured, and translated into composites and inorganic particles using a process of nanoscale silica-bioreplication. We show that crucial aspects in particle design such as particle-particle interactions, pore size, and macromolecular accessibility can be tuned using cellular responses. The durability of resultant particles provides opportunities for shape-preserving transformations into metallic, semiconductive, and ferromagnetic particles and assemblies. The ability to use cellular responses as "structure directing agents" offers an unprecedented toolset to design colloidal-scale materials.

Fermi acceleration in chaotic shape-preserving billiards.

We study theoretically and numerically the velocity dynamics of fully chaotic time-dependent shape-preserving billiards. The average velocity of an ensemble of initial conditions generally asymptotically follows the power law 〈v〉 = n(β) with respect to the number of collisions n. If a shape of a fully chaotic time-dependent billiard is not preserved it is well known that the acceleration exponent is β = 1/2. We show, on the other hand, that if a shape of a fully chaotic time-dependent billiard is preserved then there are only three possible values of β depending solely on the rotational properties of the billiard. In a special case in which the only transformation is a uniform rotation there is no acceleration, β = 0. Excluding this special case, we show that if a time-dependent transformation of a billiard is such that the angular momentum of the billiard is preserved then β = 1/6, while β = 1/4 otherwise. Our theory is centered around the detailed study of the energy fluctuations in the adiabatic limit. We show that three quantities, two scalars and one tensor, completely determine the energy fluctuations of the billiard for arbitrary time-dependent shape-preserving transformations. Finally, we provide several interesting numerical examples, all in a perfect agreement with the theory.

Correction of the Asymmetrical Projection for Accurate Camera Calibration Using Co-Planar Circular Feature

Circular features are one of the most widely used shapes for camera calibration, due to several advantages: easy to make and recognize, not sensitive to image noise, symmetry, analytic formulation is simple. However, perspective projection is generally not a shape preserving transformation. A circle often mapped as an ellipse on the image plane when the feature and the image plane are not parallel to each other, as a result, the center of the circle shift from the center of the ellipse. In this paper we present a simple and robust algorithm to compensate this bias before camera calibration. Experimental results show the algorithm is important and convenient.

Elastic Geodesic Paths in Shape Space of Parameterized Surfaces

This paper presents a novel Riemannian framework for shape analysis of parameterized surfaces. In particular, it provides efficient algorithms for computing geodesic paths which, in turn, are important for comparing, matching, and deforming surfaces. The novelty of this framework is that geodesics are invariant to the parameterizations of surfaces and other shape-preserving transformations of surfaces. The basic idea is to formulate a space of embedded surfaces (surfaces seen as embeddings of a unit sphere in IR3) and impose a Riemannian metric on it in such a way that the reparameterization group acts on this space by isometries. Under this framework, we solve two optimization problems. One, given any two surfaces at arbitrary rotations and parameterizations, we use a path-straightening approach to find a geodesic path between them under the chosen metric. Second, by modifying a technique presented in [25], we solve for the optimal rotation and parameterization (registration) between surfaces. Their combined solution provides an efficient mechanism for computing geodesic paths in shape spaces of parameterized surfaces. We illustrate these ideas using examples from shape analysis of anatomical structures and other general surfaces.

Shape-preserving transformation of monolithic porous glass into MFI-type zeolite

Shape-preserving transformations of porous glass monoliths into MFI-type zeolites by hydrothermal treatments in presence of triisopropyl ammonium bromide and triisopropyl ammonium hydroxide are described. Complete transformations were enabled by addition of a second silicon source to the synthesis solution, here colloidal silica. The impact of parameters such as the pore size and pore-wall thickness of the employed porous glass monoliths, the molar composition of the synthesis solution and the synthesis time on the synthesis product is elucidated.

On the Role of MFI Membranes During the Shape Preserving Transformation of Porous Glass into MFI-type Zeolite

On the Role of MFI Membranes During the Shape Preserving Transformation of Porous Glass into MFI-type Zeolite

Removing Shape-Preserving Transformations in Square-Root Elastic (SRE) Framework for Shape Analysis of Curves.

This paper illustrates and extends an efficient framework, called the square-root-elastic (SRE) framework, for studying shapes of closed curves, that was first introduced in [2]. This framework combines the strengths of two important ideas - elastic shape metric and path-straightening methods - for finding geodesics in shape spaces of curves. The elastic metric allows for optimal matching of features between curves while path-straightening ensures that the algorithm results in geodesic paths. This paper extends this framework by removing two important shape preserving transformations: rotations and re-parameterizations, by forming quotient spaces and constructing geodesics on these quotient spaces. These ideas are demonstrated using experiments involving 2D and 3D curves.

Shape-based retrieval in time-series databases

The shape-based retrieval is defined as the operation that searches for the (sub)sequences whose shapes are similar to that of a query sequence regardless of their actual element values. In this paper, we propose a similarity model suitable for shape-based retrieval and present an indexing method for supporting the similarity model. The proposed similarity model enables to retrieve similar shapes accurately by providing the combination of multiple shape-preserving transformations such as normalization, moving average, and time warping. Our indexing method stores every distinct subsequence concisely into the disk-based suffix tree for efficient and adaptive query processing. We allow the user to dynamically choose a similarity model suitable for a given application. More specifically, we allow the user to determine the parameter p of the distance function L p when submitting a query. The result of extensive experiments revealed that our approach not only successfully finds the subsequences whose shapes are similar to a query shape but also significantly outperforms the sequential scan method.

시계열 데이터베이스에서 복수의 모델을 지원하는 모양 기반 서브시퀀스 검색

모양 기반 검색이란 실제 요소 값과 관계없이 질의 시퀀스와 유사한 모양을 갖는 시퀀스(서브시퀀스)를 데이터베이스 내에서 검색하여 내는 연산이다. 본 논문에서는 시계열 데이터베이스에서의 모양 기반 검색을 위한 유연성 있는 새로운 유사 모델을 정의하고, 이 유사 모델을 지원하기 위한 인덱싱 및 질의 처리 방안을 제시한다. 제안된 유사 모델에서는 정규화, 이동 평균, 타임 워핑 등 다양한 변환을 지원한다. 특히 최종 유사 정도를 계산하기 위하여 사용되는<TEX>$L_p$</TEX>거리 함수론 사용자가 임의로 지정하도록 함으로써 응용에서 선호하는 유사 모델을 반영할 수 있다. 또한 이러한 모양 기반 검색을 효과적으로 지원하기 위한 압축된 서브시퀀스 트리 구조를 제안하고, 이를 기반으로 하는 효율적인 질의 처리 기법을 제시한다. 실험 결과에 의하면 제안된 기법은 진의 시퀀스와 모양이 유사한 서브시퀀스들을 사용자에 의하여 선택된 거리 함수를 사용하여 성공적으로 검색할 뿐 아니라, 순차 검색과 비교하여 거리 함수 선택에 따라 수 십배에서 수 백배까지의 성능 개선 효과를 갖는 것으로 나타났다. The shape-based retrieval is defined as the operation that searches for the (sub) sequences whose shapes are similar to that of a query sequence regardless of their actual element values. In this paper, we propose a similarity model suitable for shape-based retrieval and present an indexing method for supporting the similarity model. The proposed similarity model enables to retrieve similar shapes accurately by providing the combination of various shape-preserving transformations such as normalization, moving average, and time warping. Our indexing method stores every distinct subsequence concisely into the disk-based suffix tree for efficient and adaptive query processing. We allow the user to dynamically choose a similarity model suitable for a given application. More specifically, we allow the user to determine the parameter p of the distance function <TEX>$L_p$</TEX> when submitting a query. The result of extensive experiments revealed that our approach not only successfully finds the subsequences whose shapes are similar to a query shape but also significantly outperforms the sequence search.