Repetitive Substructures Research Articles

A symmetric substructuring method for analyzing the natural frequencies of conical origami structures

Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorption capacity. Previous investigations have commonly focused on the static characteristics of these lightweight structures. However, the efficient analysis of the natural vibrations of these structures is pivotal for designing conical origami structures with programmable stiffness and mass. In this paper, we propose a novel method to analyze the natural vibrations of such structures by combining a symmetric substructuring method (SSM) and a generalized eigenvalue analysis. SSM exploits the inherent symmetry of the structure to decompose it into a finite set of repetitive substructures. In doing so, we reduce the dimensions of matrices and improve computational efficiency by adopting the stiffness and mass matrices of the substructures in the generalized eigenvalue analysis. Finite element simulations of pin-jointed models are used to validate the computational results of the proposed approach. Moreover, the parametric analysis of the structures demonstrates the influences of the number of segments along the circumference and the radius of the cone on the structural mass and natural frequencies of the structures. Furthermore, we present a comparison between six-fold and four-fold conical origami structures and discuss the influence of various geometric parameters on their natural frequencies. This study provides a strategy for efficiently analyzing the natural vibration of symmetric origami structures and has the potential to contribute to the efficient design and customization of origami metastructures with programmable stiffness.

Graph based anomaly detection in human action video sequence

Abstract In our paper, we have proposed to use graphs to detect anomaly in human action video. Although the detection of anomaly is a widely researched topic, but very few researchers have detected anomaly in action video using graphs. in our proposed method we have represented the smaller section (sub-section) of our input video as a graph where vertices of the graph are the space time interest points in the sub-section video and the association between the space time interest points exists. Thus, graphs for each sub section are created to look for a repeated substructure. We believe most of the actions inherently are repeated in nature. Thus, we have tried to capture the repetitive sub-structure of the action represented as a graph and used this repetitive sub-structure to compress the graph. If the compressed graph has few elements that have not been compressed, we suspect them as anomaly. But the threshold value takes care not to make the proposed method very much sensitive towards the few uncompressed elements. Our proposed method has been implemented on locally created “extended KTH” and “extended Weizmann” datasets with good accuracy score. The proposed method can also be extended for few more applications such as training athletes and taking elderly care.

Comparing performance of graph matching algorithms on huge graphs

Graph matching algorithms are gaining more and more interest in the last years from different scientific communities; indeed, they allow comparing any kind of objects represented using their intrinsic structure, represented in terms of attributed relational graphs. The challenge is to make these algorithms able to provide solutions over huge graphs, with many thousands of nodes, and in a time that is adequate for practical applications; in this paper, we propose a comparison among the best performing algorithms available in the literature on a variety of very large graph databases used for performance assessment. The chosen datasets vary in terms of graph structure, size, density, presence of symmetric or repetitive substructures; this variability makes such datasets very challenging. The aim of this paper is to characterize the performance of the compared algorithms with respect to the typology, the size and other structural properties of the graphs; in this way, the user may consciously select the best suited algorithm for a given purpose. The results of an impressive experimentation that required 556 days of machine time are here presented and extensively discussed.

The BOSS is concerned with time series classification in the presence of noise

Similarity search is one of the most important and probably best studied methods for data mining. In the context of time series analysis it reaches its limits when it comes to mining raw datasets. The raw time series data may be recorded at variable lengths, be noisy, or are composed of repetitive substructures. These build a foundation for state of the art search algorithms. However, noise has been paid surprisingly little attention to and is assumed to be filtered as part of a preprocessing step carried out by a human. Our Bag-of-SFA-Symbols (BOSS) model combines the extraction of substructures with the tolerance to extraneous and erroneous data using a noise reducing representation of the time series. We show that our BOSS ensemble classifier improves the best published classification accuracies in diverse application areas and on the official UCR classification benchmark datasets by a large margin.

Dynamic Modeling and Numeration of Flexible Multi-Body System with Closed Loop

The dynamic model of flexible multi-body system with closed loop is described with natural coordinates. The method is formulaic and especially appropriate to the modeling of system with repetitive substructures, but Lagrange multipliers as unknown variables are contained in the model. The dynamic model is reduced to a system with minimum dimensions by means of null-space orthogonal basis of constraint Jacobin. The result is correspondence with the dynamic model of rigid multi- body system while the rigid and flexible coupling is considered. The numerical method and the simulation steps are given in detail. Numerical example dealing with a flexible parallel four-bar linkage widely used in engineering illustrates the performance of the proposed method. The dynamic response of the angle between flexible linkage and horizontal axis are presented. The results indicate that there are clearly fluctuation in the angular velocity and acceleration of crank. The motion of connecting linkage contains not only translation but also narrow range rotation especially in the start instant.

Efficient genome ancestry inference in complex pedigrees with inbreeding

Motivation: High-density SNP data of model animal resources provides opportunities for fine-resolution genetic variation studies. These genetic resources are generated through a variety of breeding schemes that involve multiple generations of matings derived from a set of founder animals. In this article, we investigate the problem of inferring the most probable ancestry of resulting genotypes, given a set of founder genotypes. Due to computational difficulty, existing methods either handle only small pedigree data or disregard the pedigree structure. However, large pedigrees of model animal resources often contain repetitive substructures that can be utilized in accelerating computation.Results: We present an accurate and efficient method that can accept complex pedigrees with inbreeding in inferring genome ancestry. Inbreeding is a commonly used process in generating genetically diverse and reproducible animals. It is often carried out for many generations and can account for most of the computational complexity in real-world model animal pedigrees. Our method builds a hidden Markov model that derives the ancestry probabilities through inbreeding process without explicit modeling in every generation. The ancestry inference is accurate and fast, independent of the number of generations, for model animal resources such as the Collaborative Cross (CC). Experiments on both simulated and real CC data demonstrate that our method offers comparable accuracy to those methods that build an explicit model of the entire pedigree, but much better scalability with respect to the pedigree size.Contact: weiwang@cs.unc.edu

The structure of receptor-associated protein (RAP).

The receptor-associated protein (RAP) is a molecular chaperone that binds tightly to certain newly synthesized LDL receptor family members in the endoplasmic reticulum (ER) and facilitates their delivery to the Golgi. We have adopted a divide-and-conquer strategy to solve the structures of the individual domains of RAP using NMR spectroscopy. We present here the newly determined structure of domain 2. Based on this structure and the structures of domains 1 and 3, which were solved previously, we utilized experimental small-angle neutron scattering (SANS) data and a novel simulated annealing protocol to characterize the overall structure of RAP. The results reveal that RAP adopts a unique structural architecture consisting of three independent three-helix bundles that are connected by long and flexible linkers. The flexible linkers and the quasi-repetitive structural architecture may allow RAP to adopt various possible conformations when interacting with the LDL receptors, which are also made of repetitive substructure units.

Optimal discovery of repetitions in 2D

Repetitive substructures in two-dimensional arrays emerge in speeding up searches and have been recently studied also independently in an attempt to parallel some of the classical derivations concerning repetitions in strings. The present paper focuses on repetitions in two dimensions that manifest themselves in form of two “tandem” occurrences of a same primitive rectangular pattern W where the two replicas touch each other with either one side or corner. Being primitive here means that W cannot be expressed in turn by repeated tiling of another array. The main result of the paper is an O ( n 3 log n ) algorithm for detecting all “side-sharing” repetitions in an n × n array. This is optimal, based on bounds on the number of such repetitions established in previous work. With easy adaptations, these constructions lead to an equally optimal, O ( n 4 ) algorithm for repetitions of the second type.

Optimal Parallel Searching an Array for Certain Repetitions

Abstract Repetitive substructures of two-dimensional arrays have been recently defined and studied in an attempt to parallel some of the analogous developments already known for strings. In the present paper we propose an O (log log n) time O(n3 log n) work optimally fast, optimal parallel CRCW-PRAM algorithm for detecting all repetitions of certain type in an n × n array.

Cutaneous serous glands in South‐American anurans: An ultrastructural comparison between hylid and pseudid species

An ultrastructural analysis of the secretory processes in serous cutaneous glands of some hylid species (Scinax acuminata, S. fuscovaria, S. nasica and Hyla nana) and one pseudid species (Pseudis paradoxa) revealed similar features, from the early steps to advanced maturational phases. The most consistent and peculiar trait was the occurrence of granules with repeating substructures, resulting from multi‐focal condensation of the dispersed material contained in the Golgian vesicles, which represent the early feature of the secretory activity. Since the ultimate granule features derive from comparable pathways of sequential processes ‐ including early secretory activity and maturation ‐ the similar repetitive substructure is proposed as a trait informative on the taxonomic relationships between the species considered. Comparable granule features in serous glands of different species confirm the close systematic framing of Hyla and Scinax among Hyli‐nae, while stressing phylogenetic relationships between the hylid and pseudid families.

Fibonacci arrays and their two-dimensional repetitions

Notions related to repetitive substructures in two-dimensional arrays are introduced and studied in an attempt to parallel some of the analogous developments already known for strings. In particular, sequences of “Fibonacci arrays” are defined, capable of exhibiting extremal properties in terms of certain repetitive subpatterns called “tandems”. Two types of tandems are considered. For one type, it is shown that the number of occurrences in an m×n Fibonacci array attains the general upper bound of O (m 2n logn) .

VIBRATION CHARACTERISTICS OF SYSTEMS WITH MULTIPLE BLADES

An interesting phenomenon can be observed when the state-space dynamic substructural method is applied to the eigenproblem of bladed disk–shaft systems: whether or not the shaft is flexible, each frequency of the single root-fixed blade appears as a frequency of the whole structure with a multiplicity of at least (n−3), wheren is the number of repetitive blades. The presented result can be regarded as an extension of previous findings by the authors in the sense that the commonly interfaced repetitive substructures are allowed to be treated as a rigid body in modal analysis. The defectiveness issue of the multiple eigenvalues arising from the repetitive substructures is also addressed. Examples of rotary wing models and a simplified turbine model are presented for validation together with attempting their physical explanations.

A macroelement method for catenary mode analysis

A striking feature of all sorts of catenaries is that they are composed of periodic repetitive substructures. Making use of this feature and the symmetry of the structures, we proposed a macroelement of originality and the coherence dynamic stiffness matrix of the macroelement was formed, based on the solution of beam and flexible cable elements by the boundary element method. A general dynamic analysis procedure for catenaries was also given. Such a method could greatly decrease the costs of computation as the structure would still be treated as one continuous body. On the basis of this paper a computer program simula3.0, that could analyse the modes of all sorts of catenaries, was developed.

A substructures method for the active control design of large periodic structures

A substructural control approach is presented in the control design of large periodic structures with identically repeating substructures. The approach makes use of wave propagation concepts in structural vibrations. After noting relations between vibrational displacements of a large periodic structure, the substructural controller, designed for a reference substructure, is used to assemble the global controller for the entire structure. The accuracy of the method is verified with the example of the control design of a large periodic structure consisting of 9 repetitive substructures. Since only a typical repeating substructure, the reference substructure, is used for the global control design, the technique is expected to be very attractive for the control design engineers of large periodic structures.

Multiple Eigenvalues Arising from a Class of Repetitive Substructures

Thedynamicsubstructuremethodinstatespacewasemployedtostudyeigenvalueproblemsforstructureswitha classofrepetitivesubstructures,whichsharea common interface. Theblock propertiesoftheresulting synthesized system matrices are discussed. A very interesting result on multiple eigenvalues of the considered structures was obtained: each ® xed interface eigenvalue of the singlerepetitive substructure appeared as at least ( n i ®) multiple eigenvalues of the whole structure, where n is the number of repetitive substructures; ®is a number depending on the azimuth distributions of the repetitive substructures. It takes at most nine, and it takes three in the special cases when the repetitive substructures are oriented by rotation around a ® xed axis. The mode shapes associated with the (n i ®) multiple eigenvalues were obtained and the nondefectiveness of the obtained multiple eigenvalues is discussed. Physical explanation and numerical examples were also attempted and are given. Nomenclature C r = damping matrix of the rth substructure, symmetric f r = external force vector exerted on the rth substructure A f r = internal force vector exerted on the interface of the rth substructure G r = gyroscopic matrix of the rth substructure, skew symmetric i = indication of internal variables for substructure j = indication of interface variables for substructure K r = stiffness matrix of the rth substructure, semipositive de® nite M r = mass matrix of the rth substructure, positive de® nite m r = internal degree of freedom of the rth substructure m r j = interface degree of freedom of the rth substructure m r = number of retained Jordan blocks for the rth substructure N = degree of freedom of the whole structure with the ® nite element method discretization s r = real or complex numbers used as factors of the ® xed interface mode of rth substructure in constructing the modes for the whole structure T r = transformation between the interface coordinates in local coordinate system of the rth substructure and the global interface coordinates system A T r = transformation matrix between the local coordinate system of therth substructure and the global displacement system x r = nodal displacement vector for the rth substructure yh = state vector of the common interface in global coordinate system f r = third Euler angles used for describing the azimuth of the

Multiple eigenvalues arising from a class of repetitive substructures

Multiple eigenvalues arising from a class of repetitive substructures

Knowledge discovery from structural data

Discovering repetitive substructure in a structural database improves the ability to interpret and compress the data. This paper describes the Subdue system that uses domain-independent and domain-dependent heuristics to find interesting and repetitive structures in structural data. This substructure discovery technique can be used to discover fuzzy concepts, compress the data description, and formulate hierarchical substructure definitions. Examples from the domains of scene analysis, chemical compound analysis, computer-aided design, and program analysis demonstrate the benefits of the discovery technique.

Substructure discovery using minimum description length and background knowledge

The ability to identify interesting and repetitive substructures is an essential component to discovering knowledge in structural data. We describe a new version of our SUBDUE substructure discover...

Substructure Discovery Using Minimum Description Length and Background Knowledge

The ability to identify interesting and repetitive substructures is an essential component to discovering knowledge in structural data. We describe a new version of our SUBDUE substructure discovery system based on the minimum description length principle. The SUBDUE system discovers substructures that compress the original data and represent structural concepts in the data. By replacing previously-discovered substructures in the data, multiple passes of SUBDUE produce a hierarchical description of the structural regularities in the data. SUBDUE uses a computationally-bounded inexact graph match that identifies similar, but not identical, instances of a substructure and finds an approximate measure of closeness of two substructures when under computational constraints. In addition to the minimum description length principle, other background knowledge can be used by SUBDUE to guide the search towards more appropriate substructures. Experiments in a variety of domains demonstrate SUBDUE's ability to find substructures capable of compressing the original data and to discover structural concepts important to the domain. Description of Online Appendix: This is a compressed tar file containing the SUBDUE discovery system, written in C. The program accepts as input databases represented in graph form, and will output discovered substructures with their corresponding value.

Discovery of inexact concepts from structural data

Concept discovery in structural data requires the identification of repetitive substructures in the data. A method for discovering substructures in data using an inexact graph match is described. An implementation of the authors' SUBDUE system that employs an inexact graph match to discover substructures which occur often in the data, but not always in the same form, is described. This inexact substructure discovery can be used to formulate fuzzy concepts, compress the data description, and discover interesting structures in data that are found either in an identical or in a slightly convoluted form. Examples from the domains of scene analysis and chemical compound analysis demonstrate the benefits of the inexact discovery technique. >