Coordination Sequences Research Articles

Skew linear recurring sequences of maximal period over galois rings

Let p be a prime number, and R = GR(q d , p d) be a Galois ring of q d = p rd elements and of characteristic p d. Denote by S = GR(q nd , p d) a Galois extension of the ring R of dimension n and by Š the ring of all linear transformations of the module R S. We call a sequence v over the ring S with the law of recursion$$ {\mathrm{for}\ \mathrm{all}\ }i \in {\mathbb{N}_0}:v\left( {i + m} \right) = {\psi_{m - 1}}\left( {v\left( {i + m - 1} \right)} \right) + \cdots + {\psi_0}\left( {v(i)} \right),\quad {\psi_0}, \ldots, {\psi_{m - 1}} \in \textit{\v{S}} $$(i.e., a linear recurring sequence of order m over the module Š S) a skew LRS over S. It is known that the period T(v) of such a sequence satisfies the inequality T(v) ≤ τ = (q nm −1)p d−1. If T(v) = τ , then we call v a skew LRS of maximal period (a skew MP LRS) over S. A new general characterization of skew MP LRS in terms of coordinate sequences corresponding to some basis of a free module R S is given. A simple constructive method of building a big enough class of skew MP LRS is stated, and it is proved that the linear complexity of some of them (the rank of the linear recurring sequence) over the module S S is equal to mn, i.e., to the linear complexity over the module R S.

Construction and Enumeration of a Class of Primitive <I>s</I>-LFSR Sequences

PDF HTML阅读 XML下载 导出引用 引用提醒 一类本原σ-LFSR 序列的构造与计数 DOI: 10.3724/SP.J.1001.2012.04006 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: 国家自然科学基金(61003291); 国家高技术研究发展计划(863)(2009AA01Z417); 新世纪优秀人才计划(NCET-07-0384); 全国优秀博士学位论文作者专项基金(FANEDD-2007B74) Construction and Enumeration of a Class of Primitive σ-LFSR Sequences Author: Affiliation: Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:有限域GF(2k)上本原σ-LFSR 序列的分量序列均是二元域上具有相同极小多项式的m-序列,已知一条GF(2k)上本原σ-LFSR 序列的距离向量,就可以用二元域上的m-序列构造它.研究了一类本原σ-LFSR 序列——Z 本原σ-LFSR 序列距离向量的计算问题.给出了一种GF(2k)上n 级Z 本原σ-LFSR 序列距离向量的计算方法,其主要思想是,利用GF(2k)上1 级Z 本原σ-LFSR 序列的距离向量来计算n 级Z 本原σ-LFSR 序列的距离向量.与其他现有方法相比,该方法的效率更高.更有价值的是,该方法也适用于GF(2k)上n 级m-序列距离向量的计算.最后给出了GF(2k)上n 级Z 本原σ-LFSR 序列的计数公式,说明其个数比GF(2k)上n 级m-序列更多. Abstract:The coordinate sequences of a primitive σ-LFSR sequence over GF(2k) are m-sequences with the same minimal polynomial over GF(2), thus a primitive σ-LFSR sequence over GF(2k) can be constructed by m-sequences over GF(2) if its interval vector is known. This paper studies the calculation of interval vectors of a class of primitive σ-LFSR sequences—Z primitive σ-LFSR sequences and presents an improved method to calculate the interval vectors of Z primitive σ-LFSR sequences in order n over GF(2k), which uses the interval vectors of Z primitive σ-LFSR sequences of order 1 to calculate that of Z primitive σ-LFSR sequences in order n over GF(2k). In addition, it is more effective than other existing methods. More importantly, the new method can also be applied to the calculation of interval vectors of m-sequences over GF(2k). The enumeration formula of Z primitive σ-LFSR sequences of order n over GF(2k) is also presented, which shows that the number of Z primitive σ-LFSR sequences of order n is much larger than the number of m-sequences of order n over GF(2k). 参考文献 相似文献 引证文献

A system for automatic recording and analysis of motor activity in rats

We describe the design and evaluation of an electronic system for the automatic recording of motor activity in rats. The device continually locates the position of a rat inside a transparent acrylic cube (50 cm/side) with infrared sensors arranged on its walls so as to correspond to the x-, y-, and z-axes. The system is governed by two microcontrollers. The raw data are saved in a text file within a secure digital memory card, and offline analyses are performed with a library of programs that automatically compute several parameters based on the sequence of coordinates and the time of occurrence of each movement. Four analyses can be made at specified time intervals: traveled distance (cm), movement speed (cm/s), time spent in vertical exploration (s), and thigmotaxis (%). In addition, three analyses are made for the total duration of the experiment: time spent at each x-y coordinate pair (min), time spent on vertical exploration at each x-y coordinate pair (s), and frequency distribution of vertical exploration episodes of distinct durations. User profiles of frequently analyzed parameters may be created and saved for future experimental analyses, thus obtaining a full set of analyses for a group of rats in a short time. The performance of the developed system was assessed by recording the spontaneous motor activity of six rats, while their behaviors were simultaneously videotaped for manual analysis by two trained observers. A high and significant correlation was found between the values measured by the electronic system and by the observers.

Two classes of sequences derived from single cycle T-functions

Based on single cycle T-functions over Z/(2n), two classes of pseudorandom sequences are proposed in this paper. The periods of all their coordinate sequences can reach the maximal value 2n, and the distribution properties and linear complexities of the sequences are also studied. For the first class of sequences, it is shown that the less significant half of the coordinate sequences are uniformly distributed over F2 and the exact linear complexities are also derived. For the second class of sequences, lower bounds on the linear complexities of their coordinate sequences are given.

From symmetry-labeled quotient graphs of crystal nets to coordination sequences

The combinatorial topology of crystal structures may be described by finite graphs, called symmetry-labeled quotient graphs or voltage graphs, with edges labeled by symmetry operations from their space group. These symmetry operations themselves generate a space group which is generally a non-trivial subgroup of the crystal space group. The method is an extension of the so-called vector method, where translation symmetries are used as vector labels (voltages) for the edges of the graph. Non-translational symmetry operations may be used as voltages if they act freely on the net underlying the crystal structure. This extension provides a significant reduction of the size of the quotient graph. A few uninodal and binodal nets are examined as illustrations. In particular, various uninodal nets appear to be isomorphic to Cayley color graphs of space group. As an application, the full coordination sequence of the diamond net is determined.

Synthesis, structure, topology and magnetic properties of cobalt(ii) coordination polymers with 2-nitrobiphenyl-4,4′-dicarboxylic acid and bis(pyridyl) ligands

Four coordination polymers, [Co2(Hnbpdc)2(nbpdc)(bipy)2]n (1), [Co3(nbpdc)3(bipy)3(H2O)2]n·2nH2O (2), [Co4(nbpdc)4(bipy)(H2O)4]n (3), and [Co2(nbpdc)2(bpee)(3/2)]n·0.25nH2O (4) [H2nbpdc = 2-nitrobiphenyl-4,4′-dicarboxylic acid, bipy = 4,4′-bipyridine and bpee = 1,2-di(4-pyridyl)ethane] have been synthesized by hydrothermal methods and studied by means of X-ray crystallography, topological analyses and magnetic analyses. Compounds 1–3 were synthesized from the same reactants under controlled conditions (pH and ligand ratio). Compounds 1, 2 and 4 contain bis(carboxylate)-bridged dinuclear motifs as secondary building units (SBUs). In 1 and 2 the SBUs are connected into 44 layers by bis(chelating) nbpdc and pairwise bipy linkers. In 1, the layers are pillared into a 3D framework with the pcu topology by Hnbpdc, which is coordinated to one layer and hydrogen-bonded to another layer. In 2, the layers and the linear [Co(bipy)]n chains intercalated between the layers are connected by nbpdc to produce a 3D framework exhibiting a rarely observed 4,6-connected topology. In 4 the SBUs are connected by nbpdc [bis(chelating) and bis(bridging)] and bpee (single and pairwise) to yield a 3D framework, which defines a new 6-connected net with point symbol (4(10)·5(2)·6(3)). Notably, this new net and the known hex-6-P6(2)22 net represent the first examples of topologically different nets having the same coordination sequences, point and vertex symbols. Compound 3 contains carboxylate- and aqua-bridged tetranuclear motifs as SBUs, which are connected by covalent linkers (nbpdc and bipy) and sextuple O–H···O hydrogen bonds to generate a 3D framework, which defines a new 10-connected net with point symbol (4(24)·5(12)·6(8)·7) (considering only covalent linkers) and a new 12-connected net with point symbol (3(12)·4(36)·5(17)·6) (including also the hydrogen bonds as linkers). Magnetic studies on 1 and 2 demonstrated that the bis(syn–skew-carboxylate) bridges between octahedral Co(II) ions induce ferromagnetic coupling; 4 is peculiar in that octahedral and tetrahedral Co(II) ions are linked by mixed syn–syn and syn–skew carboxylate bridges, which give rise to antiferromagnetic coupling.

Structural Deflection Measurement with a Range Camera

AbstractRange cameras offer great potential for the measurement of structural deformations because of their ability to directly measure video sequences of three-dimensional coordinates of entire surfaces, their compactness, and their relatively low cost compared with other active imaging technologies such as terrestrial laser scanners. Identified limitations of range cameras for high-precision metrology applications such as deformation measurement include the high (centimeter level) noise level and scene-dependent errors. This paper proposes models and methodologies to overcome these limitations and reports on the use of a SwissRanger SR4000 range camera for the measurement of deflections in concrete beams subjected to flexural load-testing. Results from three separate tests show that submillimeter precision and accuracy—assessed by comparison with estimates derived from terrestrial laser scanner data—can be achieved. The high-accuracy range camera results were realized by eliminating the systematic, scen...

Assessment of Mitral Annulus (P3 Segment) Asymmetric Deformity in Myocardial Infarction with Ischemic Regurgitation by Real Time Three‐Dimensional Echocardiography

The three-dimensional (3D) saddle shape of the mitral annulus (MA) is well characterized in humans, but segmental MA deformity and regurgitation suffered after the ischemic damage of myocardial infarction (MI) is poorly understood. In this study, such changes were assessed in patients with ischemic mitral regurgitation (IMR) post-MI, using our computerized 3D echo technique. A patient cohort (n = 72) with IMR due to inferior or anterior MI and normal controls (n = 20) were enrolled for 3D MA echo studies. Sequential coordinates of MA were manually measured from each of 18 radial planes, cropped in midsystole, to generate 3D MA images. In addition, six segmental (A1, A2, A3, P1, P2, P3) parameters of MA and global features, such as circumference, area, and height, were calculated. All six segments of MA were significantly dilated in the IMR group compared with corresponding segments of normal controls. Although there were no significant intragroup differences in A1, A2, and A3 segments, a greater degree of P3 segmental MA deformity was observed only in patients following inferior MI. The MA dilatation observed in patients with IMR after MI was more pronounced in patients with anterior versus inferior MI. However, P3 segmental dilatation of MA was significantly greater in patients after inferior IM with significant IMR, corresponding with more severe asymmetric MA deformity. (Echocardiography 2012;29:42-50).

Design of Touch Screen Driver Based on Linux

This paper introduces the touch screen driver design based on Linux plays an important role in applications of touch screen. In order to further explore embedded touch screen driver design, and then optimize and improve existing drivers at practice level, this paper accomplished the design of touch screen driver using SPI interface and ADS7843 touch screen chip controller based on Samsung S3C2410s microprocessor. We designed the touch screen hardware interrupt program using the bottom half mechanism of the kernel timer, utilized 16 clock cycles of coordinate conversion sequences to achieve touch point based data acquisition and present the process of coordinate collection. The touch screen driver ran well on the UP-NETARM2410-S platform. The hardware design was verified to be simple and reliable while the corresponding software accomplished touch state detection and touch data conversion efficiently. The touch screen control method is simple, efficient and easy to realize.

Solving future problems: Default network and executive activity associated with goal-directed mental simulations

Mental simulations are often focused on a goal in the future or a problem to be solved. Recent neuroimaging studies have associated mental simulations of the future with default network activity, but the simulations in these studies were not typically directed toward achieving a particular goal. Goal-directed simulation requires cognitive control to maintain information, make decisions, and coordinate abstract action sequences. Therefore, it should recruit not only the default network, but also executive regions. To investigate whether default network and executive regions can be coactive in the context of goal-directed simulation, we designed a problem-solving task in which participants simulated solving several specific problems in imaginary scenarios while in the MRI scanner. We analyzed brain activity during simulation relative to a semantic elaboration task and found that goal-directed simulation engaged core regions of the default network and executive dorsolateral prefrontal cortex. A functional connectivity analysis with posterior cingulate and dorsolateral prefrontal cortex seeds revealed that activity in these regions was coupled throughout the goal-directed simulation period and associated with a distributed network of other default and executive regions, including medial prefrontal cortex, medial temporal, and parietal regions.

Reconstruction of a linear recurrence of maximal period over a Galois ring from its highest coordinate sequence

Let R = GR (qn, qn) be a Galois ring of cardinality qn and characteristic pn, q = pr, p be a prime. We call a subset K ⊂ R a coordinate set if 0 ∈ K and for any a ∈ R there exists a unique ϰ(a) ∈ K such that a ≡ ϰ(a) (mod pR). Let u be a linear recurring sequence of maximal period (MP LRS) over a ring R. Then any its term u(i) admits a unique representation in the form

THE ROLE OF BERYLLIUM IN BERYLLOSILICATE MINERAL STRUCTURES AND ZEOLITE FORMATION

Topological diagrams are constructed for all layered and framework beryllosilicates and for zeolites having related topological features. These diagrams are used to identify the secondary building units (SBU). The SBU are arranged in increasing order of ring dimension to establish a structural hierarchy for this chemical class. Vertex symbols (VS) and coordination sequences (CS) are determined for each unique tetrahedrally coordinated site in every crystal structure. The number sets, VS and CS, identify structural similarities in beryllosilicates and in natural and synthetic zeolites. The frequency of ring-size occurrence varies with Be content in both layered and framework beryllosilicates. Framework density (FD) is derived from structure diagrams, and topological density (TD) is derived from CS sums. Framework density and topological density are strongly correlated. The topological density is controlled by the Be content in tetrahedrally coordinated sites. This structural control could be used to design specific framework arrangements.

A New Image Encryption Algorithm of Input-Output Feedback Based on Multi-Chaotic System

In this paper, a new method is proposed for image encryption by using Transformed Logistic map and Cat map. First, the Transformed logistic map is used to generating two coordinate sequences, and then the primary image's pixels shuffled by the two coordinate sequences. After shuffling, the key stream is produced by the Cat map to encrypt the shuffled image. Theoretical analysis and experimental results indicate that the proposed algorithm has a perfect encryption effect and can resist common attacks

Modeling of self-organization of silicate systems: Precursor nanoclusters and self-assembly of Na3MSi3O9 (M = Y, Eu-Lu; oP256) crystal structures producing two interpenetrating diamond-type frameworks

In the M-T-O model system (M is a polyvalent metal with CN ≥ 4; T is Si), cyclic clusters have been deduced as graphs in the T/M range from one to three. The case is considered when monocyclic cluster M2T2 is modified by T-tetrahedra that form diortho groups T2. The M sites of the cluster have either topologically different local MT structures (four types) or identical local MT structures (two types). The cluster types for T/M = 3 obtained by modeling were used in analysis of one of the most complicated types of silicate crystal structures Na3MSi3O9 (M = Y; Eu-Lu; T/M = 3) with the Pearson index oP256 and 64 independent atoms. The TOPOS program package was used to carry out the complete 3D reconstruction of the self-assembly of the crystal structure: suprapolyhedral precursor nanocluster → primary chain → microlayer → microframework (supraprecursor) → ... three-dimensional framework. The calculation of the coordination sequences of site atoms in the 3D network of the MT framework MT3O9 revealed topological symmetry related to a three-dimensional separation of the framework into two interpenetrating frameworks. Each framework structure is generated by topologically equivalent cyclic precursor clusters Na2M2T6 consisting of two YO6 octahedra comprising three diortho groups Si2O7 and two Na atoms located above and below the ring center. The 3D graphs characterizing the connectivity of the centers of crystallographically equivalent clusters in the frameworks correspond to diamond-type networks.

Strictly monotonic multidimensional sequences and stable sets in pillage games

Let S ⊂ R n have size | S | > ℓ 2 n − 1 . We show that there are distinct points { x 1 , … , x ℓ + 1 } ⊂ S such that for each i ∈ [ n ] , the coordinate sequence ( x i j ) j = 1 ℓ + 1 is strictly increasing, strictly decreasing, or constant, and that this bound on | S | is best possible. This is analogous to the Erdős–Szekeres theorem on monotonic sequences in R . We apply these results to bound the size of a stable set in a pillage game. We also prove a theorem of independent combinatorial interest. Suppose { a 1 , b 1 , … , a t , b t } is a set of 2 t points in R n such that the set of pairs of points not sharing a coordinate is precisely { { a 1 , b 1 } , … , { a t , b t } } . We show that t ⩽ 2 n − 1 , and that this bound is best possible.

ALFLARSENITE: STRUCTURE AND RELATIONSHIP TO OTHER Be-Si AND ZEOLITE FRAMEWORK STRUCTURES

Alflarsenite, ideally NaCa 2 Be 3 Si 4 O 13 (OH)·2H 2 O, is a new zeolite species from the Tuften larvikite quarry, Tvedalen, Larvik, Vestfold, south Norway. The crystal structure has been solved in space group P 2 1 , with unit-cell parameters refined from single-crystal data: a 7.1222(4), b 19.8378(11), c 9.8071(5) A, β 111.287(1)°, V 1291.1(2) A 3 and Z = 4. The crystal structure, a zeolite framework, was refined to R 1 = 0.046 for 3283 observed reflections. The Be–Si framework of tetrahedra has cages containing the Na and Ca atoms and H 2 O groups. The framework has Cmcm space-group symmetry; the addition of Na and Ca cations reduces the symmetry to space group Cmc 2 1 , whereas taking into consideration the H 2 O groups, the structure reduces in symmetry to monoclinic P 2 1 . Topological diagrams were constructed for all framework beryllium silicates and for zeolites that have topological features similar to alflarsenite. These diagrams are used to identify the secondary building units (SBU), 5–1 and spiro –5, and to extract vertex symbols and coordination sequences for each topologically unique site having tetrahedral coordination. The SBUs and coordination-sequence numbers show structural similarities to bikitaite and the synthetic zeolites CAS and NSI. All four structures have slabs composed of alternating chains of 5- and 8-connected rings. The cross-linkage of these slabs varies in each structure.

Adaptive coordination and heedfulness make better cockpit crews

Team coordination during a simulated clean approach performed by 42 civil aviation cockpit crews was analysed. Several hypotheses regarding the adaptive use of implicit and explicit coordination, leadership and heedful interrelating were tested. The results indicate the adaptiveness of coordination to different levels of standardisation and task load and the general importance of explicit coordination for good performance. Leadership seems to be required mainly for work phases with little standardisation. In exploratory lag sequential analyses, heedful behaviour in the seven best and six worst performing crews was examined. The coordination sequences in high performance crews were found to be more succinct and well balanced, indicating that a shared sense of heedfulness is crucial for effectiveness. Theoretical implications for the conceptualisation of adaptive coordination and heedfulness and practical implications for improving crew training are discussed. Statement of Relevance: Analyses of team coordination during a simulated clean approach performed by civil aviation cockpit crews demonstrated the occurrence and effectiveness of adaptive coordination in response to different levels of task load and standardisation. Results also indicated the importance of heedful interrelating, both as a form of coordination and as a way of regulating the adaptiveness of coordination efforts. These findings have important implications for improving crew training, leadership practices and possibly also standard operating procedures.

On the generalized joint linear complexity profile of a class of nonlinear pseudorandom multisequences

Recently, multisequences have gained increasing interest for applications in cryptography and quasi-Monte Carlo methods. We study the (generalized) joint linear complexity of a class of nonlinear pseudorandom multisequences introduced by the first two authors as well as the linear complexity of its coordinate sequences. We prove lower bounds which are much stronger than in the case of single sequences since the multidimensional case brings in new and favourable effects.

An algorithm to restore a linear recurring sequence over the ring R = Z pn from a linear complication of its highest coordinate sequence

An algorithm to restore a linear recurring sequence over the ring R = Z pn from a linear complication of its highest coordinate sequence

Identifying Zeolite Frameworks with a Machine Learning Approach

Zeolites are microporous crystalline materials with highly regular framework structures consisting of molecular-sized pores and channels. The characteristic framework type of a zeolite is conventionally defined by combining information on its coordination sequences, vertex symbols, tiling, and transitivity information. Here we present a novel knowledge-based approach for zeolite framework type classification. We show the predicting abilities of a machine learning model that uses a nine-dimensional feature vector including novel topological descriptors obtained by computational geometry techniques, together with selected physical and chemical properties of zeolite crystals. Trained on the crystallographic structures of known zeolites, this model predicts the framework types of zeolite crystals with very high accuracy.