Hierarchical Sequences Research Articles

Components of a Variance Model for the Analysis of Repeated Measurements in Fixed-Point Comparisons

Experimental design is a statistical tool concerned with the planning of experiments to obtain the maximum amount of information from the available resources. This tool may be applied to metrology, especially for the analysis of a large number of repeated measurements (replicates) of short-term repeatability and the medium-term and long-term reproducibilities, enabling the inclusion of these “time-dependent sources of variability” in the uncertainty budget. The realization of the International Temperature Scale of 1990 (ITS-90) scale requires that laboratories usually have more than one cell for each fixed point, for comparison on a regular basis. The calculation of the uncertainty of such comparisons is considered here, taking into account these time-dependent sources of variability. These components of the uncertainty evaluated by a Type A method are obtained by the statistical analysis of the experimental results using the components of a variance model for designs consisting of nested or hierarchical sequences of measurements, as foreseen by the mainstream GUM. An application example of a balanced nested structure in the comparison of two fixed-point cells is presented.

Syntactic structure and artificial grammar learning: The learnability of embedded hierarchical structures

Embedded hierarchical structures, such as “the rat the cat ate was brown”, constitute a core generative property of a natural language theory. Several recent studies have reported learning of hierarchical embeddings in artificial grammar learning (AGL) tasks, and described the functional specificity of Broca’s area for processing such structures. In two experiments, we investigated whether alternative strategies can explain the learning success in these studies. We trained participants on hierarchical sequences, and found no evidence for the learning of hierarchical embeddings in test situations identical to those from other studies in the literature. Instead, participants appeared to solve the task by exploiting surface distinctions between legal and illegal sequences, and applying strategies such as counting or repetition detection. We suggest alternative interpretations for the observed activation of Broca’s area, in terms of the application of calculation rules or of a differential role of working memory. We claim that the learnability of hierarchical embeddings in AGL tasks remains to be demonstrated.

Basis set convergence in Hartree-Fock calculations of some diatomic molecules containing first and second-row atoms

Basis set convergence towards the numerical limit of the total Hartree-Fock (HF) energy is investigated for the hierarchical sequences of the XZP and cc-pVXZ basis sets. For both hierarchies, solid improvements are obtained with each increment in X. To estimate the complete basis set limit, an exponential form was used. Among the various approaches considered here, a three-parameter exponential extrapolation applied to the TZP, QZP, and 5ZP results yields the most accurate basis set limits. In addition, 5ZP highest occupied molecular orbital HF energies of some diatomic molecules are evaluated and compared with the corresponding ones obtained with the cc-pV5Z and numerical HF results.

Chimpanzee tool technology in the Goualougo Triangle, Republic of Congo

With the exception of humans, chimpanzees show the most diverse and complex tool-using repertoires of all extant species. Specific tool repertoires differ between wild chimpanzee populations, but no apparent genetic or environmental factors have emerged as definitive forces shaping variation between populations. However, identification of such patterns has likely been hindered by a lack of information from chimpanzee taxa residing in central Africa. We report our observations of the technological system of chimpanzees in the Goualougo Triangle, located in the Republic of Congo, which is the first study to compile a complete tool repertoire from the Lower Guinean subspecies of chimpanzee ( Pan troglodytes troglodytes). Between 1999 and 2006, we documented the tool use of chimpanzees by direct observations, remote video monitoring, and collections of tool assemblages. We observed 22 different types of tool behavior, almost half of which were habitual (shown repeatedly by several individuals) or customary (shown by most members of at least one age-sex class). Several behaviors considered universals among chimpanzees were confirmed in this population, but we also report the first observations of known individuals using tools to perforate termite nests, puncture termite nests, pound for honey, and use leafy twigs for rain cover. Tool behavior in this chimpanzee population ranged from simple tasks to hierarchical sequences. We report three different tool sets and a high degree of tool-material selectivity for particular tasks, which are otherwise rare in wild chimpanzees. Chimpanzees in the Goualougo Triangle are shown to have one of the largest and most complex tool repertoires reported in wild chimpanzee populations. We highlight new insights from this chimpanzee population to our understanding of ape technological systems and evolutionary models of tool-using behavior.

Expectation versus variation: Students’ decision making in a sampling environment

Abstract: A task adapted from one used by Tversky and Kahneman (1971) was used in an interview or questionnaire context with 122 students from Grade 3 to Grade 13. Two questions assessed student understanding of the relationship of a sample to a population and of the expected value of the arithmetic mean, with and without information on a single value from the sample. Combining responses to the two questions, increasingly complex hierarchical sequences were identified in the observed responses in relation to the expected value of the means, an expectation variable, and in relation to the degree that ideas about variation were used to support judgements, a variation variable. Using data from another task performed by 68 of the students, responses were associated with the observed development of understanding of sampling more generally, a basic sampling variable. Overall, the associations of levels of response among the variables was not strong, suggesting more explicit discussion of sampling issues is requ...

A 12-b, 150 MHz Sample/s CMOS Current Steering D/A Converter with Gradient Error Compensation

This paper discusses a circuit of 12-b, 150 MHz Sample/s current steering DAC with hierarchical symmetrical switching sequences which will compensate gradient error. The circuit of 12-b DAC employs segmented architecture, the least significant bits (LSB's) steer a binary weighted array, while the most significant bits (MSB's) are thermometer decoded and steer a unary array. The measured differential nonlinearity and integral nonlinearity are ± 0.6 least significant bit (LSB) and ±0.9 LSB, respectively. The output spectrum of the DAC is ?63 dB with an input frequency of 30 MHz at 150 MHz conversion rate. The circuit is fabricated in 0.5 ? ?m, two-poly two-metal, 5.0 V, mixed-signal CMOS process and occupies 1.27 × 0.96 mm, when operating at 150 MHz Sample/s, it dissipates 91.6 mW from 5.0 V power supply which is much lower than those of [1].

Shapes of liquid drops obtained using symbolic computation

The first aim of this paper is to show how two free boundary problems arising from fluid mechanics can be solved with a domain perturbation method. The second aim is to analyse the range of validity of the series solutions. The analysis will aim at identifying the location and the nature of the singularities characterizing these series. After expansion, the equations obtained are linear, but at each stage the length of the expressions grows exponentially. Herein we implement techniques for the automatic generation of hierarchical expression sequences and we present several tools for reducing the combinatorial blow-up of the expressions arising in these two problems.

Normal approximation for hierarchical structures

Given F:[a,b]k→[a,b] and a nonconstant X0 with P(X0∈[a,b])=1, define the hierarchical sequence of random variables {Xn}n≥0 by Xn+1=F(Xn,1,…,Xn,k), where Xn,i are i.i.d. as Xn. Such sequences arise from hierarchical structures which have been extensively studied in the physics literature to model, for example, the conductivity of a random medium. Under an averaging and smoothness condition on nontrivial F, an upper bound of the form Cγn for 0<γ<1 is obtained on the Wasserstein distance between the standardized distribution of Xn and the normal. The results apply, for instance, to random resistor networks and, introducing the notion of strict averaging, to hierarchical sequences generated by certain compositions. As an illustration, upper bounds on the rate of convergence to the normal are derived for the hierarchical sequence generated by the weighted diamond lattice which is shown to exhibit a full range of convergence rate behavior.

IMe: 4-Term Formula Method for the Symbolic Analysis of Linear Circuits

This paper is intended to show a general method (inhibition method) that relies on the superposition principle to analyze linear systems and electric circuits, based on hierarchical sequences of more simple topologies with some inhibited elements and on a simple recollecting logic to calculate the final solution from the previous partial and more elementary solutions. The result of the analysis is represented by and stored into a table (called the inhibition sequence table), which thus consists in a kind of database for the system or electric circuit being analyzed. The method follows a hierarchical structuration that is halfway physical (the hierarchical blocks have a nonabstract meaning) and halfway logical (the relationships among the blocks carry out information richer than the hierarchy itself). Once the table is calculated for a particular system, then a little calculation overhead allows some other interesting features, like the possibility to analyze an old circuit with some new branches added by analyzing the new elements only, or like the calculation of exact sensitivities without using derivatives, or like the calculation of the inverse matrix avoiding the usual matrix inversion procedure. A proof of the Inhibition Theorem is given and also some tutorial circuit examples.

Weak chaos and anomalous transport: a deterministic approach

We review how transport properties for chaotic dynamical systems may be studied through cycle expansions, and show how anomalies can be quantitatively described by hierarchical sequences of periodic orbits.

Nonlinear Approximation from Differentiable Piecewise Polynomials

We study nonlinear n-term approximation in $L_p({\mathbb R}^2)$ ($0<p\le\infty$) from hierarchical sequences of stable local bases consisting of differentiable (i.e., $C^r$ with $r\ge1$) piecewise ...

Surface plasmon–polaritons' contribution to the specific heat of quasiperiodic GaAs/SiO2 structures

It is quite interesting that the energy spectra of a variety of collective modes on quasiperiodic structures, exhibit a complex fractal profile due to the underlying long range order induced by the specific deterministic sequences used to build them up. In order to have a deep insight on the relevant thermodynamic implications of the above mentioned long range order, we have performed analytical and numerical calculations of the surface plasmon–polariton's contribution to the specific heat associated with successive hierarchical sequences of quasiperiodic Fibonacci structures. They can be traced back to the surface plasmon–polariton's self-similar energy spectra. We consider the building blocks, used to set up these structures, as the semiconductor GaAs and the insulator SiO2. At the interfaces there is a two-dimensional electron gas, modeled due to the presence of a surface density of current. We have also calculated the specific heat at the two temperature limit cases, namely when T goes to zero and infinity.

Spin wave specific heat in quasiperiodic Fibonacci structures

The energy spectra of a variety of collective modes on quasiperiodic structures exhibit a complex fractal profile. Among the modes that have attracted particular attention in this context are the spin wave spectra of quasiperiodic magnetic multilayers that obey a substitutional sequence of the Fibonacci type. They are described within the framework of the Heisenberg theory. In order to have a deep insight on the relevant thermodynamical implications of the above mentioned energy spectra's fractal profile, we have performed analytical and numerical calculations of the spin wave specific heat associated with successive hierarchical sequences of the Fibonacci quasiperiodic structures. The spectra show interesting oscillatory behavior in the low-temperature region, which can be traced back to the spin wave's self-similar energy spectrum.

A Facies Model for a Quaternary Hierarchical Depositional Sequences in the Niigata Basin, Central Japan

Dialectic prediction of reservoir distribution using conceptual facies models is one of the most direct techniques in petroleum exploration for reducing uncertainties about the factors in a petroleum system. If reservoir distribution could be predicted logically on the basis of genetics of strata and sedimentary processes with improved accuracy, then previously discovered petroleum systems might be reconsidered as future objectives of subtle entrapments. In this study a fourth-order facies model was constructed for Quaternary of the Niigata Basin within a back-arc setting, based on the concept of sequence stratigraphy.A progradational type fourth-order depositional sequence is subdivided into the following four systems tracts, which are defined by their morphologies and benthic foraminiferal faunas: (1) regressive progradational wedge systems tract (RPW), consisting of a forced-regressive strandplain system and associated depositional systems, (2) lowstand stable progradational wedge systems tract (LPW), consisting mainly of an incised-valley fill braidplain delta system and associated systems, (3) transgressive aggradational sheet systems tract (TAS), consisting of a filled-estuary system and associated depositional systems, and (4) highstand stable progradational wedge systems tract (HPW), consisting of a fluvial-dominated delta system and associated systems.The results of this study demonstrate the effectiveness of sequence stratigraphic approaches and provide useful examples of occurrence, development, and sedimentary facies distribution for the prograding coasts in active margin basins. The development of such facies models improves our ability to predict the presence of undetected sandstone reservoirs, which is one of the most important factors of petroleum systems.

Two Perturbation Calculations in Fluid Mechanics using Large-expression Management

Two fluid-flow problems are solved using perturbation expansions, with special emphasis on the reduction of intermediate expression swell. This is done by developing tools in Maple that contribute to the efficient representation and manipulation of large expressions. The tools share a common basis, which is the creation of a hierarchy of representation levels such that expressions located at higher levels are expressed using entries from lower levels. The evaluation of higher-level expressions by the algebra system does not proceed recursively to the lowest level, as would ordinarily be the case, but instead can be directly controlled by the user.The first fluid-flow problem, arising in lubrication theory, is solved by implementing a technique of switch-controlled evaluation. The processes of simplification and evaluation are controlled at each level by user-manipulated switches. A perturbation solution is derived semi-interactively with the switch-controlled evaluation being used to reduce the size of intermediate expressions. The second fluid problem, in convection, is solved by extending a perturbation series in several variables to high order by implementing techniques for the automatic generation of hierarchical expression sequences.

Age differences in anticipating hierarchical rule-based sequences

Age differences in anticipating hierarchical rule-based sequences

Critical behavior of hierarchical Ising models.

We consider the critical behavior of two-dimensional layered Ising models where the exchange couplings between neighboring layers follow hierarchical sequences. The perturbation caused by the non-periodicity could be irrelevant, relevant or marginal. For marginal sequences we have performed a detailed study, which involved analytical and numerical calculations of different surface and bulk critical quantities in the two-dimensional classical as well as in the one-dimensional quantum version of the model. The critical exponents are found to vary continuously with the strength of the modulation, while close to the critical point the system is essentially anisotropic: the correlation length is diverging with different exponents along and perpendicular to the layers.

An object-oriented library for hierarchical animation sequences

A library for generating 3D graphics and animation sequences is presented, with the following features: (1) support for coordinated animation among arbitrarily-nested graphic segments, where animation may be specified with respect to an independent coordinate system within each nested segment; (2) support for time-based simulation; (3) support for multiple viewpoints and multiple display windows; (4) an object-oriented structure (using a "camera-projector" metaphor) providing an easy programming interface and extensibility; (5) encapsulation of machine-dependencies into alternative Screen classes, for portability among several platforms (presently Macintosh, PC-compatible, and X Window System). The library has been used by undergraduate students to program complex animation sequences. It presently supports only color 2D and 3D wireframe graphics, but may be extended to include light sources and rendering alternatives. The C++ source code has been placed in the public domain.

Timing and chunking in processing temporal order

A computational framework of learning, recognition and reproduction of temporal sequences are provided, based on an interference theory of forgetting in short-term memory (STM), modelled as a network of neural units with mutual inhibition. The STM model provides information for recognition and reproduction of arbitrary temporal sequences. Sequences are acquired by a new learning rule, the attentional learning rule, which combines Hebbian learning and a normalization rule with sequential system activation. Acquired sequences can be recognized without being affected by speed of presentation or certain distortions in symbol form. Different layers of the STM model can be naturally constructed in a feedforward manner to recognize hierarchical sequences, significantly expanding the model's capability in a way similar to human information chunking. A model of sequence reproduction is presented that consists of two reciprocally connected networks, one of which behaves as a sequence recognizer. Reproduction of complex sequences can maintain interval lengths of sequence components, and vary the overall speed. A mechanism of degree self-organization based on a global inhibitor is proposed for the model to learn required context lengths in order to disambiguate associations in complex sequence reproduction. Certain implications of the model are discussed at the end of the paper.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

All the World Is Not a Stage: Emerging Contextualist Themes in Counseling and Development

Classical stage‐based theories of human development, drawn from organismic worldviews, possess many shortcomings when extended to counseling applications. In attempting to reduce development to linear, hierarchical sequences, these theories fail to account for the interactional nature of change processes and implicitly pathologize developmental diversity. Responding to these shortcomings, counselors are turning to contextualist models of development that emphasize process over outcome. In this article I review key assumptions of contextualism, as embodied in social role theory and the life‐span developmental tradition, highlighting relevant theory and research. I propose that two vital forces within current counseling—constructivism and interactional counseling—are animated by contextualist notions of development. Specific implications of contextualism for future counseling research and practice are outlined.