Hierarchy Of Operators Research Articles

Through-space and through-bridge interactions in the correlation analysis of chemical bonds

The formalism of the through-space and through-bridge communications proposed by Nalewajski within the framework of the Orbital Communication Theory is used to evaluate the correlation effect between electron populations of two chemical bonds. Proposed in this paper purely-probabilistic formalism defines the correlation between two chemical bonds as determined by the difference between appropriately normalized fourth-order joint probabilities corresponding to direct (through-space) and indirect (through-bridge) communication within a four-state time-homogeneous Markov chain. Alternative bond-correlation coefficient introduced earlier by Yamasaki and Goddard is based on the concept of the hierarchy of statistical covariance operators. The proposed correlation coefficient requires computing only the second-order probability terms when working within the condensed-atomic resolution and thus they are far less computationally expensive making them suitable for correlation analysis of chemical interactions between large molecular fragments.

Performance Evaluation of Agritainment Service Supply Chain

This paper puts forward the index system of evaluating performance of agritainment supply chain from three attribute domains, i.e. operation domain, hierarchy domain and composition domain, uses entropy technology and analytic hierarchy process to carry on the evaluation of service performance and probes into the application of agritainment supply chain theory in practice. It is quite important on enhancing the competitive power of the whole agritainment supply chain as well as the node enterprises in the agritainment supply chain. Finally, three problems that need further study in this field are pointed out.

‘The lowest rung’: Women room attendants’ perceptions of five star hotels’ operational hierarchies’

Hotel room attendants play a significant role in the overall performance and success of hotels. This study presents women room attendants’ perspectives of working in what they perceive is the lowest level of a hotel's operational hierarchy, and their experience of the power relationships inherent in these bureaucratic structures. A qualitative, constructionist grounded theory methodology was used, underpinned by a socialist-feminist, critical theory epistemology. Interviews were conducted with 46 room attendants from five ‘five-star’ hotels on the Gold Coast region of South East Queensland, Australia. Emerging from this study was the conceptualization of women room attendants’ daily work experiences at the lowest level of the operational hierarchy. Despite their conspicuous presence, women room attendants perceive themselves as near invisible through non-acknowledgement by hotel management and other staff due to their position at the lowest level of the operational hierarchy. This article contributes to theoretical research on employment experiences in hospitality, particularly on hotel operational praxis and methodologically presents the perceptions of women room attendants through embodiment of their particular voices.

On Provability Logics with Linearly Ordered Modalities

We introduce the logics GLP Λ, a generalization of Japaridze’s polymodal provability logic GLP ω where Λ is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall provide a reduction of these logics to GLP ω yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP Λ and the decidability of GLP Λ for recursive orderings Λ. Further, we give a restricted axiomatization of the variable-free fragment of GLP Λ.

Scaling and hierarchies of wave motion in solids

AbstractThe concept of wave hierarchies in the Whitham's sense is generalized to hierarchies of second order wave operators. Based on Mindlin's model of microstructured solids, the scaling procedure is described and the corresponding hierarchical equation derived which includes two wave operators. It is shown that waves in the Cosserat' medium are described by a similar hierarchical equation. These results are generalized to a multiscale case (a scale within a scale) and to nonlinear media. It is shown also how to construct hierarchies for waves in elastic ferroelectrics. The results obtained by Scott for hierarchies in thermoelasticity are presented in the similar framework. Finally, the cases with first order wave operators are described.

Simultaneous analysis of non-strange negative parity baryon properties in large Nc QCD

Non-strange excited baryons are analyzed within the Large QCD framework. The Large approach is used as an effective theory to simultaneously fit the masses and decays with corrections up to . Values of the mixing angles for the and nucleon mass eigenstates are obtained within the simultaneous analysis. The observed effective operator hierarchy is consistent with the previous studies conducted in this sector and improved results are obtained. DOI: http://dx.doi.org/10.4038/sljp.v13i2.5443 Sri Lankan Journal of Physics, Vol. 13 ( 2 ) ( 2012 ) 27 - 38

Microstructured continua and scaling for wave motion

This paper deals with wave motion in microstructured solids. A short introduction explains how the basic mathematical models for description of microstructure(s) of solids are derived. Based on the Mindlin-type micromorphic theory, the governing equations for wave motion in such solids are presented in one-dimensional setting. The focus of the paper is in explaining the importance of internal scales in microstructured solids. It is shown that the proper scaling permits to construct the mathematical models which involve hierarchies of wave operators. Depending on the scale parameter (the ratio of an internal scale over the wave length), the various operators govern the wave propagation. The main case analysed here consists of the second-order operators but the first-order operators which are characteristic to evolution equations, are also briefly explained.

T-to-C movement: syntactic licensing and dialectal variation

This paper intends to extend and elaborate the line of research initiated by Pesetsky and Torrego (2001, 2004) on the role of Tense as a licensing condition over phrasal extraction. In the context of the operation of CP-raising, it re-interprets some instances of T-to-C movement as having not a licensing but a blocking effect over CP-extraction. T-to-C Movement then is analysed as part of an integral operational cycle of gradual saturation comprizing head movement as well as head-agreement. This extended paradigm is analyzed as various degrees of operational completeness, correponding to degrees of "specificity". Within this operational hierarchy of featural specificity resides the mechanism that "opens" or "closes" the syntactic path for phrasal movement to apply. Drawing on data from Belfast English, it is observed that dialectal variation takes place on particular points that lie lower in this hierarchy, in other words at a derivational point of operational "under-specification".

Movimento de T para C: Licenciamento sintático e variação dialectal

This paper intends to extend and elaborate the line of research initiated by Pesetsky and Torrego (2001, 2004) on the role of Tense as a licensing condition over phrasal extraction. In the context of the operation of CP-raising, it re-interprets some instances of T-to-C movement as having not a licensing but a blocking effect over CP-extraction. T-to-C Movement then is analysed as part of an integral operational cycle of gradual saturation comprizing head movement as well as head-agreement. This extended paradigm is analyzed as various degrees of operational completeness, correponding to degrees of “specificity”. Within this operational hierarchy of featural specificity resides the mechanism that “opens” or “closes” the syntactic path for phrasal movement to apply. Drawing on data from Belfast English, it is observed that dialectal variation takes place on particular points that lie lower in this hierarchy, in other words at a derivational point of operational “under-specification”.

The μ-Calculus Alternation Hierarchy Collapses over Structures with Restricted Connectivity

It is known that the alternation hierarchy of least and greatest fixpoint operators in the mu-calculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of structures. A prominent instance is the class of infinite words over which the alternation-free fragment is already as expressive as the full mu-calculus. Our current understanding of when and why the mu-calculus alternation hierarchy is not strict is limited. This paper makes progress in answering these questions by showing that the alternation hierarchy of the mu-calculus collapses to the alternation-free fragment over some classes of structures, including infinite nested words and finite graphs with feedback vertex sets of a bounded size. Common to these classes is that the connectivity between the components in a structure from such a class is restricted in the sense that the removal of certain vertices from the structure's graph decomposes it into graphs in which all paths are of finite length. Our collapse results are obtained in an automata-theoretic setting. They subsume, generalize, and strengthen several prior results on the expressivity of the mu-calculus over restricted classes of structures.

Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. Rather than focusing on constructing exactly the stochastic trajectories, our approach relies on approximating the evolution of observables, such as density, coverage, correlations and so on. More specifically, we develop a spatial domain decomposition of the Markov operator (generator) that describes the evolution of all observables according to the kinetic Monte Carlo algorithm. This domain decomposition corresponds to a decomposition of the Markov generator into a hierarchy of operators and can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). Based on this operator decomposition, we formulate parallel Fractional step kinetic Monte Carlo algorithms by employing the Trotter Theorem and its randomized variants; these schemes, (a) are partially asynchronous on each fractional step time-window, and (b) are characterized by their communication schedule between processors.The proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules. We carry out a detailed benchmarking of the parallel KMC schemes using available exact solutions, for example, in Ising-type systems and we demonstrate the capabilities of the method to simulate complex spatially distributed reactions at very large scales on GPUs. Finally, we discuss work load balancing between processors and propose a re-balancing scheme based on probabilistic mass transport methods.

A Self-Learning Algebraic Multigrid Method for Extremal Singular Triplets and Eigenpairs

A self-learning algebraic multigrid method for dominant and minimal singular triplets and eigenpairs is described. The method consists of two multilevel phases. In the first, multiplicative phase (setup phase), tentative singular triplets are calculated along with a multigrid hierarchy of interpolation operators that approximately fit the tentative singular vectors in a collective and self-learning manner, using multiplicative update formulas. In the second, additive phase (solve phase), the tentative singular triplets are improved up to the desired accuracy by using an additive correction scheme with fixed interpolation operators, combined with a Ritz update. A suitable generalization of the singular value decomposition is formulated that applies to the coarse levels of the multilevel cycles. The proposed algorithm combines and extends two existing multigrid approaches for symmetric positive definite eigenvalue problems to the case of dominant and minimal singular triplets. Numerical tests on model probl...

Selected new developments in vibrational structure theory: potential construction and vibrational wave function calculations

This perspective addresses selected recent developments in the theoretical calculation of vibrational spectra, energies, wave functions and properties. The theoretical foundation and recently developed computational protocols for constructing hierarchies of vibrational Hamiltonian operators are reviewed. A many-mode second quantization (SQ) formulation is discussed prior to the discussion of anharmonic wave functions. Emphasis is put on vibrational self-consistent field (VSCF) based methods and in particular vibrational coupled cluster (VCC) theory. Other issues are also reviewed briefly, such as inclusion of thermal effects, response theoretical calculation of spectra, and the difficulty in treating dense spectra.

Flavour structure of R-violating neutralino decays at the LHC

We study signatures of R-parity violation in the production of supersymmetric particles at the LHC, and the subsequent decay of the lightest neutralino being the end product of a supersymmetric cascade decay. In doing so, we pay particular attention to the possible flavour structure of the operators, and how one may discriminate between different possibilities. A neutralino LSP would couple to all quarks and leptons and a comparative study of its decays provides an optimal channel for the simultaneous study of all 45 R-violating operators. By studying the expected signals from all these operators, we demonstrate the ability to understand whether more than one coupling dominates, and to map the experimental signatures to operator hierarchies that can then be compared against theoretical models of flavour. Detailed comparisons with backgrounds, including those from MSSM cascade decays are made, using the PYTHIA event simulator.

9.6.2 INTEGRATION OF OPERATIONS IN PROCESS SYSTEMS: COMPLEXITY AND EMERGENT PROPERTIES

AbstractThe problem of system Integration in the context of an Industrial Enterprise is a multidimensional problem with fundamental dimensions those of: (i) Purpose, goals and objectives, (ii) Overall process operations, (ii) Overall System Design/Redesign, (iii) Information, Data and Software, and (iv) Verification, validation and assurance. Each of the above areas is addressed by respective groups which consider their area as representing the entirety of the problem and they frequently ignore the other important dimensions. The aim of this paper is to consider first the general problem of integration from all its fundamental aspects and focus on the key paradigm of Global Operations. Within this area we consider the issues of system organization and in particular the problems relating to hierarchical organization of the different operational functionalities, the issues of aggregation and disaggregation and the related problems of the “top‐down” and “bottom up” approaches. System complexity is considered within this framework and the notion of emergent properties is then considered as a problem of aggregation of behaviours, which may be also seen as projections within the setup of a control and information architecture. Such an architecture is defined for the multi‐level hierarchical organisational structure that we consider. We show that systems and control concepts and problems play a central role the development of an overall integration methodology and interpreting the features of the different emergent properties. The subject of modelling emerges with a central role in the effort to develop a methodology for systems integration, as well as quantifying the predictors of relevant emergent properties. The approach introduced here is intimately linked to Multilevel hybrid systems (Hierarchy of Operations), and provides a complementary dimension to issues of System Design (and Re‐design) dominated by the theory of Structure Evolving systems [10] (in the total Design and Life‐cycle analysis) emerges as the central approach. This paper provides an overview of the subject area and focuses on the development of the general conceptual framework for integration. We additionally develop and propose a systems framework for the evolutionary integration in this paper.

On-the-Fly Adaptive Smoothed Aggregation Multigrid for Markov Chains

A new adaptive algebraic multigrid scheme is developed for the solution of Markov chains, where the hierarchy of operators is adapted on-the-fly in a setup process that is interlaced with the solution process. The setup process feeds the solution process with improved operators, while the solution process provides the adaptive setup process with better approximations on which to base further-improved operators. The approach is demonstrated using Petrov-Galerkin smoothed aggregation where only the prolongation operator is smoothed, while the restriction remains of low order. Results show that the on-the-fly adaptive scheme can improve the performance of multigrid solvers that require extensive setup computations, in both serial and parallel environments.

Explaining the Origin of Life is not Enough for a Definition of Life

The comments focus on a presumed circular reasoning in the operator hierarchy and the necessity of understanding life’s origin for defining life. Below it is shown that its layered structure prevents the operator hierarchy from circular definitions. It is argued that the origin of life is an insufficient basis for a definition of life that includes multicellular and neural network organisms.

Editing operations for irregular vertices in triangle meshes

We describe an interactive editing framework that provides control over the type, location, and number of irregular vertices in a triangle mesh. We first provide a theoretical analysis to identify the simplest possible operations for editing irregular vertices and then introduce a hierarchy of editing operations to control the type, location, and number of irregular vertices. We demonstrate the power of our editing framework with an example application in pattern design on surfaces.

Conditional symmetries for systems of PDEs: new definitions and their application for reaction–diffusion systems

New definitions of Q-conditional symmetry for systems of PDEs are presented, which generalize the standard notation of non-classical (conditional) symmetry. It is shown that different types of Q-conditional symmetry of a system generate a hierarchy of conditional symmetry operators. A class of two-component nonlinear reaction–diffusion systems is examined to demonstrate the applicability of the definitions proposed and it is shown when different definitions of Q-conditional symmetry lead to the same operators.

Mind operational semantics and brain operational architectonics: a putative correspondence.

Despite allowing for the unprecedented visualization of brain functional activity, modern neurobiological techniques have not yet been able to provide satisfactory answers to important questions about the relationship between brain and mind. The aim of this paper is to show how two different but complementary approaches, Mind Operational Semantics (OS) and Brain Operational Architectonics (OA), can help bridge the gap between a specific kind of mental activity—the higher-order reflective thought or linguistic thought—and brain. The fundamental notion that allows the two different approaches to be jointly used under a common framework is that of operation. According to OS, which is based on introspection and linguistic data, the meanings of words can be analyzed in terms of elemental mental operations (EOMC), amongst which those of attention play a key role. Linguistic thought is made possible by special kinds of elements, which OS calls “correlators”, which have the function of tying together the other elements of thought, which OS calls “correlata” (a "correlational network” that is, a sentence, is so formed). Therefore, OS conceives of linguistic thought as a hierarchy of operations of increasing complexity. Likewise, according to OA, which is based on the joint analysis of cognitive and electromagnetic data (EEG and MEG), every conscious phenomenon is brought to existence by the joint operations of many functional and transient neuronal assemblies in the brain. According to OA, the functioning of the brain is always operational (made up of operations), and its structure is characterized by a hierarchy of operations of increasing complexity: single neurons, single assemblies of neurons, synchronized neuronal assemblies or Operational Modules (OM), integrated or complex OMs. The authors put forward the hypothesis that the whole level of OS’s description (EOMC, correlators, and correlational networks) corresponds to the level of OMs (or set of them) of different complexity within OA’s theory: EOMC could correspond to simple OMs, correlators to complex OMs and the correlational network to a set of simple and complex OMs. Finally, a set of experiments is proposed to verify the putative correspondence between OS and OA and prove the existence of an integrated continuum between brain and mind.