Continuous limits for an integrable coupling system of Toda equation hierarchy

Energy Technology Data Exchange (ETDEWEB)

Li Li [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China); Yu Fajun, E-mail: yfajun@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)

2009-09-21

In this Letter, we present an integrable coupling system of lattice hierarchy and its continuous limits by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, the integrable coupling system of Toda lattice hierarchy is derived. It is shown that a new complex lattice spectral problem converges to the integrable couplings of discrete soliton equation hierarchy, which has the integrable coupling system of C-KdV hierarchy as a new kind of continuous limit.

Solving Non-Isospectral mKdV Equation and Sine-Gordon Equation Hierarchies with Self-Consistent Sources via Inverse Scattering Transform

International Nuclear Information System (INIS)

Li Qi; Zhang Dajun; Chen Dengyuan

2010-01-01

N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources and the hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse scattering transform. (general)

Hamiltonian structures and integrability for a discrete coupled KdV-type equation hierarchy

International Nuclear Information System (INIS)

Zhao Haiqiong; Zhu Zuonong; Zhang Jingli

2011-01-01

Coupled Korteweg-de Vries (KdV) systems have many important physical applications. By considering a 4 × 4 spectral problem, we derive a discrete coupled KdV-type equation hierarchy. Our hierarchy includes the coupled Volterra system proposed by Lou et al. (e-print arXiv: 0711.0420) as the first member which is a discrete version of the coupled KdV equation. We also investigate the integrability in the Liouville sense and the multi-Hamiltonian structures for the obtained hierarchy. (authors)

Conservation laws and self-consistent sources for a super-CKdV equation hierarchy

International Nuclear Information System (INIS)

Li Li

2011-01-01

From the super-matrix Lie algebras, we consider a super-extension of the CKdV equation hierarchy in the present Letter, and propose the super-CKdV hierarchy with self-consistent sources. Furthermore, we establish the infinitely many conservation laws for the integrable super-CKdV hierarchy.

Conservation laws and self-consistent sources for a super-CKdV equation hierarchy

Energy Technology Data Exchange (ETDEWEB)

Li Li, E-mail: li07099@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)

2011-03-14

From the super-matrix Lie algebras, we consider a super-extension of the CKdV equation hierarchy in the present Letter, and propose the super-CKdV hierarchy with self-consistent sources. Furthermore, we establish the infinitely many conservation laws for the integrable super-CKdV hierarchy.

From nonlinear Schrödinger hierarchy to some (2+1)-dimensional nonlinear pseudodifferential equations

Science.gov (United States)

Yang, Xiao; Du, Dianlou

2010-08-01

The Poisson structure on CN×RN is introduced to give the Hamiltonian system associated with a spectral problem which yields the nonlinear Schrödinger (NLS) hierarchy. The Hamiltonian system is proven to be Liouville integrable. Some (2+1)-dimensional equations including NLS equation, Kadomtesev-Petviashvili I (KPI) equation, coupled KPI equation, and modified Kadomtesev-Petviashvili (mKP) equation, are decomposed into Hamilton flows via the NLS hierarchy. The algebraic curve, Abel-Jacobi coordinates, and Riemann-Jacobi inversion are used to obtain the algebrogeometric solutions of these equations.

Transformations of solutions for equations and hierarchies of pseudo-spherical type

CERN Document Server

Reyes, E G

2003-01-01

It is known that if an equation describes non-trivial one-parameter families of pseudo-spherical surfaces, its conservation laws, (generalized, nonlocal) symmetries and Baecklund transformations can be studied by geometrical means [4, 10]. In this letter it is pointed out that there exist correspondences, or 'generalized Baecklund transformations', between arbitrary solutions (satisfying some genericity conditions) of any two single equations describing pseudo-spherical surfaces. Then, the notion of a hierarchy of equations of pseudo-spherical type is introduced, and a theorem stating that there also exist correspondences between arbitrary solutions of any two such hierarchies is presented. A full account of these results appears elsewhere [12, 13]. (letter to the editor)

Initial states in integrable quantum field theory quenches from an integral equation hierarchy

Directory of Open Access Journals (Sweden)

D.X. Horváth

2016-01-01

Full Text Available We consider the problem of determining the initial state of integrable quantum field theory quenches in terms of the post-quench eigenstates. The corresponding overlaps are a fundamental input to most exact methods to treat integrable quantum quenches. We construct and examine an infinite integral equation hierarchy based on the form factor bootstrap, proposed earlier as a set of conditions determining the overlaps. Using quenches of the mass and interaction in Sinh-Gordon theory as a concrete example, we present theoretical arguments that the state has the squeezed coherent form expected for integrable quenches, and supporting an Ansatz for the solution of the hierarchy. Moreover we also develop an iterative method to solve numerically the lowest equation of the hierarchy. The iterative solution along with extensive numerical checks performed using the next equation of the hierarchy provides a strong numerical evidence that the proposed Ansatz gives a very good approximation for the solution.

Initial states in integrable quantum field theory quenches from an integral equation hierarchy

Energy Technology Data Exchange (ETDEWEB)

Horváth, D.X., E-mail: esoxluciuslinne@gmail.com [MTA-BME “Momentum” Statistical Field Theory Research Group, Budafoki út 8, 1111 Budapest (Hungary); Department of Theoretical Physics, Budapest University of Technology and Economics, Budafoki út 8, 1111 Budapest (Hungary); Sotiriadis, S., E-mail: sotiriad@sissa.it [SISSA and INFN, Via Bonomea 265, 34136 Trieste (Italy); Takács, G., E-mail: takacsg@eik.bme.hu [MTA-BME “Momentum” Statistical Field Theory Research Group, Budafoki út 8, 1111 Budapest (Hungary); Department of Theoretical Physics, Budapest University of Technology and Economics, Budafoki út 8, 1111 Budapest (Hungary)

2016-01-15

We consider the problem of determining the initial state of integrable quantum field theory quenches in terms of the post-quench eigenstates. The corresponding overlaps are a fundamental input to most exact methods to treat integrable quantum quenches. We construct and examine an infinite integral equation hierarchy based on the form factor bootstrap, proposed earlier as a set of conditions determining the overlaps. Using quenches of the mass and interaction in Sinh-Gordon theory as a concrete example, we present theoretical arguments that the state has the squeezed coherent form expected for integrable quenches, and supporting an Ansatz for the solution of the hierarchy. Moreover we also develop an iterative method to solve numerically the lowest equation of the hierarchy. The iterative solution along with extensive numerical checks performed using the next equation of the hierarchy provides a strong numerical evidence that the proposed Ansatz gives a very good approximation for the solution.

Quasiclassical deformation in KP hierarchy and Benney's long wave equations

International Nuclear Information System (INIS)

Kolokol'tsov, V.N.; Lebedev, D.R.

1987-01-01

In the paper by means of the formal variant of Zakharov-Shabat ''dressing'' method various formulas are obtained for the generating functions of the conservation laws of Kadomtsev-Petvias hierarchy which turn into analogous formulas for Benney hierarchy in the quasiclassical limit. The generating fucntion of the conservation laws of Miura type is constructed for higher Benney equations and the simple proof of the related identities is given

A trick loop algebra and a corresponding Liouville integrable hierarchy of evolution equations

International Nuclear Information System (INIS)

Zhang Yufeng; Xu Xixiang

2004-01-01

A subalgebra of loop algebra A-bar 2 is first constructed, which has its own special feature. It follows that a new Liouville integrable hierarchy of evolution equations is obtained, possessing a tri-Hamiltonian structure, which is proved by us in this paper. Especially, three symplectic operators are constructed directly from recurrence relations. The conjugate operator of a recurrence operator is a hereditary symmetry. As reduction cases of the hierarchy presented in this paper, the celebrated MKdV equation and heat-conduction equation are engendered, respectively. Therefore, we call the hierarchy a generalized MKdV-H system. At last, a high-dimension loop algebra G-bar is constructed by making use of a proper scalar transformation. As a result, a type expanding integrable model of the MKdV-H system is given

New Positive and Negative Hierarchies of Integrable Differential-Difference Equations and Conservation Laws

International Nuclear Information System (INIS)

Li Xinyue; Zhao Qiulan

2009-01-01

Two hierarchies of nonlinear integrable positive and negative lattice equations are derived from a discrete spectral problem. The two lattice hierarchies are proved to have discrete zero curvature representations associated with a discrete spectral problem, which also shows that the positive and negative hierarchies correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. Moreover, the integrable lattice models in the positive hierarchy are of polynomial type, and the integrable lattice models in the negative hierarchy are of rational type. Further, we construct infinite conservation laws about the positive hierarchy.

A new hierarchy of generalized derivative nonlinear Schroedinger equations, its bi-Hamiltonian structure and finite-dimensional involutive system

International Nuclear Information System (INIS)

Yan, Z.; Zhang, H.

2001-01-01

In this paper, an isospectral problem and one associated with a new hierarchy of nonlinear evolution equations are presented. As a reduction, a representative system of new generalized derivative nonlinear Schroedinger equations in the hierarchy is given. It is shown that the hierarchy possesses bi-Hamiltonian structures by using the trace identity method and is Liouville integrable. The spectral problem is non linearized as a finite-dimensional completely integrable Hamiltonian system under a constraint between the potentials and spectral functions. Finally, the involutive solutions of the hierarchy of equations are obtained. In particular, the involutive solutions of the system of new generalized derivative nonlinear Schroedinger equations are developed

A generalized Zakharov-Shabat equation with finite-band solutions and a soliton-equation hierarchy with an arbitrary parameter

International Nuclear Information System (INIS)

Zhang Yufeng; Tam, Honwah; Feng Binlu

2011-01-01

Highlights: → A generalized Zakharov-Shabat equation is obtained. → The generalized AKNS vector fields are established. → The finite-band solution of the g-ZS equation is obtained. → By using a Lie algebra presented in the paper, a new soliton hierarchy with an arbitrary parameter is worked out. - Abstract: In this paper, a generalized Zakharov-Shabat equation (g-ZS equation), which is an isospectral problem, is introduced by using a loop algebra G ∼ . From the stationary zero curvature equation we define the Lenard gradients {g j } and the corresponding generalized AKNS (g-AKNS) vector fields {X j } and X k flows. Employing the nonlinearization method, we obtain the generalized Zhakharov-Shabat Bargmann (g-ZS-B) system and prove that it is Liouville integrable by introducing elliptic coordinates and evolution equations. The explicit relations of the X k flows and the polynomial integrals {H k } are established. Finally, we obtain the finite-band solutions of the g-ZS equation via the Abel-Jacobian coordinates. In addition, a soliton hierarchy and its Hamiltonian structure with an arbitrary parameter k are derived.

On the hierarchy of partially invariant submodels of differential equations

Energy Technology Data Exchange (ETDEWEB)

Golovin, Sergey V [Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk 630090 (Russian Federation)], E-mail: sergey@hydro.nsc.ru

2008-07-04

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

On the hierarchy of partially invariant submodels of differential equations

Science.gov (United States)

Golovin, Sergey V.

2008-07-01

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

On the hierarchy of partially invariant submodels of differential equations

International Nuclear Information System (INIS)

Golovin, Sergey V

2008-01-01

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given

Algebraic models for the hierarchy structure of evolution equations at small x

International Nuclear Information System (INIS)

Rembiesa, P.; Stasto, A.M.

2005-01-01

We explore several models of QCD evolution equations simplified by considering only the rapidity dependence of dipole scattering amplitudes, while provisionally neglecting their dependence on transverse coordinates. Our main focus is on the equations that include the processes of pomeron splittings. We examine the algebraic structures of the governing equation hierarchies, as well as the asymptotic behavior of their solutions in the large-rapidity limit

Baecklund transformation of the noncommutative Gelfand-Dickey hierarchy

International Nuclear Information System (INIS)

Zheng Zhong; He Jingsong; Cheng Yi

2004-01-01

We study the Baecklund transformation of the noncommutative Gelfand-Dickey(ncGD) hierarchy. By factorizing its Lax operator into the multiplication form of first order differential operator, the noncommutative modified KdV(ncMKdV) hierarchy and the Miura transformations are defined. Our results show that the ncMKdV equations are invariant under the cyclic permutation, and hence induces the Baecklund transformation of the ncGD hierarchy. (author)

From BBGKY hierarchy to non-Markovian evolution equations

International Nuclear Information System (INIS)

Gerasimenko, V.I.; Shtyk, V.O.; Zagorodny, A.G.

2009-01-01

The problem of description of the evolution of the microscopic phase density and its generalizations is discussed. With this purpose, the sequence of marginal microscopic phase densities is introduced, and the appropriate BBGKY hierarchy for these microscopic distributions and their average values is formulated. The microscopic derivation of the generalized evolution equation for the average value of the microscopic phase density is given, and the non-Markovian generalization of the Fokker-Planck collision integral is proposed

Integrable Hierarchy of the Quantum Benjamin-Ono Equation

Directory of Open Access Journals (Sweden)

Maxim Nazarov

2013-12-01

Full Text Available A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables x_1,x_2,…. This construction provides explicit expressions for the Hamiltonians in terms of the power sum symmetric functions p_n=x^n_1+x^n_2+⋯ and is based on our recent results from [Comm. Math. Phys. 324 (2013, 831-849].

Extension of noncommutative soliton hierarchies

International Nuclear Information System (INIS)

Dimakis, Aristophanes; Mueller-Hoissen, Folkert

2004-01-01

A linear system, which generates a Moyal-deformed two-dimensional soliton equation as an integrability condition, can be extended to a three-dimensional linear system, treating the deformation parameter as an additional coordinate. The supplementary integrability conditions result in a first-order differential equation with respect to the deformation parameter, the flow of which commutes with the flow of the deformed soliton equation. In this way, a deformed soliton hierarchy can be extended to a bigger hierarchy by including the corresponding deformation equations. We prove the extended hierarchy properties for the deformed AKNS hierarchy, and specialize to the cases of deformed NLS, KdV and mKdV hierarchies. Corresponding results are also obtained for the deformed KP hierarchy. A deformation equation determines a kind of Seiberg-Witten map from classical solutions to solutions of the respective 'noncommutative' deformed equation

Constraints and Soliton Solutions for KdV Hierarchy and AKNS Hierarchy

International Nuclear Information System (INIS)

Li Nianhua; Li Yuqi

2011-01-01

It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair, from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed. A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations (ODEs), which may be gotten by a simple but unfamiliar Lax pair. Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies. The key is a special form of Lax pair for the AKNS hierarchy. It is proved that under the constraints all equations of the AKNS hierarchy are linearizable. (general)

The multicomponent (2+1)-dimensional Glachette–Johnson (GJ) equation hierarchy and its super-integrable coupling system

International Nuclear Information System (INIS)

Yu Fajun; Zhang Hongqing

2008-01-01

This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra à M . By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent (2+1)-dimensional Glachette–Johnson (GJ) hierarchy is given. Finally, the super-integrable coupling system of multicomponent (2+1)-dimensional GJ hierarchy is established through enlarging the spectral problem

New integrable lattice hierarchies

International Nuclear Information System (INIS)

Pickering, Andrew; Zhu Zuonong

2006-01-01

In this Letter we give a new integrable four-field lattice hierarchy, associated to a new discrete spectral problem. We obtain our hierarchy as the compatibility condition of this spectral problem and an associated equation, constructed herein, for the time-evolution of eigenfunctions. We consider reductions of our hierarchy, which also of course admit discrete zero curvature representations, in detail. We find that our hierarchy includes many well-known integrable hierarchies as special cases, including the Toda lattice hierarchy, the modified Toda lattice hierarchy, the relativistic Toda lattice hierarchy, and the Volterra lattice hierarchy. We also obtain here a new integrable two-field lattice hierarchy, to which we give the name of Suris lattice hierarchy, since the first equation of this hierarchy has previously been given by Suris. The Hamiltonian structure of the Suris lattice hierarchy is obtained by means of a trace identity formula

Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation

International Nuclear Information System (INIS)

Konopelchenko, B; Alonso, L MartInez; Medina, E

2010-01-01

It is shown that the hodograph solutions of the dispersionless coupled KdV (dcKdV) hierarchies describe critical and degenerate critical points of a scalar function which obeys the Euler-Poisson-Darboux equation. Singular sectors of each dcKdV hierarchy are found to be described by solutions of higher genus dcKdV hierarchies. Concrete solutions exhibiting shock-type singularities are presented.

On self-dual Yang-Mills hierarchy

International Nuclear Information System (INIS)

Nakamura, Yoshimasa

1989-01-01

In this note, motivated by the Kadomtsev-Petviashvili (KP) hierarchy of integrable nonlinear evolution equations, a GL(n,C) self-dual Yang-Mills (SDYM) hierarchy is presented; it is an infinite system of SDYM equations having an infinite number of independent variables and being outside of the KP hierarchy. A relationship between the KP hierarchy and the SDYM hierarchy is discussed. It is also shown that GL(∞) SDYM equations introduced in this note are reduced to the GL(n,C) SDYM hierarchy by imposing an algebraic constraint. (orig.)

IT vendor selection model by using structural equation model & analytical hierarchy process

Science.gov (United States)

Maitra, Sarit; Dominic, P. D. D.

2012-11-01

Selecting and evaluating the right vendors is imperative for an organization's global marketplace competitiveness. Improper selection and evaluation of potential vendors can dwarf an organization's supply chain performance. Numerous studies have demonstrated that firms consider multiple criteria when selecting key vendors. This research intends to develop a new hybrid model for vendor selection process with better decision making. The new proposed model provides a suitable tool for assisting decision makers and managers to make the right decisions and select the most suitable vendor. This paper proposes a Hybrid model based on Structural Equation Model (SEM) and Analytical Hierarchy Process (AHP) for long-term strategic vendor selection problems. The five steps framework of the model has been designed after the thorough literature study. The proposed hybrid model will be applied using a real life case study to assess its effectiveness. In addition, What-if analysis technique will be used for model validation purpose.

Discrete integrable couplings associated with Toda-type lattice and two hierarchies of discrete soliton equations

International Nuclear Information System (INIS)

Zhang Yufeng; Fan Engui; Zhang Yongqing

2006-01-01

With the help of two semi-direct sum Lie algebras, an efficient way to construct discrete integrable couplings is proposed. As its applications, the discrete integrable couplings of the Toda-type lattice equations are obtained. The approach can be devoted to establishing other discrete integrable couplings of the discrete lattice integrable hierarchies of evolution equations

Two New Multi-component BKP Hierarchies

International Nuclear Information System (INIS)

Wu Hongxia; Liu Xiaojun; Zeng Yunbo

2009-01-01

We firstly propose two kinds of new multi-component BKP (mcBKP) hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources whose Lax representations are presented. The two mcBKP hierarchies both admit reductions to the k-constrained BKP hierarchy and to integrable (1+1)-dimensional hierarchy with self-consistent sources, which include two types of SK equation with self-consistent sources and of bi-directional SK equations with self-consistent sources.

Explorations of the extended ncKP hierarchy

International Nuclear Information System (INIS)

Dimakis, Aristophanes; Mueller-Hoissen, Folkert

2004-01-01

A recently obtained extension (xncKP) of the Moyal-deformed KP hierarchy (ncKP hierarchy) by a set of evolution equations in the Moyal-deformation parameters is further explored. Formulae are derived to compute these equations efficiently. Reductions of the xncKP hierarchy are treated, in particular to the extended ncKdV and ncBoussinesq hierarchies. Furthermore, a good part of the Sato formalism for the KP hierarchy is carried over to the generalized framework. In particular, the well-known bilinear identity theorem for the KP hierarchy, expressed in terms of the (formal) Baker-Akhiezer function, extends to the xncKP hierarchy. Moreover, it is demonstrated that N-soliton solutions of the ncKP equation are also solutions of the first few deformation equations. This is shown to be related to the existence of certain families of algebraic identities

Functional representations of integrable hierarchies

International Nuclear Information System (INIS)

Dimakis, Aristophanes; Mueller-Hoissen, Folkert

2006-01-01

We consider a general framework for integrable hierarchies in Lax form and derive certain universal equations from which 'functional representations' of particular hierarchies (such as KP, discrete KP, mKP, AKNS), i.e. formulations in terms of functional equations, are systematically and quite easily obtained. The formalism genuinely applies to hierarchies where the dependent variables live in a noncommutative (typically matrix) algebra. The obtained functional representations can be understood as 'noncommutative' analogues of 'Fay identities' for the KP hierarchy

Special polynomials associated with some hierarchies

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.

2008-01-01

Special polynomials associated with rational solutions of a hierarchy of equations of Painleve type are introduced. The hierarchy arises by similarity reduction from the Fordy-Gibbons hierarchy of partial differential equations. Some relations for these special polynomials are given. Differential-difference hierarchies for finding special polynomials are presented. These formulae allow us to obtain special polynomials associated with the hierarchy studied. It is shown that rational solutions of members of the Schwarz-Sawada-Kotera, the Schwarz-Kaup-Kupershmidt, the Fordy-Gibbons, the Sawada-Kotera and the Kaup-Kupershmidt hierarchies can be expressed through special polynomials of the hierarchy studied

The string difference equation of the D = 1 matrix model and W1+∞ symmetry of the KP hierarchy

International Nuclear Information System (INIS)

Awada, M.A.; Sin, S.J.

1992-01-01

In this paper, the authors give a connection between the D = 1 matrix model and the generalized KP hierarchy. First, the authors find a difference equation satisfied by F, the Legendre transformation of the free energy of the D = 1 matrix model on a circle of radius R. Then the authors show that it is a special case of the difference equation of the generalized KP hierarchy with its zero mode identified with the scaling variable of the D = 1 string theory. The authors propose that the massive D = 1 matrix model is described by the generalized KP hierarchy, which implies the manifest integrability of D = 1 string theory. The authors also show that the (generalized) KP hierarchy has an underlying W 1 + ∞ symmetry. By reduction, we prove that the generalized KdV hierarchy has a subalgebra of the above symmetry which again forms a W 1+ ∞ . The authors argue that there are no W constraints in D = 1 string theory, which is in contrast to D 1 + ∞ constraints

A differential-difference hierarchy associated with relativistic Toda and Volterra hierarchies

International Nuclear Information System (INIS)

Fan Engui; Dai Huihui

2008-01-01

By embedding a free function into a compatible zero curvature equation, we enlarge the original differential-difference hierarchy into a new hierarchy with the free function which still admits zero curvature representation. The new hierarchy not only includes the original hierarchy, but also the well-known relativistic Toda hierarchy and the Volterra hierarchy as special reductions by properly choosing the free function. Infinitely many conservation laws and Darboux transformation for a representative differential-difference system are constructed based on its Lax representation. The exact solutions follow by applying the Darboux transformation

On the ILW hierarchy

International Nuclear Information System (INIS)

Tutiya, Y.; Satsuma, J.

2003-01-01

In this Letter, we present a new hierarchy which includes the intermediate long wave (ILW) equation at the lowest order. This hierarchy is thought to be a novel reduction of the 1st modified KP type hierarchy. The framework of our investigation is Sato theory

Integral hierarchies and percolation

International Nuclear Information System (INIS)

Klein, W.; Stell, G.

1985-01-01

For a variation of the Potts model which has been shown to describe continuum percolation, we derive a hierarchy of integral equations of Kirkwood-Salsburg type. The distribution functions which are the solutions of this hierarchy can be simply related to the connectedness functions in continuum percolation. From this hierarchy a second set of equations is derived from which the connectedness functions can be obtained directly. This approach is extremely useful when investigating properties of systems far from the percolation transition. These hierarchies are solved exactly in the mean-field (Kac-Baker) limit and possible implications for cluster growth are discussed. The relation between the Potts model for continuum percolation and the Widom-Rowlinson model is also noted

Nonlocal integrable PDEs from hierarchies of symmetry laws: The example of Pohlmeyer-Lund-Regge equation and its reflectionless potential solutions

Science.gov (United States)

Demontis, F.; Ortenzi, G.; van der Mee, C.

2018-04-01

By following the ideas presented by Fukumoto and Miyajima in Fukumoto and Miyajima (1996) we derive a generalized method for constructing integrable nonlocal equations starting from any bi-Hamiltonian hierarchy supplied with a recursion operator. This construction provides the right framework for the application of the full machinery of the inverse scattering transform. We pay attention to the Pohlmeyer-Lund-Regge equation coming from the nonlinear Schrödinger hierarchy and construct the formula for the reflectionless potential solutions which are generalizations of multi-solitons. Some explicit examples are discussed.

On Recursion Operator of the q -KP Hierarchy

International Nuclear Information System (INIS)

Tian Ke-Lei; Zhu Xiao-Ming; He Jing-Song

2016-01-01

It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy. The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of q-shift operator θ, which originates from the Leibnitz rule of the quantum calculus. We further show that the n-reduction leads to a recursive scheme for these flow equations. The recursion operator for the flow equations of the q-KP hierarchy under the n-reduction is also derived. (paper)

The multicomponent 2D Toda hierarchy: dispersionless limit

International Nuclear Information System (INIS)

Mañas, Manuel; Alonso, Luis Martínez

2009-01-01

The factorization problem of the multi-component 2D Toda hierarchy is used to analyze the dispersionless limit of this hierarchy. A dispersive version of the Whitham hierarchy defined in terms of scalar Lax and Orlov–Schulman operators is introduced and the corresponding additional symmetries and string equations are discussed. Then, it is shown how KP and Toda pictures of the dispersionless Whitham hierarchy emerge in the dispersionless limit. Moreover, the additional symmetries and string equations for the dispersive Whitham hierarchy are studied in this limit

Multiple spatial scaling and the weak coupling approximation. II. Homogeneous kinetic equation

Energy Technology Data Exchange (ETDEWEB)

Kleinsmith, P E [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)

1977-08-01

A modified form of the Bogoliubov plasma cluster expansion is applied to the derivation of a divergence-free kinetic equation from the BBGKY hierarchy. Special attention is given to the conditions under which the Landau kinetic equation may be derived from this more general formulation.

(Non)local Hamiltonian and symplectic structures, recursions and hierarchies: a new approach and applications to the N = 1 supersymmetric KdV equation

International Nuclear Information System (INIS)

Kersten, P; Krasil'shchik, I; Verbovetsky, A

2004-01-01

Using methods of Kersten et al (2004 J. Geom. Phys. 50 273-302) and Krasil'shchik and Kersten (2000 Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations (Dordrecht: Kluwer)), we accomplish an extensive study of the N = 1 supersymmetric Korteweg-de Vries (KdV) equation. The results include a description of local and nonlocal Hamiltonian and symplectic structures, five hierarchies of symmetries, the corresponding hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws. We stress that the main point of the paper is not just the results on super-KdV equation itself, but merely exposition of the efficiency of the geometrical approach and of the computational algorithms based on it

Sato theory on the q-Toda hierarchy and its extension

International Nuclear Information System (INIS)

Li, Chuanzhong

2015-01-01

In this paper, we construct the Sato theory including the Hirota bilinear equations and tau function of a new q-deformed Toda hierarchy (QTH). Meanwhile the Block type additional symmetry and bi-Hamiltonian structure of this hierarchy are given. From Hamiltonian tau symmetry, we give another definition of tau function of this hierarchy. Afterwards, we extend the q-Toda hierarchy to an extended q-Toda hierarchy (EQTH) which satisfy a generalized Hirota quadratic equation in terms of generalized vertex operators. The Hirota quadratic equation might have further application in Gromov–Witten theory. The corresponding Sato theory including multi-fold Darboux transformations of this extended hierarchy is also constructed. At last, we construct the multicomponent extension of the q-Toda hierarchy and show the integrability including its bi-Hamiltonian structure, tau symmetry and conserved densities

AKNS hierarchy, Darboux transformation and conservation laws of the 1D nonautonomous nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Zhao Dun; Zhang Yujuan; Lou Weiwei; Luo Honggang

2011-01-01

By constructing nonisospectral Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy, we investigate the nonautonomous nonlinear Schroedinger (NLS) equations which have been used to describe the Feshbach resonance management in matter-wave solitons in Bose-Einstein condensate and the dispersion and nonlinearity managements for optical solitons. It is found that these equations are some special cases of a new integrable model of nonlocal nonautonomous NLS equations. Based on the Lax pairs, the Darboux transformation and conservation laws are explored. It is shown that the local external potentials would break down the classical infinite number of conservation laws. The result indicates that the integrability of the nonautonomous NLS systems may be nontrivial in comparison to the conventional concept of integrability in the canonical case.

Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy

International Nuclear Information System (INIS)

Bogdanov, L V

2010-01-01

We consider two-component integrable generalizations of the dispersionless two-dimensional Toda lattice (2DTL) hierarchy connected with non-Hamiltonian vector fields, similar to the Manakov-Santini hierarchy generalizing the dKP hierarchy. They form a one-parametric family connected by hodograph-type transformations. Generating equations and Lax-Sato equations are introduced, and a dressing scheme based on the vector nonlinear Riemann problem is formulated. The simplest two-component generalization of the dispersionless 2DTL equation is derived, and its differential reduction analogous to the Dunajski interpolating system is presented. A symmetric two-component generalization of the dispersionless elliptic 2DTL equation is also constructed.

A note on the dispersionless BKP hierarchy

International Nuclear Information System (INIS)

Chen, Y.-T.; Tu, M.-H.

2006-01-01

We study the integrable hierarchy underlying topological Landau-Ginzburg models of D-type proposed by Takasaki. Since this integrable hierarchy contains the dBKP hierarchy as a sub-hierarchy, we refer it to the extended dBKP (EdBKP) hierarchy. We give a dressing formulation to the EdBKP hierarchy and investigate additional symmetries associated with the solution space of the hierarchy. We obtain hodograph solutions of its finite-dimensional reductions via Riemann-Hilbert problem (twistor construction) and derive Baecklund transformations of the (2 + 1)-dimensional dBKP equation from additional flows. Finally, the modified partner of the dBKP hierarchy is also established through a Miura transformation

Selection of site specific vibration equation by using analytic hierarchy process in a quarry

Energy Technology Data Exchange (ETDEWEB)

Kalayci, Ulku, E-mail: ukalayci@istanbul.edu.tr; Ozer, Umit, E-mail: uozer@istanbul.edu.tr

2016-01-15

This paper presents a new approach for the selection of the most accurate SSVA (Site Specific Vibration Attenuation) equation for blasting processes in a quarry located near settlements in Istanbul, Turkey. In this context, the SSVA equations obtained from the same study area in the literature were considered in terms of distance between the shot points and buildings and the amount of explosive charge. In this purpose, 11 different SSVA equations obtained from the study area in the past 12 years, forecasting capabilities according to designated new conditions, using 102 vibration records as test data obtained from the study area was investigated. In this study, AHP (Analytic Hierarchy Process) was selected as an analysis method in order to determine the most accurate equation among 11 SSAV equations, and the parameters such as year, distance, charge, and r{sup 2} of the equations were used as criteria for AHP. Finally, the most appropriate equation was selected among the existing ones, and the process of selecting according to different target criteria was presented. Furthermore, it was noted that the forecasting results of the selected equation is more accurate than that formed using the test results. - Highlights: • The optimum Site Specific Vibration Attenuation equation for blasting in a quarry located near settlements was determined. • It is indicated that SSVA equations changing over the years don’t give always accurate estimates at changing conditions. • Selection of the blast induced SSVA equation was made using AHP. • Equation selection method was highlighted based on parameters such as charge, distance, and quarry geometry changes (year).

Selection of site specific vibration equation by using analytic hierarchy process in a quarry

International Nuclear Information System (INIS)

Kalayci, Ulku; Ozer, Umit

2016-01-01

This paper presents a new approach for the selection of the most accurate SSVA (Site Specific Vibration Attenuation) equation for blasting processes in a quarry located near settlements in Istanbul, Turkey. In this context, the SSVA equations obtained from the same study area in the literature were considered in terms of distance between the shot points and buildings and the amount of explosive charge. In this purpose, 11 different SSVA equations obtained from the study area in the past 12 years, forecasting capabilities according to designated new conditions, using 102 vibration records as test data obtained from the study area was investigated. In this study, AHP (Analytic Hierarchy Process) was selected as an analysis method in order to determine the most accurate equation among 11 SSAV equations, and the parameters such as year, distance, charge, and r"2 of the equations were used as criteria for AHP. Finally, the most appropriate equation was selected among the existing ones, and the process of selecting according to different target criteria was presented. Furthermore, it was noted that the forecasting results of the selected equation is more accurate than that formed using the test results. - Highlights: • The optimum Site Specific Vibration Attenuation equation for blasting in a quarry located near settlements was determined. • It is indicated that SSVA equations changing over the years don’t give always accurate estimates at changing conditions. • Selection of the blast induced SSVA equation was made using AHP. • Equation selection method was highlighted based on parameters such as charge, distance, and quarry geometry changes (year).

Poisson hierarchy of discrete strings

International Nuclear Information System (INIS)

Ioannidou, Theodora; Niemi, Antti J.

2016-01-01

The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

Poisson hierarchy of discrete strings

Energy Technology Data Exchange (ETDEWEB)

Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)

2016-01-28

The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems

Science.gov (United States)

Moix, Jeremy M.; Cao, Jianshu

2013-10-01

The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Förster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.

Gauge theories, duality relations and the tensor hierarchy

International Nuclear Information System (INIS)

Bergshoeff, Eric A.; Hohm, Olaf; Hartong, Jelle; Huebscher, Mechthild; OrtIn, Tomas

2009-01-01

We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 ≤ p ≤ D, which realize an off-shell algebra of bosonic gauge transformations. We show how these tensor hierarchies can be put on-shell by introducing a set of duality relations, thereby introducing additional scalars and a metric tensor. These so-called duality hierarchies encode the equations of motion of the bosonic part of the most general gauged supergravity theories in those dimensions, including the (projected) scalar equations of motion. We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of the same fields in the tensor hierarchy.

Matrix integral solutions to the discrete KP hierarchy and its Pfaffianized version

International Nuclear Information System (INIS)

Lafortune, Stéphane; Li, Chun-Xia

2016-01-01

Matrix integrals used in random matrix theory for the study of eigenvalues of Hermitian ensembles have been shown to provide τ -functions for several hierarchies of integrable equations. In this article, we extend this relation by showing that such integrals can also provide τ -functions for the discrete KP hierarchy and a coupled version of the same hierarchy obtained through the process of Pfaffianization. To do so, we consider the first equation of the discrete KP hierarchy, the Hirota–Miwa equation. We write the Wronskian determinant solutions to the Hirota–Miwa equation and consider a particular form of matrix integrals, which we show is an example of those Wronskian solutions. The argument is then generalized to the whole hierarchy. A similar strategy is used for the Pfaffianized version of the hierarchy except that in that case, the solutions are written in terms of Pfaffians rather than determinants. (paper)

New supersymmetrizations of the generalized KDV hierarchies

International Nuclear Information System (INIS)

Figueroa-O'Farrill, J.M.; Stanciu, S.

1993-03-01

Recently we investigated a new supersymmetrization procedure for the KdV hierarchy inspired in some recent work on supersymmetric matrix models. We extend this procedure here for the generalized KdV hierarchies. The resulting supersymmetric hierarchies are generically nonlocal, expect for the case of Boussinesque which we treat in detail. The resulting supersymmetric hierarchy is integrable and bihamiltonian and contains the Boussinesque hierarchy as a subhierarchy. In a particular realization, we extend it by defining supersymmetric odd flows. We end with some comments on a slight modification of this supersymmetrization which yields local equations for any generalized KdV hierarchy. (orig.)

Virasoro algebra action on integrable hierarchies and Virasoro contraints in matrix models

International Nuclear Information System (INIS)

Semikhatov, A.M.

1991-01-01

The action of the Virasoro algebra on integrable hierarchies of non-linear equations and on related objects ('Schroedinger' differential operators) is investigated. The method consists in pushing forward the Virasoro action to the wave function of a hierarchy, and then reconstructing its action on the dressing and Lax operators. This formulation allows one to observe a number of suggestive similarities between the structures involved in the description of the Virasoro algebra on the hierarchies and the structure of conformal field theory on the world-sheet. This includes, in particular, an 'off-shell' hierarchy version of operator products and of the Cauchy kernel. In relation to matrix models, which have been observed to be effectively described by integrable hierarchies subjected to Virasoro constraints, I propose to define general Virasoro-constrained hierarchies also in terms of dressing operators, by certain equations which carry the information of the hierarchy and the Virasoro algebra simultaneously and which suggest an interpretation as operator versions of recursion/loop equations in topological theories. These same equations provide a relation with integrable hierarchies with quantized spectral parameter introduced recently. The formulation in terms of dressing operators allows a scaling (continuum limit) of discrete (i.e. lattice) hierarchies with the Virasoro constraints into 'continuous' Virasoro-constrained hierarchies. In particular, the KP hierarchy subjected to the Virasoro constraints is recovered as a scaling limit of the Virasoro-constrained Toda hierarchy. The dressing operator method also makes is straightforward to identify the full symmetry algebra of Virasoro-constrained hierarchies, which is related to the family of W ∞ (J) algebras introduced recently. (orig./HS)

A Lax integrable hierarchy, bi-Hamiltonian structure and finite-dimensional Liouville integrable involutive systems

International Nuclear Information System (INIS)

Xia Tiecheng; Chen Xiaohong; Chen Dengyuan

2004-01-01

An eigenvalue problem and the associated new Lax integrable hierarchy of nonlinear evolution equations are presented in this paper. As two reductions, the generalized nonlinear Schroedinger equations and the generalized mKdV equations are obtained. Zero curvature representation and bi-Hamiltonian structure are established for the whole hierarchy based on a pair of Hamiltonian operators (Lenard's operators), and it is shown that the hierarchy of nonlinear evolution equations is integrable in Liouville's sense. Thus the hierarchy of nonlinear evolution equations has infinitely many commuting symmetries and conservation laws. Moreover the eigenvalue problem is nonlinearized as a finite-dimensional completely integrable system under the Bargmann constraint between the potentials and the eigenvalue functions. Finally finite-dimensional Liouville integrable system are found, and the involutive solutions of the hierarchy of equations are given. In particular, the involutive solutions are developed for the system of generalized nonlinear Schroedinger equations

Optimal mesh hierarchies in Multilevel Monte Carlo methods

KAUST Repository

Von Schwerin, Erik

2016-01-01

I will discuss how to choose optimal mesh hierarchies in Multilevel Monte Carlo (MLMC) simulations when computing the expected value of a quantity of interest depending on the solution of, for example, an Ito stochastic differential equation or a partial differential equation with stochastic data. I will consider numerical schemes based on uniform discretization methods with general approximation orders and computational costs. I will compare optimized geometric and non-geometric hierarchies and discuss how enforcing some domain constraints on parameters of MLMC hierarchies affects the optimality of these hierarchies. I will also discuss the optimal tolerance splitting between the bias and the statistical error contributions and its asymptotic behavior. This talk presents joint work with N.Collier, A.-L.Haji-Ali, F. Nobile, and R. Tempone.

Optimal mesh hierarchies in Multilevel Monte Carlo methods

KAUST Repository

Von Schwerin, Erik

2016-01-08

I will discuss how to choose optimal mesh hierarchies in Multilevel Monte Carlo (MLMC) simulations when computing the expected value of a quantity of interest depending on the solution of, for example, an Ito stochastic differential equation or a partial differential equation with stochastic data. I will consider numerical schemes based on uniform discretization methods with general approximation orders and computational costs. I will compare optimized geometric and non-geometric hierarchies and discuss how enforcing some domain constraints on parameters of MLMC hierarchies affects the optimality of these hierarchies. I will also discuss the optimal tolerance splitting between the bias and the statistical error contributions and its asymptotic behavior. This talk presents joint work with N.Collier, A.-L.Haji-Ali, F. Nobile, and R. Tempone.

MULTIPLE CRITERA METHODS WITH FOCUS ON ANALYTIC HIERARCHY PROCESS AND GROUP DECISION MAKING

Directory of Open Access Journals (Sweden)

Lidija Zadnik-Stirn

2010-12-01

Full Text Available Managing natural resources is a group multiple criteria decision making problem. In this paper the analytic hierarchy process is the chosen method for handling the natural resource problems. The one decision maker problem is discussed and, three methods: the eigenvector method, data envelopment analysis method, and logarithmic least squares method are presented for the derivation of the priority vector. Further, the group analytic hierarchy process is discussed and six methods for the aggregation of individual judgments or priorities: weighted arithmetic mean method, weighted geometric mean method, and four methods based on data envelopment analysis are compared. The case study on land use in Slovenia is applied. The conclusions review consistency, sensitivity analyses, and some future directions of research.

Two hierarchies of integrable lattice equations associated with a discrete matrix spectral problem

International Nuclear Information System (INIS)

Li Xinyue; Xu Xixiang; Zhao Qiulan

2008-01-01

Two hierarchies of nonlinear integrable positive and negative lattice models are derived from a discrete spectral problem. The two lattice hierarchies are proved to have discrete zero curvature representations associated with a discrete spectral problem, which also shows that the positive and negative hierarchies correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. Moreover, the integrable lattice models in the positive hierarchy are of polynomial type, and the integrable lattice models in the negative hierarchy are of rational type. Further, we construct infinite conservation laws of the positive hierarchy, then, the integrable coupling systems of the positive hierarchy are derived from enlarging Lax pair

A lattice hierarchy and its continuous limits

International Nuclear Information System (INIS)

Fan Engui

2008-01-01

By introducing a discrete spectral problem, we derive a lattice hierarchy which is integrable in Liouville's sense and possesses a multi-Hamiltonian structure. It is show that the discrete spectral problem converges to the well-known AKNS spectral problem under a certain continuous limit. In particular, we construct a sequence of equations in the lattice hierarchy which approximates the AKNS hierarchy as a continuous limit

Delegation Within Hierarchies

DEFF Research Database (Denmark)

Dobrajska, Magdalena; Billinger, Stephan; Karim, Samina

2015-01-01

We investigate trade-offs associated with delegating authority over multiple interrelated decisions in a complex task structure. The empirical setting is a business process of a global Fortune 50 firm. The firm decentralized its organization and redefined decision authority across organizational......-relevant knowledge, the matching of required knowledge and managers’ expertise, and information processing intensity affect (a) the occurrence of delegation and, (b) if delegation occurs, how far down the organizational hierarchy authority is delegated. We discuss how these findings complement existing theories...... on delegation by providing insights into when and how interrelated decisions are delegated across multiple levels of an organizational hierarchy....

WDVV equation and triple-product relation

International Nuclear Information System (INIS)

Shigechi, Keiichi; Wadati, Miki; Wang Ning

2005-01-01

We study the relation between the WDVV equations and the τ-function of the noncommutative KP (NCKP) hierarchy. WDVV-like equations (Hirota triple-product relation) in the noncommutative context appear as a consequence of the nontrivial equation for τ-function of the NC KP hierarchy, while the prepotential in the Seiberg-Witten (SW) theory has been identified to the τ-function of the Whitham hierarchy. We show that the spectral curve for the SW theory is the same as the Toda-chain hierarchy. We also show explicitly that Whitham hierarchy includes commutative Toda/KP hierarchy. Further, we comment on the origin of the Hirota triple-product relation in the context of the SW theory

Standard model fermion hierarchies with multiple Higgs doublets

International Nuclear Information System (INIS)

Solaguren-Beascoa Negre, Ana

2016-01-01

The hierarchies between the Standard Model (SM) fermion masses and mixing angles and the origin of neutrino masses are two of the biggest mysteries in particle physics. We extend the SM with new Higgs doublets to solve these issues. The lightest fermion masses and the mixing angles are generated through radiative effects, correctly reproducing the hierarchy pattern. Neutrino masses are generated in the see-saw mechanism.

Visualising large hierarchies with Flextree

Science.gov (United States)

Song, Hongzhi; Curran, Edwin P.; Sterritt, Roy

2003-05-01

One of the main tasks in Information Visualisation research is creating visual tools to facilitate human understanding of large and complex information spaces. Hierarchies, being a good mechanism in organising such information, are ubiquitous. Although much research effort has been spent on finding useful representations for hierarchies, visualising large hierarchies is still a difficult topic. One of the difficulties is how to show both tructure and node content information in one view. Another is how to achieve multiple foci in a focus+context visualisation. This paper describes a novel hierarchy visualisation technique called FlexTree to address these problems. It contains some important features that have not been exploited so far. In this visualisation, a profile or contour unique to the hierarchy being visualised can be gained in a histogram-like layout. A normalised view of a common attribute of all nodes can be acquired, and selection of this attribute is controllable by the user. Multiple foci are consistently accessible within a global context through interaction. Furthermore it can handle a large hierarchy that contains several thousand nodes in a PC environment. In addition results from an informal evaluation are also presented.

A generalized AKNS hierarchy and its bi-Hamiltonian structures

International Nuclear Information System (INIS)

Xia Tiecheng; You Fucai; Chen Dengyuan

2005-01-01

First we construct a new isospectral problem with 8 potentials in the present paper. And then a new Lax pair is presented. By making use of Tu scheme, a class of new soliton hierarchy of equations is derived, which is integrable in the sense of Liouville and possesses bi-Hamiltonian structures. After making some reductions, the well-known AKNS hierarchy and other hierarchies of evolution equations are obtained. Finally, in order to illustrate that soliton hierarchy obtained in the paper possesses bi-Hamiltonian structures exactly, we prove that the linear combination of two-Hamiltonian operators admitted are also a Hamiltonian operator constantly. We point out that two Hamiltonian operators obtained of the system are directly derived from a recurrence relations, not from a recurrence operator

A density tensor hierarchy for open system dynamics: retrieving the noise

International Nuclear Information System (INIS)

Adler, Stephen L

2007-01-01

We develop a density tensor hierarchy for open system dynamics that recovers information about fluctuations (or 'noise') lost in passing to the reduced density matrix. For the case of fluctuations arising from a classical probability distribution, the hierarchy is formed from expectations of products of pure state density matrix elements and can be compactly summarized by a simple generating function. For the case of quantum fluctuations arising when a quantum system interacts with a quantum environment in an overall pure state, the corresponding hierarchy is defined as the environmental trace of products of system matrix elements of the full density matrix. Whereas all members of the classical noise hierarchy are system observables, only the lowest member of the quantum noise hierarchy is directly experimentally measurable. The unit trace and idempotence properties of the pure state density matrix imply descent relations for the tensor hierarchies, that relate the order n tensor, under contraction of appropriate pairs of tensor indices, to the order n - 1 tensor. As examples to illustrate the classical probability distribution formalism, we consider a spatially isotropic ensemble of spin-1/2 pure states, a quantum system evolving by an Ito stochastic Schroedinger equation and a quantum system evolving by a jump process Schroedinger equation. As examples to illustrate the corresponding trace formalism in the quantum fluctuation case, we consider the tensor hierarchies for collisional Brownian motion of an infinite mass Brownian particle and for the weak coupling Born-Markov master equation. In different specializations, the latter gives the hierarchies generalizing the quantum optical master equation and the Caldeira-Leggett master equation. As a further application of the density tensor, we contrast stochastic Schroedinger equations that reduce and that do not reduce the state vector, and discuss why a quantum system coupled to a quantum environment behaves like

An extended integrable fractional-order KP soliton hierarchy

International Nuclear Information System (INIS)

Li Li

2011-01-01

In this Letter, we consider the modified derivatives and integrals of fractional-order pseudo-differential operators. A sequence of Lax KP equations hierarchy and extended fractional KP (fKP) hierarchy are introduced, and the fKP hierarchy has Lax presentations with the extended Lax operators. In the case of the extension with the half-order pseudo-differential operators, a new integrable fKP hierarchy is obtained. A few particular examples of fractional order will be listed, together with their Lax pairs.

An extended integrable fractional-order KP soliton hierarchy

Energy Technology Data Exchange (ETDEWEB)

Li Li, E-mail: li07099@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)

2011-01-17

In this Letter, we consider the modified derivatives and integrals of fractional-order pseudo-differential operators. A sequence of Lax KP equations hierarchy and extended fractional KP (fKP) hierarchy are introduced, and the fKP hierarchy has Lax presentations with the extended Lax operators. In the case of the extension with the half-order pseudo-differential operators, a new integrable fKP hierarchy is obtained. A few particular examples of fractional order will be listed, together with their Lax pairs.

Operator approach to solutions of the constrained BKP hierarchy

International Nuclear Information System (INIS)

Shen, Hsin-Fu; Lee, Niann-Chern; Tu, Ming-Hsien

2011-01-01

The operator formalism to the vector k-constrained BKP hierarchy is presented. We solve the Hirota bilinear equations of the vector k-constrained BKP hierarchy via the method of neutral free fermion. In particular, by choosing suitable group element of O(∞), we construct rational and soliton solutions of the vector k-constrained BKP hierarchy.

Adolescents' multiple versus single primary attachment figures, reorganization of attachment hierarchy, and adjustments: the important people interview approach.

Science.gov (United States)

Umemura, Tomotaka; Lacinová, Lenka; Kraus, Jakub; Horská, Eliška; Pivodová, Lenka

2018-04-20

Using 212 adolescents from a central-European country (mean age = 14.02, SD = 2.05, ranged from 11 to 18 years; females = 54%) and a multi-informant method to measure adolescents' behavioral and emotional adjustments, the present study explored three aspects regarding the attachment hierarchy. (1) The three types of behavioral systems of Rosenthal and Kobak's important people interview (IPI) were initially validated using an exploratory factor analysis with a US sample. Using a confirmatory factor analysis with a Czech sample, we replicated these three behavioral systems: attachment bond, support seeking, and affiliation. (2) We found that adolescents who developed attachment bond to multiple primary attachment figures were likely to score lower on both teacher-rated and parent-rated internalizing problems compared to those who had a single primary attachment figure. These multiple primary attachment figures tended to be family members (not peers). (3) Early adolescents who placed parents low in their attachment hierarchy scored higher on self-reported negative affect and lower on self-reported positive affect compared to early adolescents who placed parents high. The present study highlights multiple (vs. single) primary attachment figures as a protective factor and the premature reorganization of attachment hierarchy as a risk factor for adolescents' emotional and affective adjustments.

On a non-local gas dynamics like integrable hierarchy

International Nuclear Information System (INIS)

Brunelli, Jose Carlos; Das, Ashok

2004-01-01

We study a new hierarchy of equations derived from the system of isentropic gas dynamics equations where the pressure is a non-local function of the density. We show that the hierarchy of equations is integrable. We construct the two compatible Hamiltonian structures and show that the first structure has three distinct Casimirs while the second has one. The existence of Casimirs allows us to extend the flows to local ones. We construct an infinite series of commuting local Hamiltonians as well as three infinite series (related to the three Casimirs) of non-local charges. We discuss the zero curvature formulation of the system where we obtain a simple expression for the non-local conserved charges, which also clarifies the existence of the three series from a Lie algebraic point of view. We point out that the non-local hierarchy of Hunter-Zheng equations can be obtained from our non-local flows when the dynamical variables are properly constrained. (author)

A study on the hierarchy model of nuclear reactions

International Nuclear Information System (INIS)

Kitazoe, Yasuhiro; Sekiya, Tamotsu

1975-01-01

The application of the hierarchy model of nuclear reaction is discussed, and the hierarchy model means that the compound nucleus state is formed after several steps, at least, one step of reaction. This model was applied to the analysis of the observed cross sections of 235 U and some other elements. Neglecting exchange scattering effect, the equations for the total neutron cross section of 235 U were obtained. One of these equations describes explicitly the hierarchy of the transition from intermediate reaction state Xm into the compound nucleus state Xs, and another one describes the cross section averaged over an energy interval larger than the average level spacing of compound nucleus eigenvalues. The hierarchy of reaction mechanism was investigated in more detail, and the hierarchy model was applied to the case of unresolved energy region. It was not tried to evaluate the strength function in the mass region (A>140), since the effect of nuclear deformation was neglected in the task. (Iwase, T.)

Multistate electron transfer dynamics in the condensed phase: Exact calculations from the reduced hierarchy equations of motion approach

International Nuclear Information System (INIS)

Tanaka, Midori; Tanimura, Yoshitaka

2010-01-01

Multiple displaced oscillators coupled to an Ohmic heat bath are used to describe electron transfer (ET) in a dissipative environment. By performing a canonical transformation, the model is reduced to a multilevel system coupled to a heat bath with the Brownian spectral distribution. A reduced hierarchy equations of motion approach is introduced for numerically rigorous simulation of the dynamics of the three-level system with various oscillator configurations, for different nonadiabatic coupling strengths and damping rates, and at different temperatures. The time evolution of the reduced density matrix elements illustrates the interplay of coherences between the electronic and vibrational states. The ET reaction rates, defined as a flux-flux correlation function, are calculated using the linear response of the system to an external perturbation as a function of activation energy. The results exhibit an asymmetric inverted parabolic profile in a small activation regime due to the presence of the intermediate state between the reactant and product states and a slowly decaying profile in a large activation energy regime, which arises from the quantum coherent transitions.

Minimal string theories and integrable hierarchies

Science.gov (United States)

Iyer, Ramakrishnan

Well-defined, non-perturbative formulations of the physics of string theories in specific minimal or superminimal model backgrounds can be obtained by solving matrix models in the double scaling limit. They provide us with the first examples of completely solvable string theories. Despite being relatively simple compared to higher dimensional critical string theories, they furnish non-perturbative descriptions of interesting physical phenomena such as geometrical transitions between D-branes and fluxes, tachyon condensation and holography. The physics of these theories in the minimal model backgrounds is succinctly encoded in a non-linear differential equation known as the string equation, along with an associated hierarchy of integrable partial differential equations (PDEs). The bosonic string in (2,2m-1) conformal minimal model backgrounds and the type 0A string in (2,4 m) superconformal minimal model backgrounds have the Korteweg-de Vries system, while type 0B in (2,4m) backgrounds has the Zakharov-Shabat system. The integrable PDE hierarchy governs flows between backgrounds with different m. In this thesis, we explore this interesting connection between minimal string theories and integrable hierarchies further. We uncover the remarkable role that an infinite hierarchy of non-linear differential equations plays in organizing and connecting certain minimal string theories non-perturbatively. We are able to embed the type 0A and 0B (A,A) minimal string theories into this single framework. The string theories arise as special limits of a rich system of equations underpinned by an integrable system known as the dispersive water wave hierarchy. We find that there are several other string-like limits of the system, and conjecture that some of them are type IIA and IIB (A,D) minimal string backgrounds. We explain how these and several other string-like special points arise and are connected. In some cases, the framework endows the theories with a non

Auto-Bäcklund transformations and special integrals for differential-delay Painlevé hierarchies

Science.gov (United States)

Fedorov, Yuri; Gordoa, Pilar R.; Pickering, Andrew

2014-10-01

The six Painlevé equations have attracted much interest over the last thirty years or so. More recently many authors have begun to explore properties of higher-order versions of both these equations and their discrete analogues. However, little attention has been paid to differential-delay Painlevé equations, i.e., analogues of the Painlevé equations involving both shifts in and derivatives with respect to the independent variable, and even less to higher-order analogues of these last. In the current paper we discuss the phenomenon whereby members of one differential-delay Painlevé hierarchy define solutions of higher-order members of a second differential-delay Painlevé hierarchy. We also give an auto-Bäcklund transformation for a differential-delay Painlevé hierarchy. The key to our approach is the underlying Hamiltonian structure of related completely integrable lattice hierarchies.

Conformal fields. From Riemann surfaces to integrable hierarchies

International Nuclear Information System (INIS)

Semikhatov, A.M.

1991-01-01

I discuss the idea of translating ingredients of conformal field theory into the language of hierarchies of integrable differential equations. Primary conformal fields are mapped into (differential or matrix) operators living on the phase space of the hierarchy, whereas operator insertions of, e.g., a current or the energy-momentum tensor, become certain vector fields on the phase space and thus acquire a meaning independent of a given Riemann surface. A number of similarities are observed between the structures arising on the hierarchy and those of the theory on the world-sheet. In particular, there is an analogue of the operator product algebra with the Cauchy kernel replaced by its 'off-shell' hierarchy version. Also, hierarchy analogues of certain operator insertions admit two (equivalent, but distinct) forms, resembling the 'bosonized' and 'fermionized' versions respectively. As an application, I obtain a useful reformulation of the Virasoro constraints of the type that arise in matrix models, as a system of equations on dressing (or Lax) operators (rather than correlation functions, i.e., residues or traces). This also suggests an interpretation in terms of a 2D topological field theory, which might be extended to a correspondence between Virasoro-constrained hierarchies and topological theories. (orig.)

Generalized non-linear Schroedinger hierarchy

International Nuclear Information System (INIS)

Aratyn, H.; Gomes, J.F.; Zimerman, A.H.

1994-01-01

The importance in studying the completely integrable models have became evident in the last years due to the fact that those models present an algebraic structure extremely rich, providing the natural scenery for solitons description. Those models can be described through non-linear differential equations, pseudo-linear operators (Lax formulation), or a matrix formulation. The integrability implies in the existence of a conservation law associated to each of degree of freedom. Each conserved charge Q i can be associated to a Hamiltonian, defining a time evolution related to to a time t i through the Hamilton equation ∂A/∂t i =[A,Q i ]. Particularly, for a two-dimensions field theory, infinite degree of freedom exist, and consequently infinite conservation laws describing the time evolution in space of infinite times. The Hamilton equation defines a hierarchy of models which present a infinite set of conservation laws. This paper studies the generalized non-linear Schroedinger hierarchy

The multi-component WKI hierarchy

International Nuclear Information System (INIS)

Yao Yuqin; Zhang Yufeng

2005-01-01

Firstly a new loop algebra G∼ M with 3M dimensions is constructed, which is devoted to establishing a new isospectral problem. Then the multi-component WKI hierarchy of soliton equations is obtained

Functional equation for the Mordell-Tornheim multiple zeta-function

OpenAIRE

Okamoto, Takuya; Onozuka, Tomokazu

2016-01-01

We show a relation between the Mordell-Tornheim multiple zeta-function and the confluent hypergeometric function, and using it, we give the functional equation for the Mordell-Tornheim multiple zeta-function. In the double case, the functional equation includes the known functional equation for the Euler-Zagier double zeta-function.

On a class of reductions of the Manakov-Santini hierarchy connected with the interpolating system

International Nuclear Information System (INIS)

Bogdanov, L V

2010-01-01

Using the Lax-Sato formulation of the Manakov-Santini hierarchy, we introduce a class of reductions such that the zero-order reduction of this class corresponds to the dKP hierarchy, and the first-order reduction gives the hierarchy associated with the interpolating system introduced by Dunajski. We present the Lax-Sato form of a reduced hierarchy for the interpolating system and also for the reduction of arbitrary order. Similar to the dKP hierarchy, the Lax-Sato equations for L (the Lax function) split from the Lax-Sato equations for M (the Orlov function) due to the reduction, and the reduced hierarchy for an arbitrary order of reduction is defined by Lax-Sato equations for L only. A characterization of the class of reductions in terms of the dressing data is given. We also consider a waterbag reduction of the interpolating system hierarchy, which defines (1+1)-dimensional systems of hydrodynamic type.

Generalized NLS hierarchies from rational W algebras

International Nuclear Information System (INIS)

Toppan, F.

1993-11-01

Finite rational W algebras are very natural structures appearing in coset constructions when a Kac-Moody subalgebra is factored out. The problem of relating these algebras to integrable hierarchies of equations is studied by showing how to associate to a rational W algebra its corresponding hierarchy. Two examples are worked out, the sl(2)/U(1) coset, leading to the Non-Linear Schroedinger hierarchy, and the U(1) coset of the Polyakov-Bershadsky W algebra, leading to a 3-field representation of the KP hierarchy already encountered in the literature. In such examples a rational algebra appears as algebra of constraints when reducing a KP hierarchy to a finite field representation. This fact arises the natural question whether rational algebras are always associated to such reductions and whether a classification of rational algebras can lead to a classification of the integrable hierarchies. (author). 19 refs

The Helmholtz Hierarchy: Phase Space Statistics of Cold Dark Matter

OpenAIRE

Tassev, Svetlin

2010-01-01

We present a new formalism to study large-scale structure in the universe. The result is a hierarchy (which we call the "Helmholtz Hierarchy") of equations describing the phase space statistics of cold dark matter (CDM). The hierarchy features a physical ordering parameter which interpolates between the Zel'dovich approximation and fully-fledged gravitational interactions. The results incorporate the effects of stream crossing. We show that the Helmholtz hierarchy is self-consistent and obeys...

Variable-coefficient nonisospectral Toda lattice hierarchy and its

Indian Academy of Sciences (India)

In this paper, a hierarchy of nonisospectral equations with variable coefficients is derived from the compatibility condition of Toda spectral problem and its time evolution. In order to solve the derived Toda lattice hierarchy, the inverse scattering transformation is utilized. As a result, new and more general exact solutions are ...

On an extended second Painlevé hierarchy

Science.gov (United States)

Gordoa, P. R.; Pickering, A.

2017-10-01

We present a new extension of the second Painlevé hierarchy and study its properties. In addition to Lax pairs, Bäcklund transformations, auto-Bäcklund transformations and basic special integrals, we also consider a new phenomenon whereby we obtain relations between systems of different orders but of the same form. The extension made here of the second Painlevé hierarchy is based on the use of non-isospectral scattering problems and so is quite general. We thus expect to be able to obtain similar extensions of other Painlevé hierarchies, including not only for continuous examples but also for discrete and differential-delay examples. We believe that our work is also of relevance for Painlevé classification, since it gives information about classes of equation that may be of interest and in addition provides a key to the possible identification of equations isolated in such a process.

The Helmholtz Hierarchy: phase space statistics of cold dark matter

International Nuclear Information System (INIS)

Tassev, Svetlin V.

2011-01-01

We present a new formalism to study large-scale structure in the universe. The result is a hierarchy (which we call the ''Helmholtz Hierarchy'') of equations describing the phase space statistics of cold dark matter (CDM). The hierarchy features a physical ordering parameter which interpolates between the Zel'dovich approximation and fully-fledged gravitational interactions. The results incorporate the effects of stream crossing. We show that the Helmholtz hierarchy is self-consistent and obeys causality to all orders. We present an interpretation of the hierarchy in terms of effective particle trajectories

The Virasoro algebra in integrable hierarchies and the method of matrix models

International Nuclear Information System (INIS)

Semikhatov, A.M.

1992-01-01

The action of the Virasoro algebra on hierarchies of nonlinear integrable equations, and also the structure and consequences of Virasoro constraints on these hierarchies, are studied. It is proposed that a broad class of hierarchies, restricted by Virasoro constraints, can be defined in terms of dressing operators hidden in the structure of integrable systems. The Virasoro-algebra representation constructed on the dressing operators displays a number of analogies with structures in conformal field theory. The formulation of the Virasoro constraints that stems from this representation makes it possible to translate into the language of integrable systems a number of concepts from the method of the 'matrix models' that describe nonperturbative quantum gravity, and, in particular, to realize a 'hierarchical' version of the double scaling limit. From the Virasoro constraints written in terms of the dressing operators generalized loop equations are derived, and this makes it possible to do calculations on a reconstruction of the field-theoretical description. The reduction of the Kadomtsev-Petviashvili (KP) hierarchy, subject to Virasoro constraints, to generalized Korteweg-deVries (KdV) hierarchies is implemented, and the corresponding representation of the Virasoro algebra on these hierarchies is found both in the language of scalar differential operators and in the matrix formalism of Drinfel'd and Sokolov. The string equation in the matrix formalism does not replicate the structure of the scalar string equation. The symmetry algebras of the KP and N-KdV hierarchies restricted by Virasoro constraints are calculated: A relationship is established with algebras from the family W ∞ (J) of infinite W-algebras

A multi-component matrix loop algebra and a unified expression of the multi-component AKNS hierarchy and the multi-component BPT hierarchy

International Nuclear Information System (INIS)

Zhang Yufeng

2005-01-01

A set of multi-component matrix Lie algebra is constructed, which is devote to obtaining a new loop algebra A-bar M-1 . It follows that an isospectral problem is established. By making use of Tu scheme, a Liouville integrable multi-component hierarchy of soliton equations is generated, which possesses the bi-Hamiltonian structures. As its reduction cases, the multi-component AKNS hierarchy and the formalism of the multi-component BPT hierarchy are given, respectively

Hamiltonian structure of the integrable coupling of the Jaulent-Miodek hierarchy

International Nuclear Information System (INIS)

Zhang, Yufeng; Fan, Engui

2006-01-01

A scheme for deducing Hamiltonian structures of the higher-dimensional hierarchies of evolution equations is presented which is devoting to obtaining the Hamiltonian structures of integrable coupling of the Jaulent-Miodek hierarchy

A remark on Kac-Wakimoto hierarchies of D-type

International Nuclear Information System (INIS)

Wu Chaoxzhong

2010-01-01

For the Kac-Wakimoto hierarchy constructed from the principal vertex operator realization of the basic representation of the affine Lie algebra D (1) n , we compute the coefficients of the corresponding Hirota bilinear equations, and verify the coincidence of these bilinear equations with the ones that are satisfied by Givental's total descendant potential of the D n singularity, as conjectured by Givental and Milanov (2005 Simple singularities and integrable hierarchies The Breadth of Symplectic and Poisson Geometry (Prog. Math. vol 232) (Boston: Birkhaeuser) pp 173-201).

Information slows down hierarchy growth.

Science.gov (United States)

Czaplicka, Agnieszka; Suchecki, Krzysztof; Miñano, Borja; Trias, Miquel; Hołyst, Janusz A

2014-06-01

We consider models of growing multilevel systems wherein the growth process is driven by rules of tournament selection. A system can be conceived as an evolving tree with a new node being attached to a contestant node at the best hierarchy level (a level nearest to the tree root). The proposed evolution reflects limited information on system properties available to new nodes. It can also be expressed in terms of population dynamics. Two models are considered: a constant tournament (CT) model wherein the number of tournament participants is constant throughout system evolution, and a proportional tournament (PT) model where this number increases proportionally to the growing size of the system itself. The results of analytical calculations based on a rate equation fit well to numerical simulations for both models. In the CT model all hierarchy levels emerge, but the birth time of a consecutive hierarchy level increases exponentially or faster for each new level. The number of nodes at the first hierarchy level grows logarithmically in time, while the size of the last, "worst" hierarchy level oscillates quasi-log-periodically. In the PT model, the occupations of the first two hierarchy levels increase linearly, but worse hierarchy levels either do not emerge at all or appear only by chance in the early stage of system evolution to further stop growing at all. The results allow us to conclude that information available to each new node in tournament dynamics restrains the emergence of new hierarchy levels and that it is the absolute amount of information, not relative, which governs such behavior.

Information slows down hierarchy growth

Science.gov (United States)

Czaplicka, Agnieszka; Suchecki, Krzysztof; Miñano, Borja; Trias, Miquel; Hołyst, Janusz A.

2014-06-01

We consider models of growing multilevel systems wherein the growth process is driven by rules of tournament selection. A system can be conceived as an evolving tree with a new node being attached to a contestant node at the best hierarchy level (a level nearest to the tree root). The proposed evolution reflects limited information on system properties available to new nodes. It can also be expressed in terms of population dynamics. Two models are considered: a constant tournament (CT) model wherein the number of tournament participants is constant throughout system evolution, and a proportional tournament (PT) model where this number increases proportionally to the growing size of the system itself. The results of analytical calculations based on a rate equation fit well to numerical simulations for both models. In the CT model all hierarchy levels emerge, but the birth time of a consecutive hierarchy level increases exponentially or faster for each new level. The number of nodes at the first hierarchy level grows logarithmically in time, while the size of the last, "worst" hierarchy level oscillates quasi-log-periodically. In the PT model, the occupations of the first two hierarchy levels increase linearly, but worse hierarchy levels either do not emerge at all or appear only by chance in the early stage of system evolution to further stop growing at all. The results allow us to conclude that information available to each new node in tournament dynamics restrains the emergence of new hierarchy levels and that it is the absolute amount of information, not relative, which governs such behavior.

Solutions of the bigraded Toda hierarchy

International Nuclear Information System (INIS)

Li Chuanzhong

2011-01-01

The (N, M)-bigraded Toda hierarchy is an extension of the original Toda lattice hierarchy. The pair of numbers (N, M) represents the band structure of the Lax matrix which has N upper and M lower diagonals, and the original one is referred to as the (1, 1)-bigraded Toda hierarchy. Because of this band structure, one can introduce M + N - 1 commuting flows which give a parametrization of a small phase space for a topological field theory. In this paper, first we show that there exists a natural symmetry between the (N, M)- and (M, N)-bigraded Toda hierarchies. We then derive the Hirota bilinear form for those commuting flows, which consist of two-dimensional Toda hierarchy, the discrete KP hierarchy and its Baecklund transformations. We also discuss the solution structure of the (N, M)-bigraded Toda equation in terms of the moment matrix defined via the wave operators associated with the Lax operator and construct some of the explicit solutions. In particular, we give the rational solutions which are expressed by the products of the Schur polynomials corresponding to the non-rectangular Young diagrams.

Matrix biorthogonal polynomials on the unit circle and non-Abelian Ablowitz-Ladik hierarchy

International Nuclear Information System (INIS)

Cafasso, Mattia

2009-01-01

Adler and van Moerbeke (2001 Commun. Pure Appl. Math. 54 153-205) described a reduction of the 2D-Toda hierarchy called the Toeplitz lattice. This hierarchy turns out to be equivalent to the one originally described by Ablowitz and Ladik (1975 J. Math. Phys. 16 598-603) using semidiscrete zero- curvature equations. In this paper, we obtain the original semidiscrete zero-curvature equations starting directly from the Toeplitz lattice and we generalize these computations to the matrix case. This generalization leads us to the semidiscrete zero-curvature equations for the non-Abelian (or multicomponent) version of the Ablowitz-Ladik equations (Gerdzhikov and Ivanov 1982 Theor. Math. Phys. 52 676-85). In this way, we extend the link between biorthogonal polynomials on the unit circle and the Ablowitz-Ladik hierarchy to the matrix case.

Flows, scaling, and the control of moment hierarchies for stochastic chemical reaction networks

Science.gov (United States)

Smith, Eric; Krishnamurthy, Supriya

2017-12-01

Stochastic chemical reaction networks (CRNs) are complex systems that combine the features of concurrent transformation of multiple variables in each elementary reaction event and nonlinear relations between states and their rates of change. Most general results concerning CRNs are limited to restricted cases where a topological characteristic known as deficiency takes a value 0 or 1, implying uniqueness and positivity of steady states and surprising, low-information forms for their associated probability distributions. Here we derive equations of motion for fluctuation moments at all orders for stochastic CRNs at general deficiency. We show, for the standard base case of proportional sampling without replacement (which underlies the mass-action rate law), that the generator of the stochastic process acts on the hierarchy of factorial moments with a finite representation. Whereas simulation of high-order moments for many-particle systems is costly, this representation reduces the solution of moment hierarchies to a complexity comparable to solving a heat equation. At steady states, moment hierarchies for finite CRNs interpolate between low-order and high-order scaling regimes, which may be approximated separately by distributions similar to those for deficiency-zero networks and connected through matched asymptotic expansions. In CRNs with multiple stable or metastable steady states, boundedness of high-order moments provides the starting condition for recursive solution downward to low-order moments, reversing the order usually used to solve moment hierarchies. A basis for a subset of network flows defined by having the same mean-regressing property as the flows in deficiency-zero networks gives the leading contribution to low-order moments in CRNs at general deficiency, in a 1 /n expansion in large particle numbers. Our results give a physical picture of the different informational roles of mean-regressing and non-mean-regressing flows and clarify the dynamical

An integrable coupling system of lattice hierarchy and its continuous limits

International Nuclear Information System (INIS)

Yu Fajun; Li Li

2009-01-01

In [E.G. Fan, Phys. Lett. A 372 (2008) 6368], Fan present a lattice hierarchy and its continuous limits. In this Letter, we extend this method, by introducing a complex discrete spectral problem, a coupling lattice hierarchy is derived. It is shown that a new sequence of combinations of complex lattice spectral problem converges to the integrable coupling couplings of soliton equation hierarchy, which has the integrable coupling system of AKNS hierarchy as a continuous limit.

A generalized Tu formula and Hamiltonian structures of fractional AKNS hierarchy

International Nuclear Information System (INIS)

Wu, Guo-cheng; Zhang, Sheng

2011-01-01

In this Letter, a generalized Tu formula is firstly presented to construct Hamiltonian structures of fractional soliton equations. The obtained results can be reduced to the classical Hamiltonian hierarchy of AKNS in ordinary calculus. -- Highlights: → A generalized Tu formula is first established based on the fractional variational theory for non-differentiable functions. → Hamiltonian structures of fractional AKNS hierarchy are obtained. → The classical AKNS hierarchy is just a special case of the fractional hierarchy.

A generalized Tu formula and Hamiltonian structures of fractional AKNS hierarchy

Energy Technology Data Exchange (ETDEWEB)

Wu, Guo-cheng, E-mail: wuguocheng2002@yahoo.com.cn [Key Laboratory of Numerical Simulation of Sichuan Province, Neijiang, Sichuan 641112 (China); College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan 641112 (China); Zhang, Sheng, E-mail: zhshaeng@yahoo.com.cn [School of Mathematical Sciences, Dalian University of Technology, Dalian 116024 (China)

2011-10-03

In this Letter, a generalized Tu formula is firstly presented to construct Hamiltonian structures of fractional soliton equations. The obtained results can be reduced to the classical Hamiltonian hierarchy of AKNS in ordinary calculus. -- Highlights: → A generalized Tu formula is first established based on the fractional variational theory for non-differentiable functions. → Hamiltonian structures of fractional AKNS hierarchy are obtained. → The classical AKNS hierarchy is just a special case of the fractional hierarchy.

A note on the extended dispersionless Toda hierarchy

Science.gov (United States)

Lee, Niann-Chern; Tu, Ming-Hsien

2013-04-01

We derive dispersionless Hirota equations for the extended dispersionless Toda hierarchy. We show that the dispersionless Hirota equations are just a direct consequence of the genus-zero topological recurrence relation for the topological ℂP1 model. Using the dispersionless Hirota equations, we compute the twopoint functions and express the result in terms of Catalan numbers

A Computational Glimpse at the Leibniz and Frege Hierarchies

Czech Academy of Sciences Publication Activity Database

Moraschini, Tommaso

2018-01-01

Roč. 169, č. 1 (2018), s. 1-20 ISSN 0168-0072 R&D Projects: GA ČR GA13-14654S Institutional support: RVO:67985807 Keywords : abstract algebraic logic * Leibniz hierarchy * Frege hierarchy Leibniz congruence * decidability * Diophantine equations * relation algebras Subject RIV: BA - General Mathematics Impact factor: 0.647, year: 2016

New Integrable Couplings of Generalized Kaup-Newell Hierarchy and Its Hamiltonian Structures

International Nuclear Information System (INIS)

Xia Tiecheng; Zhang Gailian; Fan Engui

2011-01-01

A new isospectral problem is firstly presented, then we derive integrable system of soliton hierarchy. Also we obtain new integrable couplings of the generalized Kaup-Newell soliton equations hierarchy and its Hamiltonian structures by using Tu scheme and the quadratic-form identity. The method can be generalized to other soliton hierarchy. (general)

A Liouville integrable hierarchy, symmetry constraint, new finite-dimensional integrable systems, involutive solution and expanding integrable models

International Nuclear Information System (INIS)

Sun Yepeng; Chen Dengyuan

2006-01-01

A new spectral problem and the associated integrable hierarchy of nonlinear evolution equations are presented in this paper. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses bi-Hamiltonian structure. An explicit symmetry constraint is proposed for the Lax pairs and the adjoint Lax pairs of the hierarchy. Moreover, the corresponding Lax pairs and adjoint Lax pairs are nonlinearized into a hierarchy of commutative, new finite-dimensional completely integrable Hamiltonian systems in the Liouville sense. Further, an involutive representation of solution of each equation in the hierarchy is given. Finally, expanding integrable models of the hierarchy are constructed by using a new Loop algebra

Super Hamiltonian structure of the even order SKP hierarchy without reduction

International Nuclear Information System (INIS)

Watanabe, Yoshihide

1987-01-01

The super Hamiltonian operator which is different from that of Manin and Radul is derived from the even order SKP hierarchy without reduction and in terms of the operator, the equation in the hierarchy is written in a Hamiltonian form. (orig.)

Hydrodynamics beyond Navier-Stokes: exact solution to the lattice Boltzmann hierarchy.

Science.gov (United States)

Ansumali, S; Karlin, I V; Arcidiacono, S; Abbas, A; Prasianakis, N I

2007-03-23

The exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at nonvanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of moments with boundary conditions for populations enables us to derive closed-form solutions for all higher-order moments. A convergence of results suggests that the LB hierarchy with larger velocity sets is the novel way to approximate kinetic theory.

On the nesting of Painlevé hierarchies: A Hamiltonian approach

International Nuclear Information System (INIS)

Pickering, A.

2012-01-01

Highlights: ► Explanation of nesting of Painlevé hierarchies in terms of Hamiltonian structures. ► Approach generally phrased and applicable to continuous and discrete systems. ► Importance of related integrable hierarchies in understanding Painlevé hierarchies. - Abstract: We consider the phenomenon whereby two different Painlevé hierarchies, related to the same hierarchy of completely integrable equations, are such that solutions of one member of one of the Painlevé hierarchies are also solutions of a higher-order member of the other Painlevé hierarchy. An explanation is given in terms of the Hamiltonian structures of the related underlying completely integrable hierarchies, and is sufficiently generally formulated so as to be applicable equally to both continuous and discrete Painlevé hierarchies. Special integrals of a further Painlevé hierarchy related by Bäcklund transformation to the other Painlevé hierarchy mentioned above can also be constructed. Examples of the application of this approach to Painlevé hierarchies related to the Korteweg–de Vries, dispersive water wave, Toda and Volterra integrable hierarchies are considered. Our results provide further evidence of the importance of the underlying structures of related completely integrable hierarchies in understanding the properties of Painlevé hierarchies.

New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation

International Nuclear Information System (INIS)

Chen Huaitang; Zhang Hongqing

2004-01-01

A generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation which has more new solutions. More new multiple soliton solutions are obtained for the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation

Closed hierarchy of correlations in Markovian open quantum systems

International Nuclear Information System (INIS)

Žunkovič, Bojan

2014-01-01

We study the Lindblad master equation in the space of operators and provide simple criteria for closeness of the hierarchy of equations for correlations. We separately consider the time evolution of closed and open systems and show that open systems satisfying the closeness conditions are not necessarily of Gaussian type. In addition, we show that dissipation can induce the closeness of the hierarchy of correlations in interacting quantum systems. As an example we study an interacting optomechanical model, the Fermi–Hubbard model, and the Rabi model, all coupled to a fine-tuned Markovian environment and obtain exact analytic expressions for the time evolution of two-point correlations. (paper)

Generalized Fokker-Planck equations for coloured, multiplicative Gaussian noise

International Nuclear Information System (INIS)

Cetto, A.M.; Pena, L. de la; Velasco, R.M.

1984-01-01

With the help of Novikov's theorem, it is possible to derive a master equation for a coloured, multiplicative, Gaussian random process; the coefficients of this master equation satisfy a complicated auxiliary integro-differential equation. For small values of the Kubo number, the master equation reduces to an approximate generalized Fokker-Planck equation. The diffusion coefficient is explicitly written in terms of correlation functions. Finally, a straightforward and elementary second order perturbative treatment is proposed to derive the same approximate Fokker-Planck equation. (author)

An Algebraic Construction of the First Integrals of the Stationary KdV Hierarchy

Science.gov (United States)

Matsushima, Masatomo; Ohmiya, Mayumi

2009-09-01

The stationary KdV hierarchy is constructed using a kind of recursion operator called Λ-operator. The notion of the maximal solution of the n-th stationary KdV equation is introduced. Using this maximal solution, a specific differential polynomial with the auxiliary spectral parameter called the spectral M-function is constructed as the quadratic form of the fundamental system of the eigenvalue problem for the 2-nd order linear ordinary differential equation which is related to the linearizing operator of the hierarchy. By calculating a perfect square condition of the quadratic form by an elementary algebraic method, the complete set of first integrals of this hierarchy is constructed.

Super-Hamiltonian Structures and Conservation Laws of a New Six-Component Super-Ablowitz-Kaup-Newell-Segur Hierarchy

Directory of Open Access Journals (Sweden)

Fucai You

2014-01-01

Full Text Available A six-component super-Ablowitz-Kaup-Newell-Segur (-AKNS hierarchy is proposed by the zero curvature equation associated with Lie superalgebras. Supertrace identity is used to furnish the super-Hamiltonian structures for the resulting nonlinear superintegrable hierarchy. Furthermore, we derive the infinite conservation laws of the first two nonlinear super-AKNS equations in the hierarchy by utilizing spectral parameter expansions. PACS: 02.30.Ik; 02.30.Jr; 02.20.Sv.

Structural hierarchy of autism spectrum disorder symptoms: an integrative framework.

Science.gov (United States)

Kim, Hyunsik; Keifer, Cara M; Rodriguez-Seijas, Craig; Eaton, Nicholas R; Lerner, Matthew D; Gadow, Kenneth D

2018-01-01

In an attempt to resolve questions regarding the symptom classification of autism spectrum disorder (ASD), previous research generally aimed to demonstrate superiority of one model over another. Rather than adjudicating which model may be optimal, we propose an alternative approach that integrates competing models using Goldberg's bass-ackwards method, providing a comprehensive understanding of the underlying symptom structure of ASD. The study sample comprised 3,825 individuals, consecutive referrals to a university hospital developmental disabilities specialty clinic or a child psychiatry outpatient clinic. This study analyzed DSM-IV-referenced ASD symptom statements from parent and teacher versions of the Child and Adolescent Symptom Inventory-4R. A series of exploratory structural equation models was conducted in order to produce interpretable latent factors that account for multivariate covariance. Results indicated that ASD symptoms were structured into an interpretable hierarchy across multiple informants. This hierarchy includes five levels; key features of ASD bifurcate into different constructs with increasing specificity. This is the first study to examine an underlying structural hierarchy of ASD symptomatology using the bass-ackwards method. This hierarchy demonstrates how core features of ASD relate at differing levels of resolution, providing a model for conceptualizing ASD heterogeneity and a structure for integrating divergent theories of cognitive processes and behavioral features that define the disorder. These findings suggest that a more coherent and complete understanding of the structure of ASD symptoms may be reflected in a metastructure rather than at one level of resolution. © 2017 Association for Child and Adolescent Mental Health.

Multiple solutions to some singular nonlinear Schrodinger equations

Directory of Open Access Journals (Sweden)

Monica Lazzo

2001-01-01

Full Text Available We consider the equation $$ - h^2 Delta u + V_varepsilon(x u = |u|^{p-2} u $$ which arises in the study of standing waves of a nonlinear Schrodinger equation. We allow the potential $V_varepsilon$ to be unbounded below and prove existence and multiplicity results for positive solutions.

Inequality matters: classroom status hierarchy and adolescents' bullying.

Science.gov (United States)

Garandeau, Claire F; Lee, Ihno A; Salmivalli, Christina

2014-07-01

The natural emergence of status hierarchies in adolescent peer groups has long been assumed to help prevent future intragroup aggression. However, clear evidence of this beneficial influence is lacking. In fact, few studies have examined between-group differences in the degree of status hierarchy (defined as within-group variation in individual status) and how they are related to bullying, a widespread form of aggression in schools. Data from 11,296 eighth- and ninth-graders (mean age = 14.57, 50.6 % female) from 583 classes in 71 schools were used to determine the direction of the association between classroom degree of status hierarchy and bullying behaviors, and to investigate prospective relationships between these two variables over a 6-month period. Multilevel structural equation modeling analyses showed that higher levels of classroom status hierarchy were concurrently associated with higher levels of bullying at the end of the school year. Higher hierarchy in the middle of the school year predicted higher bullying later in the year. No evidence was found to indicate that initial bullying predicted future hierarchy. These findings highlight the importance of a shared balance of power in the classroom for the prevention of bullying among adolescents.

Multi-component bi-Hamiltonian Dirac integrable equations

Energy Technology Data Exchange (ETDEWEB)

Ma Wenxiu [Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700 (United States)], E-mail: mawx@math.usf.edu

2009-01-15

A specific matrix iso-spectral problem of arbitrary order is introduced and an associated hierarchy of multi-component Dirac integrable equations is constructed within the framework of zero curvature equations. The bi-Hamiltonian structure of the obtained Dirac hierarchy is presented be means of the variational trace identity. Two examples in the cases of lower order are computed.

Multiplicity Control in Structural Equation Modeling

Science.gov (United States)

Cribbie, Robert A.

2007-01-01

Researchers conducting structural equation modeling analyses rarely, if ever, control for the inflated probability of Type I errors when evaluating the statistical significance of multiple parameters in a model. In this study, the Type I error control, power and true model rates of famsilywise and false discovery rate controlling procedures were…

From fusion hierarchy to excited state TBA

International Nuclear Information System (INIS)

Juettner, G.; Kluemper, A.

1998-01-01

Functional relations among the fusion hierarchy of quantum transfer matrices give a novel derivation of the TBA equations, namely without string hypothesis. This is demonstrated for two important models of 1D highly correlated electron systems, the supersymmetric t-J model and the supersymmetric extended Hubbard model. As a consequence, ''the excited state TBA'' equations, which characterize correlation lengths, are explicitly derived for the t-J model. To the authors' knowledge, this is the first explicit derivation of excited state TBA equations for 1D lattice electron systems. (orig.)

Large radiative corrections to the effective potential and the gauge hierarchy problem

International Nuclear Information System (INIS)

Sachrajda, C.T.C.

1982-01-01

We study the higher order corrections to the effective potential in a simple toy model and in the SU(5) grand unified theory, with a view to seeing what their effects are on the stability equations, and hence on the gauge hierarchy problem for these theories. These corrections contain powers of log (v 2 /h 2 ), where v and h are the large and small vacuum expectation values respectively, and hence cannot a priori be neglected. Nevertheless, after summing these large logarithms we find that the stability equations always contain two equations for v (i.e. these equations are independent of h) and hence can only be satisfied by a special (and hence unnatural) choice of parameters. This we claim is the precise statement of the gauge hierarchy problem. (orig.)

Learning of Alignment Rules between Concept Hierarchies

Science.gov (United States)

Ichise, Ryutaro; Takeda, Hideaki; Honiden, Shinichi

With the rapid advances of information technology, we are acquiring much information than ever before. As a result, we need tools for organizing this data. Concept hierarchies such as ontologies and information categorizations are powerful and convenient methods for accomplishing this goal, which have gained wide spread acceptance. Although each concept hierarchy is useful, it is difficult to employ multiple concept hierarchies at the same time because it is hard to align their conceptual structures. This paper proposes a rule learning method that inputs information from a source concept hierarchy and finds suitable location for them in a target hierarchy. The key idea is to find the most similar categories in each hierarchy, where similarity is measured by the κ(kappa) statistic that counts instances belonging to both categories. In order to evaluate our method, we conducted experiments using two internet directories: Yahoo! and LYCOS. We map information instances from the source directory into the target directory, and show that our learned rules agree with a human-generated assignment 76% of the time.

Quadratic Hierarchy Flavor Rule as the Origin of Dirac CP-Violating Phases

OpenAIRE

Lipmanov, E. M.

2007-01-01

The premise of an organizing quadratic hierarchy rule in lepton-quark flavor physics was used earlier for explanation of the hierarchy patterns of four generic pairs of flavor quantities 1) charged-lepton and 2) neutrino deviations from mass-degeneracy, 3) deviations of lepton mixing from maximal magnitude and 4) deviations of quark mixing from minimal one. Here it is shown that the quadratic hierarchy equation that is uniquely related to three flavor particle generations may have yet another...

Truncation of the many body hierarchy and relaxation times in the McKean model

International Nuclear Information System (INIS)

Schmitt, K.J.

1987-01-01

In the McKean model the BBGKY-hierarchy is equivalent to a simple hierarchy of coupled equations for the p-particle correlation functions. Truncation effects and the convergence of the one-particle distribution towards its exact shape have been studied. In the long time limit the equations can be solved in a closed form. It turns out that the p-particle correlation decays p-times faster than the non-equilibrium one-particle distribution

TRUNCATION OF THE MANY BODY HIERARCHY AND RELAXATION TIMES IN THE McKEAN MODEL

OpenAIRE

Schmitt , K.-J.

1987-01-01

In the McKean model the BBGKY-hierarchy is equivalent to a simple hierarchy of coupled equations for the p-particle correlation functions. Truncation effects and the convergence of the one-particle distribution towards its exact shape have been studied. In the long time limit the equations can be solved in a closed form. It turns out that the p-particle correlation decays p-times faster than the non-equilibrium one-particle distribution.

Elliptic Euler–Poisson–Darboux equation, critical points and integrable systems

International Nuclear Information System (INIS)

Konopelchenko, B G; Ortenzi, G

2013-01-01

The structure and properties of families of critical points for classes of functions W(z, z-bar ) obeying the elliptic Euler–Poisson–Darboux equation E(1/2, 1/2) are studied. General variational and differential equations governing the dependence of critical points in variational (deformation) parameters are found. Explicit examples of the corresponding integrable quasi-linear differential systems and hierarchies are presented. There are the extended dispersionless Toda/nonlinear Schrödinger hierarchies, the ‘inverse’ hierarchy and equations associated with the real-analytic Eisenstein series E(β, β-bar ;1/2) among them. The specific bi-Hamiltonian structure of these equations is also discussed. (paper)

Analysis of random response of structure with uncertain parameters. Combination of substructure synthesis method and hierarchy method

International Nuclear Information System (INIS)

Iwatsubo, Takuzo; Kawamura, Shozo; Mori, Hiroyuki.

1995-01-01

In this paper, the method to obtain the random response of a structure with uncertain parameters is proposed. The proposed method is a combination of the substructure synthesis method and the hierarchy method. The concept of the proposed method is that the hierarchy equation of each substructure is obtained using the hierarchy method, and the hierarchy equation of the overall structure is obtained using the substructure synthesis method. Using the proposed method, the reduced order hierarchy equation can be obtained without analyzing the original whole structure. After the calculation of the mean square value of response, the reliability analysis can be carried out based on the first passage problem and Poisson's excursion rate. As a numerical example of structure, a simple piping system is considered. The damping constant of the support is considered as the uncertainty parameter. Then the random response is calculated using the proposed method. As a result, the proposed method is useful to analyze the random response in terms of the accuracy, computer storage and calculation time. (author)

Flexible scheme to truncate the hierarchy of pure states.

Science.gov (United States)

Zhang, P-P; Bentley, C D B; Eisfeld, A

2018-04-07

The hierarchy of pure states (HOPS) is a wavefunction-based method that can be used for numerically modeling open quantum systems. Formally, HOPS recovers the exact system dynamics for an infinite depth of the hierarchy. However, truncation of the hierarchy is required to numerically implement HOPS. We want to choose a "good" truncation method, where by "good" we mean that it is numerically feasible to check convergence of the results. For the truncation approximation used in previous applications of HOPS, convergence checks are numerically challenging. In this work, we demonstrate the application of the "n-particle approximation" to HOPS. We also introduce a new approximation, which we call the "n-mode approximation." We then explore the convergence of these truncation approximations with respect to the number of equations required in the hierarchy in two exemplary problems: absorption and energy transfer of molecular aggregates.

Flexible scheme to truncate the hierarchy of pure states

Science.gov (United States)

Zhang, P.-P.; Bentley, C. D. B.; Eisfeld, A.

2018-04-01

The hierarchy of pure states (HOPS) is a wavefunction-based method that can be used for numerically modeling open quantum systems. Formally, HOPS recovers the exact system dynamics for an infinite depth of the hierarchy. However, truncation of the hierarchy is required to numerically implement HOPS. We want to choose a "good" truncation method, where by "good" we mean that it is numerically feasible to check convergence of the results. For the truncation approximation used in previous applications of HOPS, convergence checks are numerically challenging. In this work, we demonstrate the application of the "n-particle approximation" to HOPS. We also introduce a new approximation, which we call the "n-mode approximation." We then explore the convergence of these truncation approximations with respect to the number of equations required in the hierarchy in two exemplary problems: absorption and energy transfer of molecular aggregates.

Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy

International Nuclear Information System (INIS)

Aoyama, S.; Kodama, Y.

1996-01-01

Based on the dispersionless KP (dKP) theory, we study a topological Landau-Ginzburg (LG) theory characterized by a rational potential. Writing the dKP hierarchy in a general form treating all the primaries in an equal basis, we find that the hierarchy naturally includes the dispersionless (continuous) limit of Toda hierarchy and its generalizations having a finite number of primaries. Several flat solutions of the topological LG theory are obtained in this formulation, and are identified with those discussed by Dubrovin. We explicitly construct gravitational descendants for all the primary fields. Giving a residue formula for the 3-point functions of the fields, we show that these 3-point functions satisfy the topological recursion relation. The string equation is obtained as the generalized hodograph solutions of the dKP hierarchy, which show that all the gravitational effects to the constitutive equations (2-point functions) can be renormalized into the coupling constants in the small phase space. (orig.)

Multiple spatial scaling and the weak-coupling approximation. I. General formulation and equilibrium theory

Energy Technology Data Exchange (ETDEWEB)

Kleinsmith, P E [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)

1976-04-01

Multiple spatial scaling is incorporated in a modified form of the Bogoliubov plasma cluster expansion; then this proposed reformulation of the plasma weak-coupling approximation is used to derive, from the BBGKY Hierarchy, a decoupled set of equations for the one-and two-particle distribution functions in the limit as the plasma parameter goes to zero. Because the reformulated cluster expansion permits retention of essential two-particle collisional information in the limiting equations, while simultaneously retaining the well-established Debye-scale relative ordering of the correlation functions, decoupling of the Hierarchy is accomplished without introduction of the divergence problems encountered in the Bogoliubov theory, as is indicated by an exact solution of the limiting equations for the equilibrium case. To establish additional links with existing plasma equilibrium theories, the two-particle equilibrium correlation function is used to calculate the interaction energy and the equation of state. The limiting equation for the equilibrium three-particle correlation function is then developed, and a formal solution is obtained.

Variable-coefficient nonisospectral Toda lattice hierarchy and its ...

Indian Academy of Sciences (India)

In this paper, a hierarchy of nonisospectral equations with variable coefficients is derived from the ..... from the definitions of Lax integrability and Lax pairs [26] that the variable-coefficient ..... studying which will be the topic for our future study.

An integrable Hamiltonian hierarchy and its constrained flows with generalized Hamiltonian regular representations, as well as its expanding integrable system

International Nuclear Information System (INIS)

Zhang Yufeng

2003-01-01

A new subalgebra of loop algebra A-tilde 2 is first constructed. It follows that an isospectral problem is established. Using Tu-pattern gives rise to a new integrable hierarchy, which possesses bi-Hamiltonian structure. As its reduction cases, the well-known standard Schrodinger equation and MKdV equation are presented, respectively. Furthermore, by making use of bi-symmetry constraints, generalized Hamiltonian regular representations for the hierarchy are obtained. At last, we obtain an expanding integrable system of this hierarchy by applying a scalar transformation between two isospectral problems and constructing a five-dimensional loop algebra G-tilde. In particular, the expanding integrable models of Schrodinger equation and MKdV equation are presented, respectively

Multiple solutions and stability of the steady transonic small-disturbance equation

Directory of Open Access Journals (Sweden)

Ya Liu

2017-09-01

Full Text Available Numerical solutions of the steady transonic small-disturbance (TSD potential equation are computed using the conservative Murman−Cole scheme. Multiple solutions are discovered and mapped out for the Mach number range at zero angle of attack and the angle of attack range at Mach number 0.85 for the NACA 0012 airfoil. We present a linear stability analysis method by directly assembling and evaluating the Jacobian matrix of the nonlinear finite-difference equation of the TSD equation. The stability of all the discovered multiple solutions are then determined by the proposed eigen analysis. The relation of stability to convergence of the iterative method for solving the TSD equation is discussed. Computations and the stability analysis demonstrate the possibility of eliminating the multiple solutions and stabilizing the remaining unique solution by adding a sufficiently long splitter plate downstream the airfoil trailing edge. Finally, instability of the solution of the TSD equation is shown to be closely connected to the onset of transonic buffet by comparing with experimental data.

Does ℏ play a role in multidimensional spectroscopy? Reduced hierarchy equations of motion approach to molecular vibrations.

Science.gov (United States)

Sakurai, Atsunori; Tanimura, Yoshitaka

2011-04-28

To investigate the role of quantum effects in vibrational spectroscopies, we have carried out numerically exact calculations of linear and nonlinear response functions for an anharmonic potential system nonlinearly coupled to a harmonic oscillator bath. Although one cannot carry out the quantum calculations of the response functions with full molecular dynamics (MD) simulations for a realistic system which consists of many molecules, it is possible to grasp the essence of the quantum effects on the vibrational spectra by employing a model Hamiltonian that describes an intra- or intermolecular vibrational motion in a condensed phase. The present model fully includes vibrational relaxation, while the stochastic model often used to simulate infrared spectra does not. We have employed the reduced quantum hierarchy equations of motion approach in the Wigner space representation to deal with nonperturbative, non-Markovian, and nonsecular system-bath interactions. Taking the classical limit of the hierarchy equations of motion, we have obtained the classical equations of motion that describe the classical dynamics under the same physical conditions as in the quantum case. By comparing the classical and quantum mechanically calculated linear and multidimensional spectra, we found that the profiles of spectra for a fast modulation case were similar, but different for a slow modulation case. In both the classical and quantum cases, we identified the resonant oscillation peak in the spectra, but the quantum peak shifted to the red compared with the classical one if the potential is anharmonic. The prominent quantum effect is the 1-2 transition peak, which appears only in the quantum mechanically calculated spectra as a result of anharmonicity in the potential or nonlinearity of the system-bath coupling. While the contribution of the 1-2 transition is negligible in the fast modulation case, it becomes important in the slow modulation case as long as the amplitude of the

The q-deformed mKP hierarchy with self-consistent sources, Wronskian solutions and solitons

International Nuclear Information System (INIS)

Lin Runliang; Peng Hua; Manas, Manuel

2010-01-01

Based on the eigenfunction symmetry constraint of the q-deformed modified KP hierarchy, a q-deformed mKP hierarchy with self-consistent sources (q-mKPHSCSs) is constructed. The q-mKPHSCSs contain two types of q-deformed mKP equation with self-consistent sources. By the combination of the dressing method and the method of variation of constants, a generalized dressing approach is proposed to solve the q-deformed KP hierarchy with self-consistent sources (q-KPHSCSs). Using the gauge transformation between the q-KPHSCSs and the q-mKPHSCSs, the q-deformed Wronskian solutions for the q-KPHSCSs and the q-mKPHSCSs are obtained. The one-soliton solutions for the q-deformed KP (mKP) equation with a source are given explicitly.

An algebraic scheme associated with the non-commutative KP hierarchy and some of its extensions

International Nuclear Information System (INIS)

Dimakis, Aristophanes; Mueller-Hoissen, Folkert

2005-01-01

A well-known ansatz ('trace method') for soliton solutions turns the equations of the (non-commutative) KP hierarchy, and those of certain extensions, into families of algebraic sum identities. We develop an algebraic formalism, in particular involving a (mixable) shuffle product, to explore their structure. More precisely, we show that the equations of the non-commutative KP hierarchy and its extension (xncKP) in the case of a Moyal-deformed product, as derived in previous work, correspond to identities in this algebra. Furthermore, the Moyal product is replaced by a more general associative product. This leads to a new even more general extension of the non-commutative KP hierarchy. Relations with Rota-Baxter algebras are established

Controllability of partial differential equations governed by multiplicative controls

CERN Document Server

Khapalov, Alexander Y

2010-01-01

The goal of this monograph is to address the issue of the global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. The mathematical models we examine include the linear and nonlinear parabolic and hyperbolic PDE's, the Schrödinger equation, and coupled hybrid nonlinear distributed parameter systems modeling the swimming phenomenon. The book offers a new, high-quality and intrinsically nonlinear methodology to approach the aforementioned highly nonlinear controllability problems.

Langevin equations with multiplicative noise: application to domain growth

International Nuclear Information System (INIS)

Sancho, J.M.; Hernandez-Machado, A.; Ramirez-Piscina, L.; Lacasta, A.M.

1993-01-01

Langevin equations of Ginzburg-Landau form with multiplicative noise, are proposed to study the effects of fluctuations in domain growth. These equations are derived from a coarse-grained methodology. The Cahn-Hilliard-Cook linear stability analysis predicts some effects in the transitory regime. We also derive numerical algorithms for the computer simulation of these equations. The numerical results corroborate the analytical productions of the linear analysis. We also present simulation results for spinodal decomposition at large times. (author). 28 refs, 2 figs

Multiple attenuation to reflection seismic data using Radon filter and Wave Equation Multiple Rejection (WEMR) method

Energy Technology Data Exchange (ETDEWEB)

Erlangga, Mokhammad Puput [Geophysical Engineering, Institut Teknologi Bandung, Ganesha Street no.10 Basic Science B Buliding fl.2-3 Bandung, 40132, West Java Indonesia puput.erlangga@gmail.com (Indonesia)

2015-04-16

Separation between signal and noise, incoherent or coherent, is important in seismic data processing. Although we have processed the seismic data, the coherent noise is still mixing with the primary signal. Multiple reflections are a kind of coherent noise. In this research, we processed seismic data to attenuate multiple reflections in the both synthetic and real seismic data of Mentawai. There are several methods to attenuate multiple reflection, one of them is Radon filter method that discriminates between primary reflection and multiple reflection in the τ-p domain based on move out difference between primary reflection and multiple reflection. However, in case where the move out difference is too small, the Radon filter method is not enough to attenuate the multiple reflections. The Radon filter also produces the artifacts on the gathers data. Except the Radon filter method, we also use the Wave Equation Multiple Elimination (WEMR) method to attenuate the long period multiple reflection. The WEMR method can attenuate the long period multiple reflection based on wave equation inversion. Refer to the inversion of wave equation and the magnitude of the seismic wave amplitude that observed on the free surface, we get the water bottom reflectivity which is used to eliminate the multiple reflections. The WEMR method does not depend on the move out difference to attenuate the long period multiple reflection. Therefore, the WEMR method can be applied to the seismic data which has small move out difference as the Mentawai seismic data. The small move out difference on the Mentawai seismic data is caused by the restrictiveness of far offset, which is only 705 meter. We compared the real free multiple stacking data after processing with Radon filter and WEMR process. The conclusion is the WEMR method can more attenuate the long period multiple reflection than the Radon filter method on the real (Mentawai) seismic data.

A high-order q-difference equation for q-Hahn multiple orthogonal polynomials

DEFF Research Database (Denmark)

Arvesú, J.; Esposito, Chiara

2012-01-01

A high-order linear q-difference equation with polynomial coefficients having q-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation coincides with the number of orthogonality conditions that these polynomials satisfy. Some limiting situations when are studie....... Indeed, the difference equation for Hahn multiple orthogonal polynomials given in Lee [J. Approx. Theory (2007), ), doi: 10.1016/j.jat.2007.06.002] is obtained as a limiting case....

A Bayesian Sampler for Optimization of Protein Domain Hierarchies

Science.gov (United States)

2014-01-01

Abstract The process of identifying and modeling functionally divergent subgroups for a specific protein domain class and arranging these subgroups hierarchically has, thus far, largely been done via manual curation. How to accomplish this automatically and optimally is an unsolved statistical and algorithmic problem that is addressed here via Markov chain Monte Carlo sampling. Taking as input a (typically very large) multiple-sequence alignment, the sampler creates and optimizes a hierarchy by adding and deleting leaf nodes, by moving nodes and subtrees up and down the hierarchy, by inserting or deleting internal nodes, and by redefining the sequences and conserved patterns associated with each node. All such operations are based on a probability distribution that models the conserved and divergent patterns defining each subgroup. When we view these patterns as sequence determinants of protein function, each node or subtree in such a hierarchy corresponds to a subgroup of sequences with similar biological properties. The sampler can be applied either de novo or to an existing hierarchy. When applied to 60 protein domains from multiple starting points in this way, it converged on similar solutions with nearly identical log-likelihood ratio scores, suggesting that it typically finds the optimal peak in the posterior probability distribution. Similarities and differences between independently generated, nearly optimal hierarchies for a given domain help distinguish robust from statistically uncertain features. Thus, a future application of the sampler is to provide confidence measures for various features of a domain hierarchy. PMID:24494927

Boltzmann hierarchy for interacting neutrinos I: formalism

International Nuclear Information System (INIS)

Oldengott, Isabel M.; Rampf, Cornelius; Wong, Yvonne Y.Y.

2015-01-01

Starting from the collisional Boltzmann equation, we derive for the first time and from first principles the Boltzmann hierarchy for neutrinos including interactions with a scalar particle. Such interactions appear, for example, in majoron-like models of neutrino mass generation. We study two limits of the scalar mass: (i) An extremely massive scalar whose only role is to mediate an effective 4-fermion neutrino-neutrino interaction, and (ii) a massless scalar that can be produced in abundance and thus demands its own Boltzmann hierarchy. In contrast to, e.g., the first-order Boltzmann hierarchy for Thomson-scattering photons, our interacting neutrino/scalar Boltzmann hierarchies contain additional momentum-dependent collision terms arising from a non-negligible energy transfer in the neutrino-neutrino and neutrino-scalar interactions. This necessitates that we track each momentum mode of the phase space distributions individually, even if the particles were massless. Comparing our hierarchy with the commonly used (c eff 2 ,c vis 2 )-parameterisation, we find no formal correspondence between the two approaches, which raises the question of whether the latter parameterisation even has an interpretation in terms of particle scattering. Lastly, although we have invoked majoron-like models as a motivation for our study, our treatment is in fact generally applicable to all scenarios in which the neutrino and/or other ultrarelativistic fermions interact with scalar particles

The nonlinear differential equations governing a hierarchy of self-exciting coupled Faraday-disk homopolar dynamos

Science.gov (United States)

Hide, Raymond

1997-02-01

This paper discusses the derivation of the autonomous sets of dimensionless nonlinear ordinary differential equations (ODE's) that govern the behaviour of a hierarchy of related electro-mechanical self-exciting Faraday-disk homopolar dynamo systems driven by steady mechanical couples. Each system comprises N interacting units which could be arranged in a ring or lattice. Within each unit and connected in parallel or in series with the coil are electric motors driven into motion by the dynamo, all having linear characteristics, so that nonlinearity arises entirely through the coupling between components. By introducing simple extra terms into the equations it is possible to represent biasing effects arising from impressed electromotive forces due to thermoelectric or chemical processes and from the presence of ambient magnetic fields. Dissipation in the system is due not only to ohmic heating but also to mechanical friction in the disk and the motors, with the latter agency, no matter how weak, playing an unexpectedly crucial rôle in the production of régimes of chaotic behaviour. This has already been demonstrated in recent work on a case of a single unit incorporating just one series motor, which is governed by a novel autonomous set of nonlinear ODE's with three time-dependent variables and four control parameters. It will be of mathematical as well as geophysical and astrophysical interest to investigate systematically phase and amplitude locking and other types of behaviour in the more complicated cases that arise when N > 1, which can typically involve up to 6 N dependent variables and 19 N-5 control parameters. Even the simplest members of the hierarchy, with N as low as 1, 2 or 3, could prove useful as physically-realistic low-dimensional models in theoretical studies of fluctuating stellar and planetary magnetic fields. Geomagnetic polarity reversals could be affected by the presence of the Earth's solid metallic inner core, driven like an electric motor

(2 + 1)-Dimensional Dirac hierarchy and its integrable couplings as well as multi-component integrable system

International Nuclear Information System (INIS)

Li Zhu; Dong Huanhe

2008-01-01

Under the frame of the (2 + 1)-dimensional zero curvature equation and Tu model, (2 + 1)-dimensional Dirac hierarchy is obtained. Again by use of the expanding loop algebra the integrable coupling system of the above hierarchy is given

On W∞ algebras, gauge equivalence of K P hierarchies, two-bosons realizations and their KdV reductions

International Nuclear Information System (INIS)

Aratyn, H.; Ferreira, L.A.; Gomes, J.F.; Zimerman, A.H.

1994-01-01

The gauge equivalence between basic KP hierarchies is discussed. The first two Hamiltonian structures for KP hierarchies leading to the linear and non-linear W ∞ algebras are derived. The realization of the corresponding generators in terms of two boson currents is presented and it is shown to be related to many integrable models which are bi-Hamiltonian. We can also realize those generators by adding extra currents, coupled in a particular way allowing for instance a description of multi-layered Benney equations or multi- component non-linear Schroedinger equation. In this case we can have a second Hamiltonian bracket structure which violates Jacobi identity. We consider the reduction to one-boson systems leading to KdV and mKdV hierarchies. A Miura transformation relating these two hierarchies is obtained by restricting gauge transformation between corresponding two-boson hierarchies. Connection to Drinfeld-Sokolov approach is also discussed in the SL (2, IR) gauge theory. (author)

Baicklund transformation and multiple soliton solutions for the (3+1)-dimensional Jimbo-Miwa equation

Institute of Scientific and Technical Information of China (English)

张解放; 吴锋民

2002-01-01

We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Jimbo-Miwa (JM) equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3+1)-dimensional JM equation into a linear partial differential equation and two bilinear partial differential equations. Starting from these linear and bilinear partial differential equations, some multiple soliton solutions for the (3+1)-dimensional JM equation are obtained by introducing a class of formal solutions.

'Universality' of the Ablowitz-Ladik hierarchy

International Nuclear Information System (INIS)

Vekslerchik, V.E.

1998-05-01

The aim of this paper is to summarize some recently obtained relations between the Ablowitz-Ladik hierarchy (ALH) and other integrable equations. It has been shown that solutions of finite subsystems of the ALH can be used to derive a wide range of solutions for, e.g., the 2D Toda lattice, nonlinear Schroedinger, Davey-Stewartson, Kadomtsev-Petviashvili (DP) and some other equations. Similar approach has been used to construct new integrable models: O(3,1) and multi field sigma models. Such 'universality' of the ALH becomes more transparent in the framework of the Hirota's bilinear method. The ALH, which is usually considered as an infinite set of differential-difference equations, has been presented as a finite system of functional-difference equations, which can be viewed as a generalization of the famous bilinear identities for the KP tau-functions. (author)

The non-isospectral AKNS hierarchy with reality conditions restriction

International Nuclear Information System (INIS)

Zhou Lingjun

2008-01-01

In this paper, we will prove the existence of the non-isospectral AKNS hierarchy with reality conditions restriction and construct the matrix form Darboux transformation. Using this Darboux transformation, the solutions of the relevant nonlinear equations can be expressed explicitly

Poisson-Nernst-Planck equations with steric effects - non-convexity and multiple stationary solutions

Science.gov (United States)

Gavish, Nir

2018-04-01

We study the existence and stability of stationary solutions of Poisson-Nernst-Planck equations with steric effects (PNP-steric equations) with two counter-charged species. We show that within a range of parameters, steric effects give rise to multiple solutions of the corresponding stationary equation that are smooth. The PNP-steric equation, however, is found to be ill-posed at the parameter regime where multiple solutions arise. Following these findings, we introduce a novel PNP-Cahn-Hilliard model, show that it is well-posed and that it admits multiple stationary solutions that are smooth and stable. The various branches of stationary solutions and their stability are mapped utilizing bifurcation analysis and numerical continuation methods.

Simplifying Differential Equations for Multiscale Feynman Integrals beyond Multiple Polylogarithms.

Science.gov (United States)

Adams, Luise; Chaubey, Ekta; Weinzierl, Stefan

2017-04-07

In this Letter we exploit factorization properties of Picard-Fuchs operators to decouple differential equations for multiscale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to an ϵ form.

Mass hierarchy sensitivity of medium baseline reactor neutrino experiments with multiple detectors

Energy Technology Data Exchange (ETDEWEB)

Wang, Hong-Xin, E-mail: hxwang@iphy.me [Department of Physics, Nanjing University, Nanjing 210093 (China); Zhan, Liang; Li, Yu-Feng; Cao, Guo-Fu [Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 (China); Chen, Shen-Jian [Department of Physics, Nanjing University, Nanjing 210093 (China)

2017-05-15

We report the neutrino mass hierarchy (MH) determination of medium baseline reactor neutrino experiments with multiple detectors, where the sensitivity of measuring the MH can be significantly improved by adding a near detector. Then the impact of the baseline and target mass of the near detector on the combined MH sensitivity has been studied thoroughly. The optimal selections of the baseline and target mass of the near detector are ∼12.5 km and ∼4 kton respectively for a far detector with the target mass of 20 kton and the baseline of 52.5 km. As typical examples of future medium baseline reactor neutrino experiments, the optimal location and target mass of the near detector are selected for the specific configurations of JUNO and RENO-50. Finally, we discuss distinct effects of the reactor antineutrino energy spectrum uncertainty for setups of a single detector and double detectors, which indicate that the spectrum uncertainty can be well constrained in the presence of the near detector.

Generalized intermediate long-wave hierarchy in zero-curvature representation with noncommutative spectral parameter

Science.gov (United States)

Degasperis, A.; Lebedev, D.; Olshanetsky, M.; Pakuliak, S.; Perelomov, A.; Santini, P. M.

1992-11-01

The simplest generalization of the intermediate long-wave hierarchy (ILW) is considered to show how to extend the Zakharov-Shabat dressing method to nonlocal, i.e., integro-partial differential, equations. The purpose is to give a procedure of constructing the zero-curvature representation of this class of equations. This result obtains by combining the Drinfeld-Sokolov formalism together with the introduction of an operator-valued spectral parameter, namely, a spectral parameter that does not commute with the space variable x. This extension provides a connection between the ILWk hierarchy and the Saveliev-Vershik continuum graded Lie algebras. In the case of ILW2 the Fairlie-Zachos sinh-algebra was found.

Kinetic equations for an unstable plasma; Equations cinetiques d'un plasma instable

Energy Technology Data Exchange (ETDEWEB)

Laval, G; Pellat, R [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires

1968-07-01

In this work, we establish the plasma kinetic equations starting from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy of equations. We demonstrate that relations existing between correlation functions may help to justify the truncation of the hierarchy. Then we obtain the kinetic equations of a stable or unstable plasma. They do not reduce to an equation for the one-body distribution function, but generally involve two coupled equations for the one-body distribution function and the spectral density of the fluctuating electric field. We study limiting cases where the Balescu-Lenard equation, the quasi-linear theory, the Pines-Schrieffer equations and the equations of weak turbulence in the random phase approximation are recovered. At last we generalise the H-theorem for the system of equations and we define conditions for irreversible behaviour. (authors) [French] Dans ce travail nous etablissons les equations cinetiques d'un plasma a partir des equations de la recurrence de Bogoliubov, Born, Green, Kirkwood et Yvon. Nous demontrons qu'entre les fonctions de correlation d'un plasma existent des relations qui permettent de justifier la troncature de la recurrence. Nous obtenons alors les equations cinetiques d'un plasma stable ou instable. En general elles ne se reduisent pas a une equation d'evolution pour la densite simple, mais se composent de deux equations couplees portant sur la densite simple et la densite spectrale du champ electrique fluctuant. Nous etudions le cas limites ou l'on retrouve l'equation de Balescu-Lenard, les equations de la theorie quasi-lineaire, les equations de Pines et Schrieffer et les equations de la turbulence faible dans l'approximation des phases aleatoires. Enfin, nous generalisons le theoreme H pour ce systeme d'equations et nous precisons les conditions d'evolution irreversible. (auteurs)

Two new integrable couplings of the soliton hierarchies with self-consistent sources

International Nuclear Information System (INIS)

Tie-Cheng, Xia

2010-01-01

A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with s-tilde l(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613). Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra s-tilde l(4). In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources. (general)

The Lax operator approach for the Virasoro and the W-constraints in the generalized KdV hierarchy

International Nuclear Information System (INIS)

Panda, S.; Roy, S.

1992-08-01

We show directly in the Lax operator approach how the Virasoro and W-constraints on the τ-function arise in the p-reduced KP hierarchy or Generalized KdV hierarchy. In particular, we consider the KdV and the Boussinesq hierarchy to show that the Virasoro and the W-constraints follow from the string equation by expanding the ''additional symmetry'' operator in terms of the Lax operator. We also mention how this method could be generalized for higher KdV hierarchies. (author). 34 refs

Exact non-Markovian master equations for multiple qubit systems: Quantum-trajectory approach

Science.gov (United States)

Chen, Yusui; You, J. Q.; Yu, Ting

2014-11-01

A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum-state diffusion equations. These exact master equations arise naturally from the quantum decoherence dynamics of qubit system as a quantum memory coupled to a collective colored noisy source. The exact master equations are also important in optimal quantum control, quantum dissipation, and quantum thermodynamics. In this paper, we show that the exact non-Markovian master equation for a dissipative N -qubit system can be derived explicitly from the statistical average of the corresponding non-Markovian quantum trajectories. We illustrated our general formulation by an explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This multiple qubit master equation offers an accurate time evolution of quantum systems in various domains, and paves the way to investigate the memory effect of an open system in a non-Markovian regime without any approximation.

Infinitely many conservation laws for two integrable lattice hierarchies associated with a new discrete Schroedinger spectral problem

International Nuclear Information System (INIS)

Zhu, Zuo-nong; Tam, Hon-Wah; Ding, Qing

2003-01-01

In this Letter, by means of considering matrix form of a new Schroedinger discrete spectral operator equation, and constructing opportune time evolution equations, and using discrete zero curvature representation, two discrete integrable lattice hierarchies proposed by Boiti et al. [J. Phys. A: Math. Gen. 36 (2003) 139] are re-derived. From the matrix Lax representations, we demonstrate the existence of infinitely many conservation laws for the two lattice hierarchies and give the corresponding conserved densities and the associated fluxes by means of formulae. Thus their integrability is further confirmed. Specially we obtain the infinitely many conservation laws for a new discrete version of the KdV equation. A connection between the conservation laws of the discrete KdV equation and the ones of the KdV equation is discussed by two examples

q-Deformed KP Hierarchy and q-Deformed Constrained KP Hierarchy

OpenAIRE

He, Jingsong; Li, Yinghua; Cheng, Yi

2006-01-01

Using the determinant representation of gauge transformation operator, we have shown that the general form of $au$ function of the $q$-KP hierarchy is a $q$-deformed generalized Wronskian, which includes the $q$-deformed Wronskian as a special case. On the basis of these, we study the $q$-deformed constrained KP ($q$-cKP) hierarchy, i.e. $l$-constraints of $q$-KP hierarchy. Similar to the ordinary constrained KP (cKP) hierarchy, a large class of solutions of $q$-cKP hierarchy can be represent...

On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations

International Nuclear Information System (INIS)

Zhang Yu-Feng; Tam, Honwah

2016-01-01

In the paper, we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly. By the approach the various loop algebras of the Lie algebra A_1 are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained, respectively. A reduction of the later hierarchy is just right the famous Ablowitz–Ladik hierarchy. Finally, via two different enlarging Lie algebras of the Lie algebra A_1, we derive two resulting differential-difference integrable couplings of the Toda hierarchy, of course, they are all various discrete expanding integrable models of the Toda hierarchy. When the introduced spectral matrices are higher degrees, the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple. (paper)

A Global Mitigation Hierarchy for Nature Conservation

Science.gov (United States)

Bull, Joseph W; Addison, Prue F E; Burgass, Michael J; Gianuca, Dimas; Gorham, Taylor M; Jacob, Céline; Watson, James E M; Wilcox, Chris; Milner-Gulland, E J

2018-01-01

Abstract Efforts to conserve biodiversity comprise a patchwork of international goals, national-level plans, and local interventions that, overall, are failing. We discuss the potential utility of applying the mitigation hierarchy, widely used during economic development activities, to all negative human impacts on biodiversity. Evaluating all biodiversity losses and gains through the mitigation hierarchy could help prioritize consideration of conservation goals and drive the empirical evaluation of conservation investments through the explicit consideration of counterfactual trends and ecosystem dynamics across scales. We explore the challenges in using this framework to achieve global conservation goals, including operationalization and monitoring and compliance, and we discuss solutions and research priorities. The mitigation hierarchy's conceptual power and ability to clarify thinking could provide the step change needed to integrate the multiple elements of conservation goals and interventions in order to achieve successful biodiversity outcomes. PMID:29731513

Minimal models from W-constrained hierarchies via the Kontsevich-Miwa transform

CERN Document Server

Gato-Rivera, Beatriz

1992-01-01

A direct relation between the conformal formalism for 2d-quantum gravity and the W-constrained KP hierarchy is found, without the need to invoke intermediate matrix model technology. The Kontsevich-Miwa transform of the KP hierarchy is used to establish an identification between W constraints on the KP tau function and decoupling equations corresponding to Virasoro null vectors. The Kontsevich-Miwa transform maps the $W^{(l)}$-constrained KP hierarchy to the $(p^\\prime,p)$ minimal model, with the tau function being given by the correlator of a product of (dressed) $(l,1)$ (or $(1,l)$) operators, provided the Miwa parameter $n_i$ and the free parameter (an abstract $bc$ spin) present in the constraints are expressed through the ratio $p^\\prime/p$ and the level $l$.

Lagrangian and Hamiltonian structures in an integrable hierarchy and space–time duality

International Nuclear Information System (INIS)

Avan, Jean; Caudrelier, Vincent; Doikou, Anastasia; Kundu, Anjan

2016-01-01

We define and illustrate the novel notion of dual integrable hierarchies, on the example of the nonlinear Schrödinger (NLS) hierarchy. For each integrable nonlinear evolution equation (NLEE) in the hierarchy, dual integrable structures are characterized by the fact that the zero-curvature representation of the NLEE can be realized by two Hamiltonian formulations stemming from two distinct choices of the configuration space, yielding two inequivalent Poisson structures on the corresponding phase space and two distinct Hamiltonians. This is fundamentally different from the standard bi-Hamiltonian or generally multitime structure. The first formulation chooses purely space-dependent fields as configuration space; it yields the standard Poisson structure for NLS. The other one is new: it chooses purely time-dependent fields as configuration space and yields a different Poisson structure at each level of the hierarchy. The corresponding NLEE becomes a space evolution equation. We emphasize the role of the Lagrangian formulation as a unifying framework for deriving both Poisson structures, using ideas from covariant field theory. One of our main results is to show that the two matrices of the Lax pair satisfy the same form of ultralocal Poisson algebra (up to a sign) characterized by an r-matrix structure, whereas traditionally only one of them is involved in the classical r-matrix method. We construct explicit dual hierarchies of Hamiltonians, and Lax representations of the triggered dynamics, from the monodromy matrices of either Lax matrix. An appealing procedure to build a multi-dimensional lattice of Lax pair, through successive uses of the dual Poisson structures, is briefly introduced.

Lagrangian and Hamiltonian structures in an integrable hierarchy and space–time duality

Energy Technology Data Exchange (ETDEWEB)

Avan, Jean, E-mail: Jean.Avan@u-cergy.fr [Laboratoire de Physique Théorique et Modélisation (CNRS UMR 8089), Université de Cergy-Pontoise, F-95302 Cergy-Pontoise (France); Caudrelier, Vincent, E-mail: v.caudrelier@city.ac.uk [Department of Mathematics, City University London, Northampton Square, EC1V 0HB London (United Kingdom); Doikou, Anastasia, E-mail: A.Doikou@hw.ac.uk [Department of Mathematics, Heriot-Watt University, EH14 4AS, Edinburgh (United Kingdom); Kundu, Anjan, E-mail: Anjan.Kundu@saha.ac.in [Saha Institute of Nuclear Physics, Theory Division, Kolkata (India)

2016-01-15

We define and illustrate the novel notion of dual integrable hierarchies, on the example of the nonlinear Schrödinger (NLS) hierarchy. For each integrable nonlinear evolution equation (NLEE) in the hierarchy, dual integrable structures are characterized by the fact that the zero-curvature representation of the NLEE can be realized by two Hamiltonian formulations stemming from two distinct choices of the configuration space, yielding two inequivalent Poisson structures on the corresponding phase space and two distinct Hamiltonians. This is fundamentally different from the standard bi-Hamiltonian or generally multitime structure. The first formulation chooses purely space-dependent fields as configuration space; it yields the standard Poisson structure for NLS. The other one is new: it chooses purely time-dependent fields as configuration space and yields a different Poisson structure at each level of the hierarchy. The corresponding NLEE becomes a space evolution equation. We emphasize the role of the Lagrangian formulation as a unifying framework for deriving both Poisson structures, using ideas from covariant field theory. One of our main results is to show that the two matrices of the Lax pair satisfy the same form of ultralocal Poisson algebra (up to a sign) characterized by an r-matrix structure, whereas traditionally only one of them is involved in the classical r-matrix method. We construct explicit dual hierarchies of Hamiltonians, and Lax representations of the triggered dynamics, from the monodromy matrices of either Lax matrix. An appealing procedure to build a multi-dimensional lattice of Lax pair, through successive uses of the dual Poisson structures, is briefly introduced.

A calderón multiplicative preconditioner for the combined field integral equation

KAUST Repository

Bagci, Hakan; Andriulli, Francesco P.; Cools, Kristof; Olyslager, Femke; Michielssen, Eric

2009-01-01

A Calderón multiplicative preconditioner (CMP) for the combined field integral equation (CFIE) is developed. Just like with previously proposed Caldern-preconditioned CFIEs, a localization procedure is employed to ensure that the equation

Reciprocal link for a coupled Camassa–Holm type equation

International Nuclear Information System (INIS)

Li, Nianhua; Zhang, Jinshun; Wu, Lihua

2016-01-01

Highlights: • We construct a reciprocal transformation for a coupled Camassa–Holm type equation proposed by Geng and Xue. • The transformed coupled Camassa–Holm type system is a reduction of the first negative flow in a modified Drinfeld–Sokolov III hierarchy. • The Lax pair and bi-Hamiltonian structure behaviors of the coupled Camassa–Holm type equation under the reciprocal transformation are analyzed. - Abstract: A coupled Camassa–Holm type equation is linked to the first negative flow in a modified Drinfeld–Sokolov III hierarchy by a transformation of reciprocal type. Meanwhile the Lax pair and bi-Hamiltonian structure behaviors of this coupled Camassa–Holm type equation under the reciprocal transformation are analyzed.

Mass hierarchy sensitivity of medium baseline reactor neutrino experiments with multiple detectors

Directory of Open Access Journals (Sweden)

Hong-Xin Wang

2017-05-01

Full Text Available We report the neutrino mass hierarchy (MH determination of medium baseline reactor neutrino experiments with multiple detectors, where the sensitivity of measuring the MH can be significantly improved by adding a near detector. Then the impact of the baseline and target mass of the near detector on the combined MH sensitivity has been studied thoroughly. The optimal selections of the baseline and target mass of the near detector are ∼12.5 km and ∼4 kton respectively for a far detector with the target mass of 20 kton and the baseline of 52.5 km. As typical examples of future medium baseline reactor neutrino experiments, the optimal location and target mass of the near detector are selected for the specific configurations of JUNO and RENO-50. Finally, we discuss distinct effects of the reactor antineutrino energy spectrum uncertainty for setups of a single detector and double detectors, which indicate that the spectrum uncertainty can be well constrained in the presence of the near detector.

A stochastic model of multiple scattering of charged particles: process, transport equation and solutions

International Nuclear Information System (INIS)

Papiez, L.; Moskvin, V.; Tulovsky, V.

2001-01-01

The process of angular-spatial evolution of multiple scattering of charged particles can be described by a special case of Boltzmann integro-differential equation called Lewis equation. The underlying stochastic process for this evolution is the compound Poisson process on the surface of the unit sphere. The significant portion of events that constitute compound Poisson process that describes multiple scattering have diffusional character. This property allows to analyze the process of angular-spatial evolution of multiple scattering of charged particles as combination of soft and hard collision processes and compute appropriately its transition densities. These computations provide a method of the approximate solution to the Lewis equation. (orig.)

Reduction of infinite dimensional equations

Directory of Open Access Journals (Sweden)

Zhongding Li

2006-02-01

Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.

A linear multiple balance method for discrete ordinates neutron transport equations

International Nuclear Information System (INIS)

Park, Chang Je; Cho, Nam Zin

2000-01-01

A linear multiple balance method (LMB) is developed to provide more accurate and positive solutions for the discrete ordinates neutron transport equations. In this multiple balance approach, one mesh cell is divided into two subcells with quadratic approximation of angular flux distribution. Four multiple balance equations are used to relate center angular flux with average angular flux by Simpson's rule. From the analysis of spatial truncation error, the accuracy of the linear multiple balance scheme is ο(Δ 4 ) whereas that of diamond differencing is ο(Δ 2 ). To accelerate the linear multiple balance method, we also describe a simplified additive angular dependent rebalance factor scheme which combines a modified boundary projection acceleration scheme and the angular dependent rebalance factor acceleration schme. It is demonstrated, via fourier analysis of a simple model problem as well as numerical calculations, that the additive angular dependent rebalance factor acceleration scheme is unconditionally stable with spectral radius < 0.2069c (c being the scattering ration). The numerical results tested so far on slab-geometry discrete ordinates transport problems show that the solution method of linear multiple balance is effective and sufficiently efficient

Making Sense of the Abstraction Hierarchy in the Power Plant Domain

DEFF Research Database (Denmark)

Lind, Morten

2003-01-01

The paper discusses the abstraction hierarchy proposed by Rasmussen [(1986) Information processing and human-machine interaction, North-Holland] for design of human-machine interfaces for supervisory control. The purpose of the abstraction hierarchy is to represent a work domain by multiple levels...... of means-end and part-whole abstractions. It is argued in the paper that the abstraction hierarchy suffers from both methodological and conceptual problems. A cluster of selected problems are analyzed and illustrated by concrete examples from the power plant domain. It is concluded that the semantics...... in the model-building process. It is also pointed out that attempts to clarify the semantics of the abstraction hierarchy will invariably reduce the range of work domains where it can be applied....

Sintering equation: determination of its coefficients by experiments - using multiple regression

International Nuclear Information System (INIS)

Windelberg, D.

1999-01-01

Sintering is a method for volume-compression (or volume-contraction) of powdered or grained material applying high temperature (less than the melting point of the material). Maekipirtti tried to find an equation which describes the process of sintering by its main parameters sintering time, sintering temperature and volume contracting. Such equation is called a sintering equation. It also contains some coefficients which characterise the behaviour of the material during the process of sintering. These coefficients have to be determined by experiments. Here we show that some linear regressions will produce wrong coefficients, but multiple regression results in an useful sintering equation. (orig.)

Discrete coupled derivative nonlinear Schroedinger equations and their quasi-periodic solutions

International Nuclear Information System (INIS)

Geng Xianguo; Su Ting

2007-01-01

A hierarchy of nonlinear differential-difference equations associated with a discrete isospectral problem is proposed, in which a typical differential-difference equation is a discrete coupled derivative nonlinear Schroedinger equation. With the help of the nonlinearization of the Lax pairs, the hierarchy of nonlinear differential-difference equations is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems. Based on the theory of algebraic curve, the Abel-Jacobi coordinates are introduced to straighten out the corresponding flows, from which quasi-periodic solutions for these differential-difference equations are obtained resorting to the Riemann-theta functions. Moreover, a (2+1)-dimensional discrete coupled derivative nonlinear Schroedinger equation is proposed and its quasi-periodic solutions are derived

The master T-operator for the Gaudin model and the KP hierarchy

International Nuclear Information System (INIS)

Alexandrov, Alexander; Leurent, Sebastien; Tsuboi, Zengo; Zabrodin, Anton

2014-01-01

Following the approach of [1], we construct the master T-operator for the quantum Gaudin model with twisted boundary conditions and show that it satisfies the bilinear identity and Hirota equations for the classical KP hierarchy. We also characterize the class of solutions to the KP hierarchy that correspond to eigenvalues of the master T-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum Gaudin model and the classical Calogero–Moser system of particles

Renormalization group equations with multiple coupling constants

International Nuclear Information System (INIS)

Ghika, G.; Visinescu, M.

1975-01-01

The main purpose of this paper is to study the renormalization group equations of a renormalizable field theory with multiple coupling constants. A method for the investigation of the asymptotic stability is presented. This method is applied to a gauge theory with Yukawa and self-quartic couplings of scalar mesons in order to find the domains of asymptotic freedom. An asymptotic expansion for the solutions which tend to the origin of the coupling constants is given

Hierarchy of modular graph identities

Energy Technology Data Exchange (ETDEWEB)

D’Hoker, Eric; Kaidi, Justin [Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy,University of California,Los Angeles, CA 90095 (United States)

2016-11-09

The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.

Hierarchy of modular graph identities

International Nuclear Information System (INIS)

D’Hoker, Eric; Kaidi, Justin

2016-01-01

The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.

The (2+1)-dimensional nonisospectral relativistic Toda hierarchy related to the generalized discrete Painleve hierarchy

International Nuclear Information System (INIS)

Zhu Zuonong

2007-01-01

In this paper, we will concentrate on the topic of integrable discrete hierarchies in 2+1 dimensions, and their connection with discrete Painleve hierarchies. By considering a (2+1)-dimensional nonisospectral discrete linear problem, two new (2+1)-dimensional nonisospectral integrable lattice hierarchies-the 2+1 nonisospectral relativistic Toda lattice hierarchy and the 2+1 nonisospectral negative relativistic Toda lattice hierarchy-are constructed. It is shown that the reductions of the two new 2+1 nonisospectral lattice hierarchies lead to the (2+1)-dimensional nonisospectral Volterra lattice hierarchy and the (2+1)-dimensional nonisospectral negative Volterra lattice hierarchy. We also obtain two new (1+1)-dimensional nonisospectral integrable lattice hierarchies and two new ordinary difference hierarchies which are direct reductions of the two 2+1 nonisospectral integrable lattice hierarchies. One of the two difference hierarchies yields our previously obtained generalized discrete first Painleve (dP I ) hierarchy and another one yields a generalized alternative discrete second Painleve (alt-dP II ) hierarchy

A New Riemann Type Hydrodynamical Hierarchy and its Integrability Analysis

International Nuclear Information System (INIS)

Golenia, Jolanta Jolanta; Bogolubov, Nikolai N. Jr.; Popowicz, Ziemowit; Pavlov, Maxim V.; Prykarpatsky, Anatoliy K.

2009-12-01

Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The well defined regularization of the model is constructed and its Lax type integrability is discussed. A generalized hydrodynamical Riemann type system is considered, infinite hierarchies of conservation laws, related compatible co-symplectic structures and Lax type representations for the special cases N = 2, 3 and N = 4 are constructed. (author)

Bi-Hamiltonian operators, integrable flows of curves using moving frames and geometric map equations

International Nuclear Information System (INIS)

Anco, Stephen C

2006-01-01

Moving frames of various kinds are used to derive bi-Hamiltonian operators and associated hierarchies of multi-component soliton equations from group-invariant flows of non-stretching curves in constant-curvature manifolds and Lie-group manifolds. The hierarchy in the constant-curvature case consists of a vector mKdV equation coming from a parallel frame, a vector potential mKdV equation coming from a covariantly constant frame, and higher order counterparts generated by an underlying vector mKdV recursion operator. In the Lie-group case, the hierarchy comprises a group-invariant analogue of the vector NLS equation coming from a left-invariant frame, along with higher order counterparts generated by a recursion operator that is like a square root of the mKdV one. The corresponding respective curve flows are found to be given by geometric nonlinear PDEs, specifically mKdV and group-invariant analogues of Schroedinger maps. In all cases the hierarchies also contain variants of vector sine-Gordon equations arising from the kernel of the respective recursion operators. The geometric PDEs that describe the corresponding curve flows are shown to be wave maps

Bi-Hamiltonian operators, integrable flows of curves using moving frames and geometric map equations

Energy Technology Data Exchange (ETDEWEB)

Anco, Stephen C [Department of Mathematics, Brock University, St Catharines, ON (Canada)

2006-03-03

Moving frames of various kinds are used to derive bi-Hamiltonian operators and associated hierarchies of multi-component soliton equations from group-invariant flows of non-stretching curves in constant-curvature manifolds and Lie-group manifolds. The hierarchy in the constant-curvature case consists of a vector mKdV equation coming from a parallel frame, a vector potential mKdV equation coming from a covariantly constant frame, and higher order counterparts generated by an underlying vector mKdV recursion operator. In the Lie-group case, the hierarchy comprises a group-invariant analogue of the vector NLS equation coming from a left-invariant frame, along with higher order counterparts generated by a recursion operator that is like a square root of the mKdV one. The corresponding respective curve flows are found to be given by geometric nonlinear PDEs, specifically mKdV and group-invariant analogues of Schroedinger maps. In all cases the hierarchies also contain variants of vector sine-Gordon equations arising from the kernel of the respective recursion operators. The geometric PDEs that describe the corresponding curve flows are shown to be wave maps.

Why hierarchies thrive.

Science.gov (United States)

Leavitt, Harold J

2003-03-01

Hardly anyone has a good word to say about hierarchies. Academics, consultants, and management gurus regularly forecast their imminent replacement because hierarchies--even when populated by considerate and intelligent people--can be cruel and stupid. They routinely transform motivated and loyal employees into disaffected Dilberts. It's no wonder that we continue to search for more humane and productive alternatives to them. Yet the intensity with which we struggle against hierarchies only serves to highlight their durability. Hierarchy, it seems, may be intrinsic not only to the natural world but also to our own natures. In this article, organizational behavior expert Harold J. Leavitt presents neither a defense of human hierarchies nor another attack on them. Instead, he offers a reality check, a reminder that hierarchy remains the basic structure of most, if not all, large, ongoing human organizations. That's because although they are often depicted as being out of date, hierarchies have proved to be extraordinarily adaptive. Over the past 50 years, for example, they have co-opted the three major managerial movements--human relations, analytic management, and communities of practice. Hierarchies also persist because they deliver real practical and psychological value, and they fulfill our deep need for order and security. Despite the good they may do, hierarchies are inevitably authoritarian. That authoritarianism shows up in all kinds of ways and influences everything in organizations, particularly communication. In multilevel organizations, for instance, messages get distorted as they travel up and down the ladder of command. Self-protection and self-interest weigh in, and relevant information is lost as messages make stops along the route. Sensitive leaders take steps to make speaking the truth as painless as possible. But it never is in organizations, because authoritarianism is an immutable element of hierarchy.

A calderón multiplicative preconditioner for the combined field integral equation

KAUST Repository

Bagci, Hakan

2009-10-01

A Calderón multiplicative preconditioner (CMP) for the combined field integral equation (CFIE) is developed. Just like with previously proposed Caldern-preconditioned CFIEs, a localization procedure is employed to ensure that the equation is resonance-free. The iterative solution of the linear system of equations obtained via the CMP-based discretization of the CFIE converges rapidly regardless of the discretization density and the frequency of excitation. © 2009 IEEE.

Diffusion equations and hard collisions in multiple scattering of charged particles

International Nuclear Information System (INIS)

Papiez, Lech; Tulovsky, Vladimir

1998-01-01

The processes of angular-spatial evolution of multiple scattering of charged particles are described by the Lewis (special case of Boltzmann) integro-differential equation. The underlying stochastic process for this evolution is the compound Poisson process with transition densities satisfying the Lewis equation. In this paper we derive the Lewis equation from the compound Poisson process and show that the effective method of the solution of this equation can be based on the idea of decomposition of the compound Poisson process into processes of soft and hard collisions. Formulas for transition densities of soft and hard collision processes are provided in this paper together with the formula expressing the general solution of the Lewis equation in terms of those transition densities

Diffusion equations and hard collisions in multiple scattering of charged particles

Energy Technology Data Exchange (ETDEWEB)

Papiez, Lech [Department of Radiation Oncology, Indiana University, Indianapolis, IN (United States); Tulovsky, Vladimir [Department of Mathematics, St. John' s College, Staten Island, New York, NY (United States)

1998-09-01

The processes of angular-spatial evolution of multiple scattering of charged particles are described by the Lewis (special case of Boltzmann) integro-differential equation. The underlying stochastic process for this evolution is the compound Poisson process with transition densities satisfying the Lewis equation. In this paper we derive the Lewis equation from the compound Poisson process and show that the effective method of the solution of this equation can be based on the idea of decomposition of the compound Poisson process into processes of soft and hard collisions. Formulas for transition densities of soft and hard collision processes are provided in this paper together with the formula expressing the general solution of the Lewis equation in terms of those transition densities.

Application of analytic hierarchy process to extract the user's purpose of expert systems

International Nuclear Information System (INIS)

Gofuku, Akio; Wakabayashi, Jiro; Morimoto, Takashi.

1992-01-01

This paper deals with an application of analytic hierarchy process (AHP) to extract the user's purpose which must be input to expert systems. In the AHP, the process to obtain the weights for criteria by pairwise comparisons is interpreted as the extraction of the decision marker's idea about the importance of each criterion. With this interpretation, the analytic hierarchy process is applied to extract the analyst's idea of the weights of several factors to select constitutive equations suitable for a target analysis in a model selection support expert system under development for numerical simulation of nuclear thermal-hydraulics; the constitutive equations are ordinary introduced in a liquid-vapor two-phase flow analysis. Furthermore, an algorithm by applying the graph theory is shown to evaluate covering condition to obtain the weights from incomplete pairwise comparisons. (author)

Hierarchy of models: From qualitative to quantitative analysis of circadian rhythms in cyanobacteria

Science.gov (United States)

Chaves, M.; Preto, M.

2013-06-01

A hierarchy of models, ranging from high to lower levels of abstraction, is proposed to construct "minimal" but predictive and explanatory models of biological systems. Three hierarchical levels will be considered: Boolean networks, piecewise affine differential (PWA) equations, and a class of continuous, ordinary, differential equations' models derived from the PWA model. This hierarchy provides different levels of approximation of the biological system and, crucially, allows the use of theoretical tools to more exactly analyze and understand the mechanisms of the system. The Kai ABC oscillator, which is at the core of the cyanobacterial circadian rhythm, is analyzed as a case study, showing how several fundamental properties—order of oscillations, synchronization when mixing oscillating samples, structural robustness, and entrainment by external cues—can be obtained from basic mechanisms.

A formula relating infinitesimal Backlund transformations to hierarchy generating operators

International Nuclear Information System (INIS)

Hou, B.Y.; Tu, G.Z.

1982-12-01

Let u'=Bsub(eta)u and l be, respectively, the elementary Backlund transformation and hierarchy generating operators for the AKNS equations. It is shown that (dB/d eta)(Bsub(eta)) - 1 =σ 3 /(l-eta). A similar formula relating to the general NxN matrix spectral problem is also derived. (author)

N = 2 local and N = 4 non-local reductions of supersymmetric KP hierarchy in N = 2 superspace

International Nuclear Information System (INIS)

Delduc, F.; Gallot, L.; Sorin, A.

1999-01-01

An N = 4 supersymmetric matrix KP hierarchy is proposed and a wide class of its reductions which are characterized by a finite number of fields are described. This class includes the one-dimensional reduction of the two-dimensional N = (2,2) superconformal Toda lattice hierarchy possessing the N = 4 supersymmetry -- the N = 4 Toda chain hierarchy - which may be relevant in the construction of supersymmetric matrix models. The Lax-pair representations of the bosonic and fermionic flows, corresponding local and non-local Hamiltonians, finite and infinite discrete symmetries, the first two Hamiltonian structures and the recursion operator connecting all evolution equations and the Hamiltonian structures of the N = 4 Toda chain hierarchy are constructed in explicit form. Is secondary reduction to the N 4 supersymmetric α = - 2 KdV hierarchy is

Constructing New Discrete Integrable Coupling System for Soliton Equation by Kronecker Product

International Nuclear Information System (INIS)

Yu Fajun; Zhang Hongqing

2008-01-01

It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of soliton equation hierarchy in this paper. A direct application to the fractional cubic Volterra lattice spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is also indicated that the study of discrete integrable couplings by using the Kronecker product is an efficient and straightforward method. This method can be used generally

A new subalgebra of the Lie algebra A2 and two types of integrable Hamiltonian hierarchies, expanding integrable models

International Nuclear Information System (INIS)

Yan Qingyou; Zhang Yufeng; Wei Xiaopeng

2004-01-01

A new subalgebra G of the Lie algebra A 2 is first constructed. Then two loop algebra G-bar 1 , G-bar 2 are presented in terms of different definitions of gradations. Using G-bar 1 , G-bar 2 designs two isospectral problems, respectively. Again utilizing Tu-pattern obtains two types of various integrable Hamiltonian hierarchies of evolution equations. As reduction cases, the well-known Schroedinger equation and MKdV equation are obtained. At last, we turn the subalgebras G-bar 1 , G-bar 2 of the loop algebra A-bar 2 into equivalent subalgebras of the loop algebra A-bar 1 by making a suitable linear transformation so that the two types of 5-dimensional loop algebras are constructed. Two kinds of integrable couplings of the obtained hierarchies are showed. Specially, the integrable couplings of Schroedinger equation and MKdV equation are obtained, respectively

Exploring memory hierarchy design with emerging memory technologies

CERN Document Server

Sun, Guangyu

2014-01-01

This book equips readers with tools for computer architecture of high performance, low power, and high reliability memory hierarchy in computer systems based on emerging memory technologies, such as STTRAM, PCM, FBDRAM, etc.  The techniques described offer advantages of high density, near-zero static power, and immunity to soft errors, which have the potential of overcoming the “memory wall.”  The authors discuss memory design from various perspectives: emerging memory technologies are employed in the memory hierarchy with novel architecture modification;  hybrid memory structure is introduced to leverage advantages from multiple memory technologies; an analytical model named “Moguls” is introduced to explore quantitatively the optimization design of a memory hierarchy; finally, the vulnerability of the CMPs to radiation-based soft errors is improved by replacing different levels of on-chip memory with STT-RAMs.   ·         Provides a holistic study of using emerging memory technologies i...

A computational procedure for finding multiple solutions of convective heat transfer equations

International Nuclear Information System (INIS)

Mishra, S; DebRoy, T

2005-01-01

In recent years numerical solutions of the convective heat transfer equations have provided significant insight into the complex materials processing operations. However, these computational methods suffer from two major shortcomings. First, these procedures are designed to calculate temperature fields and cooling rates as output and the unidirectional structure of these solutions preclude specification of these variables as input even when their desired values are known. Second, and more important, these procedures cannot determine multiple pathways or multiple sets of input variables to achieve a particular output from the convective heat transfer equations. Here we propose a new method that overcomes the aforementioned shortcomings of the commonly used solutions of the convective heat transfer equations. The procedure combines the conventional numerical solution methods with a real number based genetic algorithm (GA) to achieve bi-directionality, i.e. the ability to calculate the required input variables to achieve a specific output such as temperature field or cooling rate. More important, the ability of the GA to find a population of solutions enables this procedure to search for and find multiple sets of input variables, all of which can lead to the desired specific output. The proposed computational procedure has been applied to convective heat transfer in a liquid layer locally heated on its free surface by an electric arc, where various sets of input variables are computed to achieve a specific fusion zone geometry defined by an equilibrium temperature. Good agreement is achieved between the model predictions and the independent experimental results, indicating significant promise for the application of this procedure in finding multiple solutions of convective heat transfer equations

Inverse scattering scheme for the Dirac equation at fixed energy

International Nuclear Information System (INIS)

Leeb, H.; Lehninger, H.; Schilder, C.

2001-01-01

Full text: Based on the concept of generalized transformation operators a new hierarchy of Dirac equations with spherical symmetric scalar and fourth component vector potentials is presented. Within this hierarchy closed form expressions for the solutions, the potentials and the S-matrix can be given in terms of solutions of the original Dirac equation. Using these transformations an inverse scattering scheme has been constructed for the Dirac equation which is the analog to the rational scheme in the non-relativistic case. The given method provides for the first time an inversion scheme with closed form expressions for the S-matrix for non-relativistic scattering problems with central and spin-orbit potentials. (author)

Solving the wrong hierarchy problem

International Nuclear Information System (INIS)

Blinov, Nikita; Hook, Anson

2016-01-01

Many theories require augmenting the Standard Model with additional scalar fields with large order one couplings. We present a new solution to the hierarchy problem for these scalar fields. We explore parity- and Z_2-symmetric theories where the Standard Model Higgs potential has two vacua. The parity or Z_2 copy of the Higgs lives in the minimum far from the origin while our Higgs occupies the minimum near the origin of the potential. This approach results in a theory with multiple light scalar fields but with only a single hierarchy problem, since the bare mass is tied to the Higgs mass by a discrete symmetry. The new scalar does not have a new hierarchy problem associated with it because its expectation value and mass are generated by dimensional transmutation of the scalar quartic coupling. The location of the second Higgs minimum is not a free parameter, but is rather a function of the matter content of the theory. As a result, these theories are extremely predictive. We develop this idea in the context of a solution to the strong CP problem. Lastly, we show this mechanism postdicts the top Yukawa to be within 1σ of the currently measured value and predicts scalar color octets with masses in the range 9-200 TeV

Hamiltonian structures of some non-linear evolution equations

International Nuclear Information System (INIS)

Tu, G.Z.

1983-06-01

The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)

PC analysis of stochastic differential equations driven by Wiener noise

KAUST Repository

Le Maitre, Olivier

2015-03-01

A polynomial chaos (PC) analysis with stochastic expansion coefficients is proposed for stochastic differential equations driven by additive or multiplicative Wiener noise. It is shown that for this setting, a Galerkin formalism naturally leads to the definition of a hierarchy of stochastic differential equations governing the evolution of the PC modes. Under the mild assumption that the Wiener and uncertain parameters can be treated as independent random variables, it is also shown that the Galerkin formalism naturally separates parametric uncertainty and stochastic forcing dependences. This enables us to perform an orthogonal decomposition of the process variance, and consequently identify contributions arising from the uncertainty in parameters, the stochastic forcing, and a coupled term. Insight gained from this decomposition is illustrated in light of implementation to simplified linear and non-linear problems; the case of a stochastic bifurcation is also considered.

Integration of the BBGKY equations for the development of strongly nonlinear clustering in an expanding universe

International Nuclear Information System (INIS)

Davis, M.; Peebles, P.J.E.

1977-01-01

The evolution of density correlations in an expanding universe can be described by the BBGKY equations. This approach has been the subject of several previous studies, but always under the assumption of small-amplitude fluctuations, where the hierarchy of equations has a natural truncation. Reslts of these studies cannot be compared to the present universe because the galaxy two-point correlation function xi (r) is much greater than unity at r9 or approx. =1h -1 Mpc, and the three-point function zeta is on the order of xi (r) 2 . In this strongly nonlinear situation the hierarchy is dominated by terms ignored in the linear analysis. Our method of truncating the hierarchy is based on the empirical result that zeta can be represented to good accuracy as a simple function of xi. We solve the equations via the velocity-moment method, and we truncate the resulting velocity-moment hierarchy for the two-point function by assuming that the distribution in the relative velocity of particle pairs has zero skewness about the mean. The second equation in this velocity-moment hierarchy is our main equation for xi. It involves the three-point spatial correlation function zeta, which we write as a function of xi following the empirical result. The third equation involves the first velocity moment of the three-point position and velocity correlation function. We model this term in a way consistent with our model for zeta and with a constraint equation that expresses conservation of triplets.The equations admit a similarity transformation if (1) the effects of the discreteness of particles can be ignored, (2) the initial spectrum of density perturbations assumes a power law shape, and (3) the universe is described by an Einstein-de Sitter model (Ωapprox. =1). The numerical results presented here are based on this similarity solution

Extracting Tag Hierarchies

Science.gov (United States)

Tibély, Gergely; Pollner, Péter; Vicsek, Tamás; Palla, Gergely

2013-01-01

Tagging items with descriptive annotations or keywords is a very natural way to compress and highlight information about the properties of the given entity. Over the years several methods have been proposed for extracting a hierarchy between the tags for systems with a "flat", egalitarian organization of the tags, which is very common when the tags correspond to free words given by numerous independent people. Here we present a complete framework for automated tag hierarchy extraction based on tag occurrence statistics. Along with proposing new algorithms, we are also introducing different quality measures enabling the detailed comparison of competing approaches from different aspects. Furthermore, we set up a synthetic, computer generated benchmark providing a versatile tool for testing, with a couple of tunable parameters capable of generating a wide range of test beds. Beside the computer generated input we also use real data in our studies, including a biological example with a pre-defined hierarchy between the tags. The encouraging similarity between the pre-defined and reconstructed hierarchy, as well as the seemingly meaningful hierarchies obtained for other real systems indicate that tag hierarchy extraction is a very promising direction for further research with a great potential for practical applications. Tags have become very prevalent nowadays in various online platforms ranging from blogs through scientific publications to protein databases. Furthermore, tagging systems dedicated for voluntary tagging of photos, films, books, etc. with free words are also becoming popular. The emerging large collections of tags associated with different objects are often referred to as folksonomies, highlighting their collaborative origin and the “flat” organization of the tags opposed to traditional hierarchical categorization. Adding a tag hierarchy corresponding to a given folksonomy can very effectively help narrowing or broadening the scope of search

Extracting tag hierarchies.

Directory of Open Access Journals (Sweden)

Gergely Tibély

Full Text Available Tagging items with descriptive annotations or keywords is a very natural way to compress and highlight information about the properties of the given entity. Over the years several methods have been proposed for extracting a hierarchy between the tags for systems with a "flat", egalitarian organization of the tags, which is very common when the tags correspond to free words given by numerous independent people. Here we present a complete framework for automated tag hierarchy extraction based on tag occurrence statistics. Along with proposing new algorithms, we are also introducing different quality measures enabling the detailed comparison of competing approaches from different aspects. Furthermore, we set up a synthetic, computer generated benchmark providing a versatile tool for testing, with a couple of tunable parameters capable of generating a wide range of test beds. Beside the computer generated input we also use real data in our studies, including a biological example with a pre-defined hierarchy between the tags. The encouraging similarity between the pre-defined and reconstructed hierarchy, as well as the seemingly meaningful hierarchies obtained for other real systems indicate that tag hierarchy extraction is a very promising direction for further research with a great potential for practical applications. Tags have become very prevalent nowadays in various online platforms ranging from blogs through scientific publications to protein databases. Furthermore, tagging systems dedicated for voluntary tagging of photos, films, books, etc. with free words are also becoming popular. The emerging large collections of tags associated with different objects are often referred to as folksonomies, highlighting their collaborative origin and the "flat" organization of the tags opposed to traditional hierarchical categorization. Adding a tag hierarchy corresponding to a given folksonomy can very effectively help narrowing or broadening the scope of

Extracting tag hierarchies.

Science.gov (United States)

Tibély, Gergely; Pollner, Péter; Vicsek, Tamás; Palla, Gergely

2013-01-01

Tagging items with descriptive annotations or keywords is a very natural way to compress and highlight information about the properties of the given entity. Over the years several methods have been proposed for extracting a hierarchy between the tags for systems with a "flat", egalitarian organization of the tags, which is very common when the tags correspond to free words given by numerous independent people. Here we present a complete framework for automated tag hierarchy extraction based on tag occurrence statistics. Along with proposing new algorithms, we are also introducing different quality measures enabling the detailed comparison of competing approaches from different aspects. Furthermore, we set up a synthetic, computer generated benchmark providing a versatile tool for testing, with a couple of tunable parameters capable of generating a wide range of test beds. Beside the computer generated input we also use real data in our studies, including a biological example with a pre-defined hierarchy between the tags. The encouraging similarity between the pre-defined and reconstructed hierarchy, as well as the seemingly meaningful hierarchies obtained for other real systems indicate that tag hierarchy extraction is a very promising direction for further research with a great potential for practical applications. Tags have become very prevalent nowadays in various online platforms ranging from blogs through scientific publications to protein databases. Furthermore, tagging systems dedicated for voluntary tagging of photos, films, books, etc. with free words are also becoming popular. The emerging large collections of tags associated with different objects are often referred to as folksonomies, highlighting their collaborative origin and the "flat" organization of the tags opposed to traditional hierarchical categorization. Adding a tag hierarchy corresponding to a given folksonomy can very effectively help narrowing or broadening the scope of search. Moreover

Determining the neutrino mass hierarchy with cosmology

International Nuclear Information System (INIS)

De Bernardis, Francesco; Kitching, Thomas D.; Heavens, Alan; Melchiorri, Alessandro

2009-01-01

The combination of current large-scale structure and cosmic microwave background anisotropies data can place strong constraints on the sum of the neutrino masses. Here we show that future cosmic shear experiments, in combination with cosmic microwave background constraints, can provide the statistical accuracy required to answer questions about differences in the mass of individual neutrino species. Allowing for the possibility that masses are nondegenerate we combine Fisher matrix forecasts for a weak lensing survey like Euclid with those for the forthcoming Planck experiment. Under the assumption that neutrino mass splitting is described by a normal hierarchy we find that the combination Planck and Euclid will possibly reach enough sensitivity to put a constraint on the mass of a single species. Using a Bayesian evidence calculation we find that such future experiments could provide strong evidence for either a normal or an inverted neutrino hierarchy. Finally we show that if a particular neutrino hierarchy is assumed then this could bias cosmological parameter constraints, for example, the dark energy equation of state parameter, by > or approx. 1σ, and the sum of masses by 2.3σ. We finally discuss the impact of uncertainties on the theoretical modeling of nonlinearities. The results presented in this analysis are obtained under an approximation to the nonlinear power spectrum. This significant source of uncertainty needs to be addressed in future work.

Power-law Exponent in Multiplicative Langevin Equation with Temporally Correlated Noise

Science.gov (United States)

Morita, Satoru

2018-05-01

Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. For discrete-time systems, the power-law exponent is known to decrease as the autocorrelation time of the multiplier increases. However, for continuous-time systems, it is not yet clear how the temporal correlation affects the power-law behavior. Herein, we analytically investigated a multiplicative Langevin equation with colored noise. We show that the power-law exponent depends on the details of the multiplicative noise, in contrast to the case of discrete-time systems.

On the hierarchy of partially invariant submodels of differential equations

OpenAIRE

Golovin, Sergey V.

2007-01-01

It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ...

Generalized Miura transformations, two-bosons KP hierarchies and their reduction to KdV hierarchies

International Nuclear Information System (INIS)

Aratyn, H.; Ferreira, L.A.; Gomes, J.F.; Medeiros, R.T.; Zimerman, A.H.

1993-02-01

Bracket preserving gauge equivalence is established between several two-boson generated KP type of hierarchies. These KP hierarchies reduce under symplectic reduction (via Dirac constraints) to KdV and Schwarzian KdV hierarchies. Under this reduction the gauge equivalence is taking form of the conventional Miura maps between the above KdV type of hierarchies. (author). 16 refs

Generalized Miura transformations, two-bosons KP hierarchies and their reduction to KdV hierarchies

Energy Technology Data Exchange (ETDEWEB)

Aratyn, H. [Illinois Univ., Chicago, IL (United States). Dept. of Physics; Ferreira, L.A.; Gomes, J.F.; Medeiros, R.T.; Zimerman, A.H.

1993-02-01

Bracket preserving gauge equivalence is established between several two-boson generated KP type of hierarchies. These KP hierarchies reduce under symplectic reduction (via Dirac constraints) to KdV and Schwarzian KdV hierarchies. Under this reduction the gauge equivalence is taking form of the conventional Miura maps between the above KdV type of hierarchies. (author). 16 refs.

Canonical formulation of the self-dual Yang-Mills system: Algebras and hierarchies

International Nuclear Information System (INIS)

Chau, L.; Yamanaka, I.

1992-01-01

We construct a canonical formulation of the self-dual Yang-Mills system formulated in the gauge-invariant group-valued J fields and derive their Hamiltonian and the quadratic algebras of the fundamental Dirac brackets. We also show that the quadratic algebras satisfy Jacobi identities and their structure matrices satisfy modified Yang-Baxter equations. From these quadratic algebras, we construct Kac-Moody-like and Virasoro-like algebras. We also discuss their related symmetries, involutive conserved quantities, and hierarchies of nonlinear and linear equations

Integrable Hierarchies and Dispersionless Limit

OpenAIRE

Takasaki, Kanehisa; Takebe, Takashi

1994-01-01

Analogues of the KP and the Toda lattice hierarchy called dispersionless KP and Toda hierarchy are studied. Dressing operations in the dispersionless hierarchies are introduced as a canonical transformation, quantization of which is dressing operators of the ordinary KP and Toda hierarchy. An alternative construction of general solutions of the ordinary KP and Toda hierarchy is given as twistor construction which is quatization of the similar construction of solutions of dispersionless hierar...

Toda hierarchies and their applications

Science.gov (United States)

Takasaki, Kanehisa

2018-05-01

The 2D Toda hierarchy occupies a central position in the family of integrable hierarchies of the Toda type. The 1D Toda hierarchy and the Ablowitz–Ladik (aka relativistic Toda) hierarchy can be derived from the 2D Toda hierarchy as reductions. These integrable hierarchies have been applied to various problems of mathematics and mathematical physics since 1990s. A recent example is a series of studies on models of statistical mechanics called the melting crystal model. This research has revealed that the aforementioned two reductions of the 2D Toda hierarchy underlie two different melting crystal models. Technical clues are a fermionic realization of the quantum torus algebra, special algebraic relations therein called shift symmetries, and a matrix factorization problem. The two melting crystal models thus exhibit remarkable similarity with the Hermitian and unitary matrix models for which the two reductions of the 2D Toda hierarchy play the role of fundamental integrable structures.

Reduced equations of motion for quantum systems driven by diffusive Markov processes.

Science.gov (United States)

Sarovar, Mohan; Grace, Matthew D

2012-09-28

The expansion of a stochastic Liouville equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of stochastically driven quantum systems. We expand the applicability of this technique by completely characterizing the class of diffusive Markov processes for which a useful hierarchy of equations can be derived. The expansion of this technique enables the examination of quantum systems driven by non-Gaussian stochastic processes with bounded range. We present an application of this extended technique by simulating Stark-tuned Förster resonance transfer in Rydberg atoms with nonperturbative position fluctuations.

q-conformally covariant q-Minkowski space-time and invariant equations

International Nuclear Information System (INIS)

Dobrev, V.K.

1997-09-01

We present explicitly the covariant action of the q-conformal algebra on the q-Minkowski space we proposed earlier. We also present some q-conformally invariant equations, namely a hierarchy of q-Maxwell equations, and also a q-d'Alembert equation, proposed earlier by us, in a form different from the original . (author). 19 refs

Grassmannian approach to super-KP hierarchies

International Nuclear Information System (INIS)

Takama, Michiaki.

1995-06-01

We present a theory of 'maximal' super-KP (SKP) hierarchy whose flows are maximally extended to include all those of known SKP hierarchies, including, for example, the MRSKP hierarchy of Manin and Radul and the Jacobian SKP (JSKP) introduced by Mulase and Rabin. It is shown that SKP hierarchies has a natural field theoretic description in terms of the B-C system, in analogous way as the ordinary KP hierarchy. For this SKP hierarchy, we construct the vertex operators by using Kac-van de Leur superbosonization. The vertex operators act on the τ-function and then produce the wave function and the dual wave function of the hierarchy. Thereby we achieve the description of the 'maximal' SKP hierarchy in terms of the τ-function, which seemed to be lacking till now. Mutual relations among the SKP hierarchies are clarified. The MRSKP and the JSKP hierarchies are obtained as special cases when the time variables are appropriately restricted. (author)

Quark-lepton complementarity relation and neutrino mass hierarchy

International Nuclear Information System (INIS)

Ferrandis, Javier; Pakvasa, Sandip

2005-01-01

Latest measurements have revealed that the deviation from a maximal solar mixing angle is approximately the Cabibbo angle [i.e., quark-lepton complementarity (QLC) relation]. We argue that it is not plausible that this deviation from maximality, be it a coincidence or not, comes from the charged lepton mixing. Consequently we have calculated the required corrections to the exactly bimaximal neutrino mass matrix ansatz necessary to account for the solar mass difference and the solar mixing angle. We point out that the relative size of these two corrections depends strongly on the hierarchy case under consideration. We find that the inverted hierarchy case with opposite CP parities, which is known to guarantee the renormalization group equations stability of the solar mixing angle, offers the most plausible scenario for a high-energy origin of a QLC-corrected bimaximal neutrino mass matrix. This possibility may allow us to explain the QLC relation in connection with the origin of the charged fermion mass matrices

A data-informed PIF hierarchy for model-based Human Reliability Analysis

International Nuclear Information System (INIS)

Groth, Katrina M.; Mosleh, Ali

2012-01-01

This paper addresses three problems associated with the use of Performance Shaping Factors in Human Reliability Analysis. (1) There are more than a dozen Human Reliability Analysis (HRA) methods that use Performance Influencing Factors (PIFs) or Performance Shaping Factors (PSFs) to model human performance, but there is not a standard set of PIFs used among the methods, nor is there a framework available to compare the PIFs used in various methods. (2) The PIFs currently in use are not defined specifically enough to ensure consistent interpretation of similar PIFs across methods. (3) There are few rules governing the creation, definition, and usage of PIF sets. This paper introduces a hierarchical set of PIFs that can be used for both qualitative and quantitative HRA. The proposed PIF set is arranged in a hierarchy that can be collapsed or expanded to meet multiple objectives. The PIF hierarchy has been developed with respect to a set fundamental principles necessary for PIF sets, which are also introduced in this paper. This paper includes definitions of the PIFs to allow analysts to map the proposed PIFs onto current and future HRA methods. The standardized PIF hierarchy will allow analysts to combine different types of data and will therefore make the best use of the limited data in HRA. The collapsible hierarchy provides the structure necessary to combine multiple types of information without reducing the quality of the information.

A two-component generalization of the reduced Ostrovsky equation and its integrable semi-discrete analogue

International Nuclear Information System (INIS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2017-01-01

In the present paper, we propose a two-component generalization of the reduced Ostrovsky (Vakhnenko) equation, whose differential form can be viewed as the short-wave limit of a two-component Degasperis–Procesi (DP) equation. They are integrable due to the existence of Lax pairs. Moreover, we have shown that the two-component reduced Ostrovsky equation can be reduced from an extended BKP hierarchy with negative flow through a pseudo 3-reduction and a hodograph (reciprocal) transform. As a by-product, its bilinear form and N -soliton solution in terms of pfaffians are presented. One- and two-soliton solutions are provided and analyzed. In the second part of the paper, we start with a modified BKP hierarchy, which is a Bäcklund transformation of the above extended BKP hierarchy, an integrable semi-discrete analogue of the two-component reduced Ostrovsky equation is constructed by defining an appropriate discrete hodograph transform and dependent variable transformations. In particular, the backward difference form of above semi-discrete two-component reduced Ostrovsky equation gives rise to the integrable semi-discretization of the short wave limit of a two-component DP equation. Their N -soliton solutions in terms of pffafians are also provided. (paper)

Multiplicative renormalizability and self-consistent treatments of the Schwinger-Dyson equations

International Nuclear Information System (INIS)

Brown, N.; Dorey, N.

1989-11-01

Many approximations to the Schwinger-Dyson equations place constraints on the renormalization constants of a theory. The requirement that the solutions to the equations be multiplicatively renormalizable also places constraints on these constants. Demanding that these two sets of constraints be compatible is an important test of the self-consistency of the approximations made. We illustrate this idea by considering the equation for the fermion propagator in massless quenched quantum electrodynamics, (QED), checking the consistency of various approximations. In particular, we show that the much used 'ladder' approximation is self-consistent, provided that the coupling constant is renormalized in a particular way. We also propose another approximation which satisfies this self-consistency test, but requires that the coupling be unrenormalized, as should be the case in the full quenched approximation. This new approximation admits an exact solution, which also satisfies the renormalization group equation for the quenched approximation. (author)

Multiple regression and beyond an introduction to multiple regression and structural equation modeling

CERN Document Server

Keith, Timothy Z

2014-01-01

Multiple Regression and Beyond offers a conceptually oriented introduction to multiple regression (MR) analysis and structural equation modeling (SEM), along with analyses that flow naturally from those methods. By focusing on the concepts and purposes of MR and related methods, rather than the derivation and calculation of formulae, this book introduces material to students more clearly, and in a less threatening way. In addition to illuminating content necessary for coursework, the accessibility of this approach means students are more likely to be able to conduct research using MR or SEM--and more likely to use the methods wisely. Covers both MR and SEM, while explaining their relevance to one another Also includes path analysis, confirmatory factor analysis, and latent growth modeling Figures and tables throughout provide examples and illustrate key concepts and techniques For additional resources, please visit: http://tzkeith.com/.

N = 4 super KdV hierarchy in N = 4 and N = 2 superspaces

International Nuclear Information System (INIS)

Delduc, F.

1995-10-01

The results of further analysis of the integrability properties of the N = 4 supersymmetric KdV equation deduced earlier as a Hamiltonian flow on N 4 SU(2) superconformal algebra in the harmonic N = 4 superspace are presented. To make this equation and the relevant Hamiltonian structures more tractable, it is reformulated in the ordinary N = 4 and further in N = 2 superspaces. These results provide a strong evidence that the unique N = 4 SU(2) super KdV hierarchy exists. (author)

The Balescu kinetic equation with exchange interaction

International Nuclear Information System (INIS)

Belyi, V V; Kukharenko, Yu A

2009-01-01

Starting with the quantum BBGKY hierarchy for the distribution functions, we have obtained the quantum kinetic equation including the dynamical screening of the interaction potential, which exactly takes into account the exchange scattering in the plasma. The collision integral is expressed in terms of the Green function of the linearized Hartree–Fock equation. The potential energy takes into account the polarization and exchange interaction too

On the string equation at c=1

International Nuclear Information System (INIS)

Nakatsu, Toshio.

1994-07-01

The analogue of the string equation which specifies the partition function of c=1 string with a compactification radius β is an element of Z ≥1 is described in the framework of Toda lattice hierarchy. (author)

The zero curvature form of integrable hierarchies in the Z x Z-matrices

NARCIS (Netherlands)

Helminck, G.F.; Opimakh, A.V.

2012-01-01

In this paper it is shown how one can associate to a finite number of commuting directions in the Lie algebra of upper triangular Z X Z-matrices an integrable hierarchy consisting of a set of evolution equations for perturbations of the basic directions inside the mentioned Lie algebra. They amount

Local multiplicative Schwarz algorithms for convection-diffusion equations

Science.gov (United States)

Cai, Xiao-Chuan; Sarkis, Marcus

1995-01-01

We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.

Hamiltonian structure, (anti-)self-adjoint flows in the KP hierarchy and the W1+∞ and W∞ algebras

International Nuclear Information System (INIS)

Yu Feng; Wu Yongshi

1991-01-01

The extended conformal W N algebras are known to be related to the generalized KdV hierarchies through their second hamiltonian structure. In this letter we discuss the relationship between the large-N limits of the W N algebras and the KP hierarchy which contains all generalized KdV hierarchies. We show that the Poisson bracket algebra corresponding to the hamiltonian structure found by Watanabe for the KP hierarchy is isomorphic to the classical (or centerless) W 1+∞ algebra, and it contains a subalgebra which is isomorphic to the W ∞ algebra. Moreover, the usual generators of W 1+∞ and W ∞ are explicitly expressed in terms of the KP currents, and are shown to relate in a simple way to certain KP flows satisfying a sort of (anti-)self-duality. Our results not only clarify the underlying algebraic structure of the KP hierarchy, but also hint about a possible relationship between the latter and 4D self-dual Yang-Mills equations or gravity. (orig.)

A Hierarchy of Homodesmotic Reactions for Thermochemistry

Science.gov (United States)

Schleyer, Paul v. R.

2009-01-01

Chemical equations that balance bond types and atom hybridization to different degrees are often used in computational thermochemistry, for example, to increase accuracy when lower levels of theory are employed. We expose the widespread confusion over such classes of equations and demonstrate that the two most widely used definitions of “homodesmotic” reactions are not equivalent. New definitions are introduced and a consistent hierarchy of reaction classes (RC1 – RC5) for hydrocarbons is constructed: isogyric (RC1) ⊇ isodesmic (RC2) ⊇ hypohomodesmotic (RC3) ⊇ homodesmotic (RC4) ⊇ hyperhomodesmotic (RC5). Each of these successively conserves larger molecular fragments. The concept of isodesmic bond separation reactions is generalized to all classes in this hierarchy, providing a unique sectioning of a given molecule for each reaction type. Several ab initio and density functional methods are applied to the bond separation reactions of 38 hydrocarbons containing five or six carbon atoms. RC4 and RC5 reactions provide bond separation enthalpies with errors consistently less than 0.4 kcal mol−1 across a wide range of theoretical levels, performing significantly better than the other reaction types and far superior to atomization routes. Our recommended bond separation reactions were demonstrated by determining the enthalpies of formation (at 298 K) of 1,3,5-hexatriyne (163.7 ± 0.4 kcal mol−1), 1,3,5,7-octatetrayne (217.6 ± 0.6 kcal mol−1), the larger polyynes C10H2 through C26H2, and an infinite acetylenic carbon chain. PMID:19182999

Recursion Operators for Dispersionless KP Hierarchy

International Nuclear Information System (INIS)

Cheng Qiusheng; He Jingsong

2012-01-01

Based on the corresponding theorem between dispersionless KP (dKP) hierarchy and ħ-dependent KP (ħKP) hierarchy, a general formal representation of the recursion operators for dKP hierarchy under n-reduction is given in a systematical way from the corresponding ħKP hierarchy. To illustrate this method, the recursion operators for dKP hierarchy under 2-reduction and 3-reduction are calculated in detail.

Langevin equation method for the rotational Brownian motion and orientational relaxation in liquids: II. Symmetrical top molecules

CERN Document Server

Coffey, W T; Titov, S V

2003-01-01

A theory of orientational relaxation for the inertial rotational Brownian motion of a symmetric top molecule is developed using the Langevin equation rather than the Fokker-Planck equation. The infinite hierarchy of differential-recurrence relations for the orientational correlation functions for the relaxation behaviour is derived by averaging the corresponding Euler-Langevin equations. The solution of this hierarchy is obtained using matrix continued fractions allowing the calculation of the correlation times and the spectra of the orientational correlation functions for typical values of the model parameters.

On the supersymmetric BKP hierarchy

International Nuclear Information System (INIS)

Ramos, Eduardo; Stanciu, Sonia

1994-01-01

We prove that the supersymmetric BKP-hierarchy of Yu (SBKP 2 ) is hamiltonian with respect to a nonlinear extension of the N=1 super-Virasoro algebra (W SBKP ) by fields of spin k, where k>[3]/[2] and 2k≡0,3 (mod 4). Moreover, we show how to associate in a similar manner an N=1 W-superalgebra with every integrable hierarchy of the SKdV-type. We also show using dressing transformations how to extend, in a way which is compatible with the hamiltonian structure, the SBKP 2 hierarchy by odd flows, as well as the equivalence of this extended hierarchy to the SBKP-hierarchy of Manin-Radul. ((orig.))

Higher-Order Hierarchies

DEFF Research Database (Denmark)

Ernst, Erik

2003-01-01

This paper introduces the notion of higher-order inheritance hierarchies. They are useful because they provide well-known benefits of object-orientation at the level of entire hierarchies-benefits which are not available with current approaches. Three facets must be adressed: First, it must be po...

The socio-matrix reloaded: from hierarchy to dominance profile in wild lemurs.

Science.gov (United States)

Norscia, Ivan; Palagi, Elisabetta

2015-01-01

Dominance hierarchy influences the life quality of social animals, and its definition should in principle be based on the outcome of agonistic interactions. However, defining and comparing the dominance profile of social groups is difficult due to the different dominance measures used and because no one measure explains it all. We applied different analytical methods to winner-loser sociomatrices to determine the dominance profile of five groups of wild lemurs (species: Lemur catta, Propithecus verreauxi, and Eulemur rufus x collaris) from the Berenty forest (Madagascar). They are an excellent study model because they share the same habitat and an apparently similar dominance profile: linear hierarchy and female dominance. Data were collected over more than 1200 h of observation. Our approach included four steps: (1) by applying the binary dyadic dominance relationship method (I&SI) on either aggressions or supplant sociomatrices we verified whether hierarchy was aggression or submission based; (2) by calculating normalized David's scores and measuring steepness from aggression sociomatrices we evaluated whether hierarchy was shallow or steep; (3) by comparing the ranking orders obtained with methods 1 and 2 we assessed whether hierarchy was consistent or not; and (4) by assessing triangle transitivity and comparing it with the linearity index and the level of group cohesion we determined if hierarchy was more or less cohesive. Our results show that L. catta groups have got a steep, consistent, highly transitive and cohesive hierarchy. P. verreauxi groups are characterized by a moderately steep and consistent hierarchy, with variable levels of triangle transitivity and cohesion. E. rufus x collaris group possesses a shallow and inconsistent hierarchy, with lower (but not lowest) levels of transitivity and cohesion. A multiple analytical approach on winner-loser sociomatrices other than leading to an in-depth description of the dominance profile, allows intergroup

The socio-matrix reloaded: from hierarchy to dominance profile in wild lemurs

Directory of Open Access Journals (Sweden)

Ivan Norscia

2015-01-01

Full Text Available Dominance hierarchy influences the life quality of social animals, and its definition should in principle be based on the outcome of agonistic interactions. However, defining and comparing the dominance profile of social groups is difficult due to the different dominance measures used and because no one measure explains it all. We applied different analytical methods to winner-loser sociomatrices to determine the dominance profile of five groups of wild lemurs (species: Lemur catta, Propithecus verreauxi, and Eulemur rufus x collaris from the Berenty forest (Madagascar. They are an excellent study model because they share the same habitat and an apparently similar dominance profile: linear hierarchy and female dominance. Data were collected over more than 1200 h of observation. Our approach included four steps: (1 by applying the binary dyadic dominance relationship method (I&SI on either aggressions or supplant sociomatrices we verified whether hierarchy was aggression or submission based; (2 by calculating normalized David’s scores and measuring steepness from aggression sociomatrices we evaluated whether hierarchy was shallow or steep; (3 by comparing the ranking orders obtained with methods 1 and 2 we assessed whether hierarchy was consistent or not; and (4 by assessing triangle transitivity and comparing it with the linearity index and the level of group cohesion we determined if hierarchy was more or less cohesive. Our results show that L. catta groups have got a steep, consistent, highly transitive and cohesive hierarchy. P. verreauxi groups are characterized by a moderately steep and consistent hierarchy, with variable levels of triangle transitivity and cohesion. E. rufus x collaris group possesses a shallow and inconsistent hierarchy, with lower (but not lowest levels of transitivity and cohesion. A multiple analytical approach on winner-loser sociomatrices other than leading to an in-depth description of the dominance profile

Milstein Approximation for Advection-Diffusion Equations Driven by Multiplicative Noncontinuous Martingale Noises

International Nuclear Information System (INIS)

Barth, Andrea; Lang, Annika

2012-01-01

In this paper, the strong approximation of a stochastic partial differential equation, whose differential operator is of advection-diffusion type and which is driven by a multiplicative, infinite dimensional, càdlàg, square integrable martingale, is presented. A finite dimensional projection of the infinite dimensional equation, for example a Galerkin projection, with nonequidistant time stepping is used. Error estimates for the discretized equation are derived in L 2 and almost sure senses. Besides space and time discretizations, noise approximations are also provided, where the Milstein double stochastic integral is approximated in such a way that the overall complexity is not increased compared to an Euler–Maruyama approximation. Finally, simulations complete the paper.

An extended Harry Dym hierarchy

International Nuclear Information System (INIS)

Ma Wenxiu

2010-01-01

An extended Harry Dym hierarchy is constructed by using eigenfunctions and adjoint eigenfunctions of the spectral problems of the Harry Dym hierarchy associated with the pseudo-differential operator L = u∂ + u 0 + u 1 ∂ -1 + .... The corresponding Lax presentation possesses a self-consistent source involving squared eigenfunctions. The resulting extended Harry Dym hierarchy is reduced to the Harry Dym hierarchy with self-consistent sources under the n-reduction, L n = (L n ) ≥2 , and the k-constrained Harry Dym hierarchy under the k-constraint, L k = (L k ) ≥2 + Σ N i=1 q i ∂ -1 r i ∂ 2 . A few particular examples are computed, together with their Lax pairs.

Matrix-type multiple reciprocity boundary element method for solving three-dimensional two-group neutron diffusion equations

International Nuclear Information System (INIS)

Itagaki, Masafumi; Sahashi, Naoki.

1997-01-01

The multiple reciprocity boundary element method has been applied to three-dimensional two-group neutron diffusion problems. A matrix-type boundary integral equation has been derived to solve the first and the second group neutron diffusion equations simultaneously. The matrix-type fundamental solutions used here satisfy the equation which has a point source term and is adjoint to the neutron diffusion equations. A multiple reciprocity method has been employed to transform the matrix-type domain integral related to the fission source into an equivalent boundary one. The higher order fundamental solutions required for this formulation are composed of a series of two types of analytic functions. The eigenvalue itself is also calculated using only boundary integrals. Three-dimensional test calculations indicate that the present method provides stable and accurate solutions for criticality problems. (author)

The Updated Multiple Star Catalog

Science.gov (United States)

Tokovinin, Andrei

2018-03-01

The catalog of hierarchical stellar systems with three or more components is an update of the original 1997 version. For 2000 hierarchies, the new Multiple Star Catalog (MSC) provides distances, component masses and periods, and supplementary information (astrometry, photometry, identifiers, orbits, notes). The MSC content and format are explained, and its incompleteness and strong observational selection are stressed. Nevertheless, the MSC can be used for statistical studies and is a valuable source for planning observations of multiple stars. Rare classes of stellar hierarchies found in the MSC (with six or seven components, extremely eccentric orbits, planar and possibly resonant orbits, hosting planets) are briefly presented. High-order hierarchies have smaller velocity dispersion compared to triples and are often associated with moving groups. The paper concludes with an analysis of the ratio of periods and separations between inner and outer subsystems. In wide hierarchies, the ratio of semimajor axes, estimated statistically, is distributed between 3 and 300, with no evidence of dynamically unstable systems.

Classical Affine W-Algebras and the Associated Integrable Hamiltonian Hierarchies for Classical Lie Algebras

Science.gov (United States)

De Sole, Alberto; Kac, Victor G.; Valeri, Daniele

2018-06-01

We prove that any classical affine W-algebra W (g, f), where g is a classical Lie algebra and f is an arbitrary nilpotent element of g, carries an integrable Hamiltonian hierarchy of Lax type equations. This is based on the theories of generalized Adler type operators and of generalized quasideterminants, which we develop in the paper. Moreover, we show that under certain conditions, the product of two generalized Adler type operators is a Lax type operator. We use this fact to construct a large number of integrable Hamiltonian systems, recovering, as a special case, all KdV type hierarchies constructed by Drinfeld and Sokolov.

On hierarchical solutions to the BBGKY hierarchy

Science.gov (United States)

Hamilton, A. J. S.

1988-01-01

It is thought that the gravitational clustering of galaxies in the universe may approach a scale-invariant, hierarchical form in the small separation, large-clustering regime. Past attempts to solve the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy in this regime have assumed a certain separable hierarchical form for the higher order correlation functions of galaxies in phase space. It is shown here that such separable solutions to the BBGKY equations must satisfy the condition that the clustered component of the solution has cluster-cluster correlations equal to galaxy-galaxy correlations to all orders. The solutions also admit the presence of an arbitrary unclustered component, which plays no dyamical role in the large-clustering regime. These results are a particular property of the specific separable model assumed for the correlation functions in phase space, not an intrinsic property of spatially hierarchical solutions to the BBGKY hierarchy. The observed distribution of galaxies does not satisfy the required conditions. The disagreement between theory and observation may be traced, at least in part, to initial conditions which, if Gaussian, already have cluster correlations greater than galaxy correlations.

The Monge-Ampère equation: Hamiltonian and symplectic structures, recursions, and hierarchies

NARCIS (Netherlands)

Kersten, P.H.M.; Krasil'shchik, I.; Verbovetsky, A.V.

2004-01-01

Using methods of geometry and cohomology developed recently, we study the Monge-Ampère equation, arising as the first nontrivial equation in the associativity equations, or WDVV equations. We describe Hamiltonian and symplectic structures as well as recursion operators for this equation in its

Multiple positive solutions to a coupled systems of nonlinear fractional differential equations.

Science.gov (United States)

Shah, Kamal; Khan, Rahmat Ali

2016-01-01

In this article, we study existence, uniqueness and nonexistence of positive solution to a highly nonlinear coupled system of fractional order differential equations. Necessary and sufficient conditions for the existence and uniqueness of positive solution are developed by using Perov's fixed point theorem for the considered problem. Further, we also established sufficient conditions for existence of multiplicity results for positive solutions. Also, we developed some conditions under which the considered coupled system of fractional order differential equations has no positive solution. Appropriate examples are also provided which demonstrate our results.

Brane world perspective on the cosmological constant and the hierarchy problems

International Nuclear Information System (INIS)

Flanagan, Eanna; Jones, Nicholas; Stoica, Horace; Tye, S.-H. Henry; Wasserman, Ira

2001-01-01

We elaborate on the recently proposed static brane world scenario, where the effective 4D cosmological constant is exponentially small when parallel 3-branes are far apart. We extend this result to a compactified model with two positive tension branes. In addition to an exponentially small effective 4D cosmological constant, this model incorporates a Randall-Sundrum-like solution to the hierarchy problem. Furthermore, the exponential factors for the hierarchy problem and the cosmological constant problem obey an inequality that is satisfied in nature. This inequality implies that the cosmological constant problem can be explained if the hierarchy problem is understood. The basic idea generalizes to the multibrane world scenario. We discuss models with piecewise adjustable bulk cosmological constants (to be determined by the 5-dimensional Einstein equation), a key element of the scenario. We also discuss the global structure of this scenario and clarify the physical properties of the particle (Rindler) horizons that are present. Finally, we derive a 4D effective theory in which all observers on all branes not separated by particle horizons measure the same Newton's constant and 4D cosmological constant

Development of kinetics equations from the Boltzmann equation; Etablissement des equations de la cinetique a partir de l'equation de Boltzmann

Energy Technology Data Exchange (ETDEWEB)

Plas, R.

1962-07-01

The author reports a study on kinetics equations for a reactor. He uses the conventional form of these equations but by using a dynamic multiplication factor. Thus, constants related to delayed neutrons are not modified by efficiency factors. The author first describes the theoretic kinetic operation of a reactor and develops the associated equations. He reports the development of equations for multiplication factors.

Variational Approaches for the Existence of Multiple Periodic Solutions of Differential Delay Equations

Directory of Open Access Journals (Sweden)

Rong Cheng

2010-01-01

Full Text Available The existence of multiple periodic solutions of the following differential delay equation (=−((− is established by applying variational approaches directly, where ∈ℝ, ∈(ℝ,ℝ and >0 is a given constant. This means that we do not need to use Kaplan and Yorke's reduction technique to reduce the existence problem of the above equation to an existence problem for a related coupled system. Such a reduction method introduced first by Kaplan and Yorke in (1974 is often employed in previous papers to study the existence of periodic solutions for the above equation and its similar ones by variational approaches.

Disease spread across multiple scales in a spatial hierarchy: effect of host spatial structure and of inoculum quantity and distribution.

Science.gov (United States)

Gosme, Marie; Lucas, Philippe

2009-07-01

Spatial patterns of both the host and the disease influence disease spread and crop losses. Therefore, the manipulation of these patterns might help improve control strategies. Considering disease spread across multiple scales in a spatial hierarchy allows one to capture important features of epidemics developing in space without using explicitly spatialized variables. Thus, if the system under study is composed of roots, plants, and planting hills, the effect of host spatial pattern can be studied by varying the number of plants per planting hill. A simulation model based on hierarchy theory was used to simulate the effects of large versus small planting hills, low versus high level of initial infections, and aggregated versus uniform distribution of initial infections. The results showed that aggregating the initially infected plants always resulted in slower epidemics than spreading out the initial infections uniformly. Simulation results also showed that, in most cases, disease epidemics were slower in the case of large host aggregates (100 plants/hill) than with smaller aggregates (25 plants/hill), except when the initially infected plants were both numerous and spread out uniformly. The optimal strategy for disease control depends on several factors, including initial conditions. More importantly, the model offers a framework to account for the interplay between the spatial characteristics of the system, rates of infection, and aggregation of the disease.

In praise of hierarchy.

Science.gov (United States)

Jaques, E

1990-01-01

Hierarchy has not had its day. After 3,000 years as the preferred structure for large organizations, managerial hierarchy is still the most natural and effective organizational form that a big company can employ. Now, as in the past, the key to organizational success is individual accountability, and hierarchy preserves unambiguous accountability for getting work done. Unfortunately, hierarchy is widely misunderstood and abused. Pay grades are confused with real layers of responsibility, for example, and incompetent bosses abound. As a result, many experts now urge us to adopt group-oriented or "flat" structures. But groups are never held accountable as groups for what they do or fail to do, and groups don't have careers. The proper use of hierarchy derives from the nature of work. As organizational tasks range from simple to very complex, there are sharp jumps in the level of difficulty and responsibility. Surprisingly, people in hundreds of companies in dozens of countries agree on where these jumps take place. They are tied to an objective measure-the time span of the longest task or program assigned to each managerial role-and they occur at 3 months, 1 year, 2 years, 5 years, 10 years, and 20 years. As the time span increases, so does the level of experience, knowledge, and mental stamina required to do the work. This increasing level of mental capacity lets companies put people in jobs they can do, it allows managers to add value to the work of their subordinates, it creates hierarchical layers acceptable to everyone in the organization, and it allows employees to be evaluated by people they accept as organizational superiors. Best of all, understanding hierarchy allows organizations to set up hierarchies with no more than seven layers-often fewer-and to know what the structure is good for and how it ought to perform.

A note on the KP hierarchy

International Nuclear Information System (INIS)

Depireux, D.A.

1992-01-01

In this paper, given the two boson representation of the conformal algebra W ∞ , the second Hamiltonian structure of the KP hierarchy, the author constructs a bi-Hamiltonian hierarchy for the two associated currents. The KP hierarchy appears as a composite of this new and simpler system. The bi-Hamiltonian structure of the new hierarchy gives naturally all the Hamiltonian structures of the KP system

A Soliton Hierarchy Associated with a Spectral Problem of 2nd Degree in a Spectral Parameter and Its Bi-Hamiltonian Structure

Directory of Open Access Journals (Sweden)

Yuqin Yao

2016-01-01

Full Text Available Associated with so~(3,R, a new matrix spectral problem of 2nd degree in a spectral parameter is proposed and its corresponding soliton hierarchy is generated within the zero curvature formulation. Bi-Hamiltonian structures of the presented soliton hierarchy are furnished by using the trace identity, and thus, all presented equations possess infinitely commuting many symmetries and conservation laws, which implies their Liouville integrability.

Additional symmetries of supersymmetric KP hierarchies

International Nuclear Information System (INIS)

Stanciu, S.

1994-01-01

We investigate the additional symmetries of several supersymmetric KP hierarchies: the SKP hierarchy of Manin and Radul, the SKP 2 hierarchy, and the Jacobian SKP hierarchy. In all three cases we find that the algebra of symmetries is isomorphic to the algebra of superdifferential operators, or equivalently SW 1+∞ . These results seem to suggest that despite their realization depending on the dynamics, the additional symmetries are kinematical in nature. (orig.)

Integrable peakon equations with cubic nonlinearity

International Nuclear Information System (INIS)

Hone, Andrew N W; Wang, J P

2008-01-01

We present a new integrable partial differential equation found by Vladimir Novikov. Like the Camassa-Holm and Degasperis-Procesi equations, this new equation admits peaked soliton (peakon) solutions, but it has nonlinear terms that are cubic, rather than quadratic. We give a matrix Lax pair for V Novikov's equation, and show how it is related by a reciprocal transformation to a negative flow in the Sawada-Kotera hierarchy. Infinitely many conserved quantities are found, as well as a bi-Hamiltonian structure. The latter is used to obtain the Hamiltonian form of the finite-dimensional system for the interaction of N peakons, and the two-body dynamics (N = 2) is explicitly integrated. Finally, all of this is compared with some analogous results for another cubic peakon equation derived by Zhijun Qiao. (fast track communication)

Decoupling, effective Lagrangian, and gauge hierarchy in spontaneously broken non-Abelian gauge theories

International Nuclear Information System (INIS)

Kazama, Y.; Yao, Y.

1982-01-01

In spontaneously broken non-Abelian gauge theories which admit gauge hierarchy at the tree level, we show, to all orders in perturbation theory, that (i) the superheavy particles decouple from the light sector at low energies, (ii) an effective low-energy renormalizable theory emerges together with appropriate counterterms, and (iii) the gauge hierarchy can be consistently maintained in the presence of radiative corrections. These assertions are explicitly demonstrated for O(3) gauge theory with two triplets of Higgs particles in a manner easily applicable to more realistic grand unified theories. Furthermore, as a by-product of our analysis, we obtain a systematic method of computing the parameters of the effective low-energy theory via renormalization-group equations to any desired accuracy

On the robustness of Herlihy's hierarchy

Science.gov (United States)

Jayanti, Prasad

1993-01-01

A wait-free hierarchy maps object types to levels in Z(+) U (infinity) and has the following property: if a type T is at level N, and T' is an arbitrary type, then there is a wait-free implementation of an object of type T', for N processes, using only registers and objects of type T. The infinite hierarchy defined by Herlihy is an example of a wait-free hierarchy. A wait-free hierarchy is robust if it has the following property: if T is at level N, and S is a finite set of types belonging to levels N - 1 or lower, then there is no wait-free implementation of an object of type T, for N processes, using any number and any combination of objects belonging to the types in S. Robustness implies that there are no clever ways of combining weak shared objects to obtain stronger ones. Contrary to what many researchers believe, we prove that Herlihy's hierarchy is not robust. We then define some natural variants of Herlihy's hierarchy, which are also infinite wait-free hierarchies. With the exception of one, which is still open, these are not robust either. We conclude with the open question of whether non-trivial robust wait-free hierarchies exist.

Higher order supersymmetries and fermionic conservation laws of the supersymmetric extension of the KdV equation

NARCIS (Netherlands)

Kersten, P.H.M.

1988-01-01

By the introduction of nonlocal basonic and fermionic variables we construct a recursion symmetry of the super KdV equation, leading to a hierarchy of bosonic symmetries and one of fermionic symmetries. The hierarchies of bosonic and fermionic conservation laws arise in a natural way in the

Goal hierarchy: Improving asset data quality by improving motivation

Energy Technology Data Exchange (ETDEWEB)

Unsworth, Kerrie, E-mail: Kerrie.unsworth@uwa.edu.au [UWA Business School, University of Western Australia, Crawley, WA 6009 (Australia); Adriasola, Elisa; Johnston-Billings, Amber; Dmitrieva, Alina [UWA Business School, University of Western Australia, Crawley, WA 6009 (Australia); Hodkiewicz, Melinda [School of Mechanical Engineering, University of Western Australia, Crawley, WA 6009 (Australia)

2011-11-15

Many have recognized the need for high quality data on assets and the problems in obtaining them, particularly when there is a need for human observation and manual recording. Yet very few have looked at the role of the data collectors themselves in the data quality process. This paper argues that there are benefits to more fully understanding the psychological factors that lay behind data collection and we use goal hierarchy theory to understand these factors. Given the myriad of potential reasons for poor-quality data it has previously proven difficult to identify and successfully deploy employee-driven interventions; however, the goal hierarchy approach looks at all of the goals that an individual has in their life and the connections between them. For instance, does collecting data relate to whether or not they get a promotion? Stay safe? Get a new job? and so on. By eliciting these goals and their connections we can identify commonalities across different groups, sites or organizations that can influence the quality of data collection. Thus, rather than assuming what the data collectors want, a goal hierarchy approach determines that empirically. Practically, this supports the development of customized interventions that will be much more effective and sustainable than previous efforts. - Highlights: > We need to consider psychological aspects of data collectors to improve data quality. > We show how goal hierarchy theory furthers understanding. > Looks at the multiple goals of each individual to determine their behavior.

Goal hierarchy: Improving asset data quality by improving motivation

International Nuclear Information System (INIS)

Unsworth, Kerrie; Adriasola, Elisa; Johnston-Billings, Amber; Dmitrieva, Alina; Hodkiewicz, Melinda

2011-01-01

Many have recognized the need for high quality data on assets and the problems in obtaining them, particularly when there is a need for human observation and manual recording. Yet very few have looked at the role of the data collectors themselves in the data quality process. This paper argues that there are benefits to more fully understanding the psychological factors that lay behind data collection and we use goal hierarchy theory to understand these factors. Given the myriad of potential reasons for poor-quality data it has previously proven difficult to identify and successfully deploy employee-driven interventions; however, the goal hierarchy approach looks at all of the goals that an individual has in their life and the connections between them. For instance, does collecting data relate to whether or not they get a promotion? Stay safe? Get a new job? and so on. By eliciting these goals and their connections we can identify commonalities across different groups, sites or organizations that can influence the quality of data collection. Thus, rather than assuming what the data collectors want, a goal hierarchy approach determines that empirically. Practically, this supports the development of customized interventions that will be much more effective and sustainable than previous efforts. - Highlights: → We need to consider psychological aspects of data collectors to improve data quality. → We show how goal hierarchy theory furthers understanding. → Looks at the multiple goals of each individual to determine their behavior.

The Analytical Hierarchy Process

DEFF Research Database (Denmark)

Barfod, Michael Bruhn

2007-01-01

The technical note gathers the theory behind the Analytical Hierarchy Process (AHP) and present its advantages and disadvantages in practical use.......The technical note gathers the theory behind the Analytical Hierarchy Process (AHP) and present its advantages and disadvantages in practical use....

Additional symmetries of supersymmetric KP hierarchies

International Nuclear Information System (INIS)

Stanciu, S.

1993-09-01

We investigate the additional symmetries of several supersymmetric KP hierarchies: The SKP hierarchy of Manin and Radul, the SKP 2 hierarchy, and the Jacobian SKP hierarchy. The main technical tool is the supersymmetric generalisation of a map originally due to Radul between the Lie algebra of superdifferential operators and the Lie algebra of vector fields on the space of supersymmetric Lax operators. In the case of the Manin-Radul SKP hierarchy we identify additional symmetries which form an algebra isomorphic to a subalgebra of superdifferential operators; whereas in the case of the Jacobian SKP, the (additional) symmetries are identified with the algebra itself. (orig.)

A study on the multiple solutions of the Martree-Fock-Roothaan equation for closed shell systems

International Nuclear Information System (INIS)

Malbouisson, L.A.C.

1985-01-01

An analysis of the multiple solutions of the Hartree-Fock-Roothaan equation for closed shell systems is done. The meaning of these solutions is discussed as self-consistent solutions of the pseudo-eingen-value equation and a general method for obtaining them is proposed. It is developed a criterion of stability for classifying the solutions depending on the type of the extremum point of the electronic energy function that the solution represent. It is also shown the existence of a correspondence between the multiple solutions and the several ordering rules that can be introduced for the usual iterative procedure of resolution of the equation. All the analysis and procedures developed are applied to the systems LiH, BH, Be and He. (author) [pt

Gauge-symmetry hierarchies revisited

International Nuclear Information System (INIS)

Gildener, E.

1979-01-01

It was shown by the author in a previous paper that in each order of perturbation theory there is an upper bound on the range of validity of a gauge hierarchy. Thus constructing a large hierarchy requires a fine-tuning of the scalar-field parameters. It was stated that the possibility of an inherent bound on the hierarchy exists, but the question of the actual existence of such a bound was left completely open. Since then several authors have addressed this problem. Some of what the author asserted was misunderstood, and incorrect conclusions have been drawn from recent computations. It has been claimed that the existence of large hierarchies has been demonstrated. It is the purpose of this paper to refute this claim, to help clarify the situation, and to explain why the status of this problem has in fact not really changed in recent years (author)

The family mass hierarchy problem in bosonic technicolor

International Nuclear Information System (INIS)

Kagan, A.; Samuel, S.

1990-01-01

We use a multiple Higgs system to analyze the family mass hierarchy problem in bosonic technicolor. Dependence on a wide range of Yukawa couplings, λ, for quark and lepton mass generation is greatly reduced, i.e., λ ≅ 0.1 to 1. Third and second generation masses are produced at tree-level, the latter via a see-saw mechanism. We use radiative corrections as a source for many mixing angles and first generation masses. A hierarchy of family masses with small of-diagonal Kobayashi-Maskawa entries naturally arises. A higher scale of 1-10 TeV for Higgs masses and supersymmetry breaking is needed to alleviate difficulties with flavor-changing effects. Such a large scale is a feature of bosonic technicolor and no fine-tuning is required to obtain electroweak breaking at ≅ 100 GeV. Bosonic technicolor is therefore a natural framework for multi-Higgs systems. (orig.)

Differential-difference equations associated with the fractional Lax operators

Energy Technology Data Exchange (ETDEWEB)

Adler, V E [LD Landau Institute for Theoretical Physics, 1A Ak. Semenov, Chernogolovka 142432 (Russian Federation); Postnikov, V V, E-mail: adler@itp.ac.ru, E-mail: postnikofvv@mail.ru [Sochi Branch of Peoples' Friendship University of Russia, 32 Kuibyshev str., 354000 Sochi (Russian Federation)

2011-10-14

We study integrable hierarchies associated with spectral problems of the form P{psi} = {lambda}Q{psi}, where P and Q are difference operators. The corresponding nonlinear differential-difference equations can be viewed as inhomogeneous generalizations of the Bogoyavlensky-type lattices. While the latter turn into the Korteweg-de Vries equation under the continuous limit, the lattices under consideration provide discrete analogs of the Sawada-Kotera and Kaup-Kupershmidt equations. The r-matrix formulation and several of the simplest explicit solutions are presented. (paper)

A Hierarchy Model of Income Distribution

OpenAIRE

Fix, Blair

2018-01-01

Based on worldly experience, most people would agree that firms are hierarchically organized, and that pay tends to increase as one moves up the hierarchy. But how this hierarchical structure affects income distribution has not been widely studied. To remedy this situation, this paper presents a new model of income distribution that explores the effects of social hierarchy. This ‘hierarchy model’ takes the limited available evidence on the structure of firm hierarchies and generalizes it to c...

A hierarchy of intrinsic timescales across primate cortex.

Science.gov (United States)

Murray, John D; Bernacchia, Alberto; Freedman, David J; Romo, Ranulfo; Wallis, Jonathan D; Cai, Xinying; Padoa-Schioppa, Camillo; Pasternak, Tatiana; Seo, Hyojung; Lee, Daeyeol; Wang, Xiao-Jing

2014-12-01

Specialization and hierarchy are organizing principles for primate cortex, yet there is little direct evidence for how cortical areas are specialized in the temporal domain. We measured timescales of intrinsic fluctuations in spiking activity across areas and found a hierarchical ordering, with sensory and prefrontal areas exhibiting shorter and longer timescales, respectively. On the basis of our findings, we suggest that intrinsic timescales reflect areal specialization for task-relevant computations over multiple temporal ranges.

Hierarchy is Detrimental for Human Cooperation.

Science.gov (United States)

Cronin, Katherine A; Acheson, Daniel J; Hernández, Penélope; Sánchez, Angel

2015-12-22

Studies of animal behavior consistently demonstrate that the social environment impacts cooperation, yet the effect of social dynamics has been largely excluded from studies of human cooperation. Here, we introduce a novel approach inspired by nonhuman primate research to address how social hierarchies impact human cooperation. Participants competed to earn hierarchy positions and then could cooperate with another individual in the hierarchy by investing in a common effort. Cooperation was achieved if the combined investments exceeded a threshold, and the higher ranked individual distributed the spoils unless control was contested by the partner. Compared to a condition lacking hierarchy, cooperation declined in the presence of a hierarchy due to a decrease in investment by lower ranked individuals. Furthermore, hierarchy was detrimental to cooperation regardless of whether it was earned or arbitrary. These findings mirror results from nonhuman primates and demonstrate that hierarchies are detrimental to cooperation. However, these results deviate from nonhuman primate findings by demonstrating that human behavior is responsive to changing hierarchical structures and suggests partnership dynamics that may improve cooperation. This work introduces a controlled way to investigate the social influences on human behavior, and demonstrates the evolutionary continuity of human behavior with other primate species.

Retribution as hierarchy regulation: Hierarchy preferences moderate the effect of offender socioeconomic status on support for retribution.

Science.gov (United States)

Redford, Liz; Ratliff, Kate A

2018-01-01

People punish others for various reasons, including deterring future crime, incapacitating the offender, and retribution, or payback. The current research focuses on retribution, testing whether support for retribution is motivated by the desire to maintain social hierarchies. If so, then the retributive tendencies of hierarchy enhancers or hierarchy attenuators should depend on whether offenders are relatively lower or higher in status, respectively. Three studies showed that hierarchy attenuators were more retributive against high-status offenders than for low-status offenders, that hierarchy enhancers showed a stronger orientation towards retributive justice, and that relationship was stronger for low-status, rather than high-status, criminal offenders. These findings clarify the purpose and function of retributive punishment. They also reveal how hierarchy-regulating motives underlie retribution, motives which, if allowed to influence judgements, may contribute to biased or ineffective justice systems. © 2017 The British Psychological Society.

Gauge equivalence between two-boson KP hierarchies

International Nuclear Information System (INIS)

Aratyn, H.

1994-01-01

In this paper it is explained the status of the two-boson KP hierarchy, which appears in this setting as an invariant subspace of the coadjoint orbit within the KP l=1 hierarchy. We will work with two main cases of two-boson KP hierarchies, one defined within KP l=1 hierarchy will be called Faa di Bruno KP hierarchy, while the second defined within KP hierarchy for a quadratic two-boson KP hierarchy. It will be established for them the gauge invariance playing the role of generalized Miura transformations. It is emphasized the symplectic character of equivalence of KP l=1 and KP. It is also made a point that the gauge equivalence established for two-boson systems is valid for an arbitrary n-th Poisson bracket structure and not only the first Poisson bracket structure. (author). 7 refs

Headwater biodiversity among different levels of stream habitat hierarchy

DEFF Research Database (Denmark)

Göthe, Emma; Friberg, Nikolai; Kahlert, Maria

2014-01-01

of a- and b-diversity to y-diversity between two levels of stream habitat hierarchy (catchment and region level). The relationship between species community structure and local environmental factors was also assessed. Our results show that both a- and b-diversity made a significant contribution to y......-diversity. b-diversity remained relatively constant between the two levels of habitat hierarchy even though local environmental control of the biota decreased from the catchment to the region level. To capture most of headwater y-diversity, management should therefore target sites that are locally diverse......, but at the same time select sites so that b-diversity is maximized. As environmental control of the biota peaked at the catchment level, the conservation of headwater stream diversity is likely to be most effective when management targets environmental conditions across multiple local sites within relatively...

Gravitational and electromagnetic potentials of the stationary Einstein-Maxwell field equations

International Nuclear Information System (INIS)

Jones, T.C.

1979-01-01

Associated with the stationary Einstein-Maxwell field equations is an infinite hierarchy of potentials. The basic characteristics of these potentials are examined in general and then in greater detail for the particular case of the Reissner-Nordstrom metric. Thier essential utility in the process of solution generation is elucidated, and the necessary equations for solution generation are developed. Appropriate generating functions, which contain the complete infinite hierarchy of potentials, are developed and analyzed. Particular attention is paid to the inherent gauge freedom of these generating functions. Two methods of solution generation, which yield asymptotically flat solutions in vacuum, are generalized to include electromagnetism. One method, using potentials consistent with the Harrison transformation and the Reissner-Nordstrom metric, is discussed in detail, and its resultant difficulties are explored

Quasilinear Elliptic Equations with Hardy-Sobolev Critical Exponents: Existence and Multiplicity of Nontrivial Solutions

Directory of Open Access Journals (Sweden)

Guanwei Chen

2014-01-01

Full Text Available We study the existence of positive solutions and multiplicity of nontrivial solutions for a class of quasilinear elliptic equations by using variational methods. Our obtained results extend some existing ones.

Generalized W-algebras and integrable hierarchies

International Nuclear Information System (INIS)

Burroughs, N.; De Groot, M.; Hollowood, T.; Miramontes, L.

1992-01-01

We report on generalizations of the KdV-type integrable hierarchies of Drinfel'd and Sokolov. These hierarchies lead to the existence of new classical W-algebras, which arise as the second hamiltonian structure of the hierarchies. In particular, we present a construction of the W n (l) -algebras. (orig.)

A Novel Environmental Performance Evaluation of Thailand’s Food Industry Using Structural Equation Modeling and Fuzzy Analytic Hierarchy Techniques

Directory of Open Access Journals (Sweden)

Anirut Pipatprapa

2016-03-01

Full Text Available Currently, the environment and sustainability are important topics for every industry. The food industry is particularly complicated in this regard because of the dynamic and complex character of food products and their production. This study uses structural equation modeling (SEM and a fuzzy analytic hierarchy process (FAHP to investigate which factors are suitable for evaluating the environmental performance of Thailand’s food industry. A first-stage questionnaire survey was conducted with 178 managers in the food industry that obtained a certificate from the Department of Industrial Work of Thailand to synthesize the performance measurement model and the significance of the relationship between the indicators. A second-stage questionnaire measured 18 experts’ priorities regarding the criteria and sub-factors involved in the different aspects and assessment items regarding environmental performance. SEM showed that quality management, market orientation, and innovation capability have a significantly positive effect on environmental performance. The FAHP showed that the experts were most concerned about quality management, followed by market orientation and innovation capability; the assessment items for quality policy, quality assurance, and customer orientation were of the most concern. The findings of this study can be referenced and support managerial decision making when monitoring environmental performance.

Hierarchy is Detrimental for Human Cooperation

Science.gov (United States)

Cronin, Katherine A.; Acheson, Daniel J.; Hernández, Penélope; Sánchez, Angel

2015-01-01

Studies of animal behavior consistently demonstrate that the social environment impacts cooperation, yet the effect of social dynamics has been largely excluded from studies of human cooperation. Here, we introduce a novel approach inspired by nonhuman primate research to address how social hierarchies impact human cooperation. Participants competed to earn hierarchy positions and then could cooperate with another individual in the hierarchy by investing in a common effort. Cooperation was achieved if the combined investments exceeded a threshold, and the higher ranked individual distributed the spoils unless control was contested by the partner. Compared to a condition lacking hierarchy, cooperation declined in the presence of a hierarchy due to a decrease in investment by lower ranked individuals. Furthermore, hierarchy was detrimental to cooperation regardless of whether it was earned or arbitrary. These findings mirror results from nonhuman primates and demonstrate that hierarchies are detrimental to cooperation. However, these results deviate from nonhuman primate findings by demonstrating that human behavior is responsive to changing hierarchical structures and suggests partnership dynamics that may improve cooperation. This work introduces a controlled way to investigate the social influences on human behavior, and demonstrates the evolutionary continuity of human behavior with other primate species. PMID:26692287

BBGKY hierarchy and dynamics of correlations

International Nuclear Information System (INIS)

Polishchuk, D.O.

2010-01-01

We derive the BBGKY hierarchy for the Fermi and Bose many-particle systems, using the von Neumann hierarchy for the correlation operators. The solution of the Cauchy problem of the formulated hierarchy in the case of an n-body interaction potential is constructed in the space of sequences of trace-class operators.

Affine Lie algebraic origin of constrained KP hierarchies

International Nuclear Information System (INIS)

Aratyn, H.; Gomes, J.F.; Zimerman, A.H.

1994-07-01

It is presented an affine sl(n+1) algebraic construction of the basic constrained KP hierarchy. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax formulation and we show that these approaches are equivalent. The model is recognized to be generalized non-linear Schroedinger (GNLS) hierarchy and it is used as a building block for a new class of constrained KP hierarchies. These constrained KP hierarchies are connected via similarity-Backlund transformations and interpolate between GNLS and multi-boson KP-Toda hierarchies. The construction uncovers origin of the Toda lattice structure behind the latter hierarchy. (author). 23 refs

Improved hybridization of Fuzzy Analytic Hierarchy Process (FAHP) algorithm with Fuzzy Multiple Attribute Decision Making - Simple Additive Weighting (FMADM-SAW)

Science.gov (United States)

Zaiwani, B. E.; Zarlis, M.; Efendi, S.

2018-03-01

In this research, the improvement of hybridization algorithm of Fuzzy Analytic Hierarchy Process (FAHP) with Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) in selecting the best bank chief inspector based on several qualitative and quantitative criteria with various priorities. To improve the performance of the above research, FAHP algorithm hybridization with Fuzzy Multiple Attribute Decision Making - Simple Additive Weighting (FMADM-SAW) algorithm was adopted, which applied FAHP algorithm to the weighting process and SAW for the ranking process to determine the promotion of employee at a government institution. The result of improvement of the average value of Efficiency Rate (ER) is 85.24%, which means that this research has succeeded in improving the previous research that is equal to 77.82%. Keywords: Ranking and Selection, Fuzzy AHP, Fuzzy TOPSIS, FMADM-SAW.

The Cauchy problem for the Bogolyubov hierarchy of equations. The BCS model

International Nuclear Information System (INIS)

Vidybida, A.K.

1975-01-01

A chain of Bogolyubov's kinetic equations for an infinite quantum system of particles distributed in space with the mean density 1/V and interacting with the BCS model operator is considered as a single abstract equation in some countable normalized space bsup(v) of sequences of integral operators. In this case an unique solution of the Cauchy problem has been obtained at arbitrary initial conditions from bsup(v), stationary solutions of the equation have been derived, and the class of the initial conditions which approach to stationary ones is indicated

Models of neutrino masses: Anarchy versus hierarchy

International Nuclear Information System (INIS)

Altarelli, Guido; Feruglio, Ferruccio; Masina, Isabella

2003-01-01

We present a quantitative study of the ability of models with different levels of hierarchy to reproduce the solar neutrino solutions, in particular the LA solution. As a flexible testing ground we consider models based on SU(5)xU(1) F . In this context, we have made statistical simulations of models with different patterns from anarchy to various types of hierarchy: normal hierarchical models with and without automatic suppression of the 23 (sub)determinant and inverse hierarchy models. We find that, not only for the LOW or VO solutions, but even in the LA case, the hierarchical models have a significantly better success rate than those based on anarchy. The normal hierarchy and the inverse hierarchy models have comparable performances in models with see-saw dominance, while the inverse hierarchy models are particularly good in the no see-saw versions. As a possible distinction between these categories of models, the inverse hierarchy models favour a maximal solar mixing angle and their rate of success drops dramatically as the mixing angle decreases, while normal hierarchy models are far more stable in this respect. (author)

On the evolution equations, solvable through the inverse scattering method

International Nuclear Information System (INIS)

Gerdjikov, V.S.; Khristov, E.Kh.

1979-01-01

The nonlinear evolution equations (NLEE), related to the one-parameter family of Dirac operators are considered in a uniform manner. The class of NLEE solvable through the inverse scatterina method and their conservation laws are described. The description of the hierarchy of Hamiltonian structures and the proof of complete integrability of the NLEE is presented. The class of Baecklund transformations for these NLEE is derived. The general formulae are illustrated by two important examples: the nonlinear Schroedinger equation and the sine-Gordon equation

Using Multiple-hierarchy Stratification and Life Course Approaches to Understand Health Inequalities: The Intersecting Consequences of Race, Gender, SES, and Age.

Science.gov (United States)

Brown, Tyson H; Richardson, Liana J; Hargrove, Taylor W; Thomas, Courtney S

2016-06-01

This study examines how the intersecting consequences of race-ethnicity, gender, socioeconomics status (SES), and age influence health inequality. We draw on multiple-hierarchy stratification and life course perspectives to address two main research questions. First, does racial-ethnic stratification of health vary by gender and/or SES? More specifically, are the joint health consequences of racial-ethnic, gender, and socioeconomic stratification additive or multiplicative? Second, does this combined inequality in health decrease, remain stable, or increase between middle and late life? We use panel data from the Health and Retirement Study (N = 12,976) to investigate between- and within-group differences in in self-rated health among whites, blacks, and Mexican Americans. Findings indicate that the effects of racial-ethnic, gender, and SES stratification are interactive, resulting in the greatest racial-ethnic inequalities in health among women and those with higher levels of SES. Furthermore, racial-ethnic/gender/SES inequalities in health tend to decline with age. These results are broadly consistent with intersectionality and aging-as-leveler hypotheses. © American Sociological Association 2016.

Langevin equation with multiplicative white noise: Transformation of diffusion processes into the Wiener process in different prescriptions

International Nuclear Information System (INIS)

Kwok, Sau Fa

2012-01-01

A Langevin equation with multiplicative white noise and its corresponding Fokker–Planck equation are considered in this work. From the Fokker–Planck equation a transformation into the Wiener process is provided for different orders of prescription in discretization rule for the stochastic integrals. A few applications are also discussed. - Highlights: ► Fokker–Planck equation corresponding to the Langevin equation with mul- tiplicative white noise is presented. ► Transformation of diffusion processes into the Wiener process in different prescriptions is provided. ► The prescription parameter is associated with the growth rate for a Gompertz-type model.

Testing Mediation Using Multiple Regression and Structural Equation Modeling Analyses in Secondary Data

Science.gov (United States)

Li, Spencer D.

2011-01-01

Mediation analysis in child and adolescent development research is possible using large secondary data sets. This article provides an overview of two statistical methods commonly used to test mediated effects in secondary analysis: multiple regression and structural equation modeling (SEM). Two empirical studies are presented to illustrate the…

Using the Analytic Hierarchy Process for Decision-Making in Ecosystem Management

Science.gov (United States)

Daniel L. Schmoldt; David L. Peterson

1997-01-01

Land management activities on public lands combine multiple objectives in order to create a plan of action over a finite time horizon. Because management activities are constrained by time and money, it is critical to make the best use of available agency resources. The Analytic Hierarchy Process (AHP) offers a structure for multi-objective decisionmaking so that...

SELECTION OF BUSINESS STRATEGIES FOR QUALITY IMPROVEMENT USING FUZZY ANALYTICAL HIERARCHY PROCESS

Directory of Open Access Journals (Sweden)

Prasun Das

2010-12-01

Full Text Available Fuzzy linguistic concepts are often used to enhance the traditional analytic hierarchy process (AHP in capturing the fuzziness and subjectiveness of decision makers' judgments. In this paper, fuzzy AHP methodology is adopted for selection of the strategies for business improvement in an Indian industry as a decision making problem. Due to simplicity and effectiveness, triangular fuzzy numbers are adopted as a reference to indicate the influence strength of each element in the hierarchy structure. The confidence level and the optimistic levels of multiple decision makers are captured by using ? -cut based fuzzy number methods. This fuzzy set theory based multi-attribute decision making method is found to be quite useful and effective in industrial environment.

The supersymmetric generalized modified KdV hierarchy and odd minimal superconformal field theories coupled to 2D supergravity: 2

International Nuclear Information System (INIS)

Awada, M.A.

1990-01-01

We further study the universal equations of the supersymmetric modified KdV (MKdV) hierarchy in its generalized form. We show that these equations describe the dynamical quantum equations of the odd series of N = 1 minimal (p,q) superconformal field theory coupled to N = 1 supergravity in particular those unitary series with p = 2k + 3, and q = 2k = 1. The string susceptibility of these models is γ sstr. (0) = -2/2k + 1. We demonstrate explicitly the cases k = 2; and k = 3. 10 refs

Completing the land resource hierarchy

Science.gov (United States)

The Land Resource Hierarchy of the NRCS is a hierarchal landscape classification consisting of resource areas which represent both conceptual and spatially discrete landscape units stratifying agency programs and practices. The Land Resource Hierarchy (LRH) scales from discrete points (soil pedon an...

Hierarchy, Dominance, and Deliberation: Egalitarian Values Require Mental Effort.

Science.gov (United States)

Van Berkel, Laura; Crandall, Christian S; Eidelman, Scott; Blanchar, John C

2015-09-01

Hierarchy and dominance are ubiquitous. Because social hierarchy is early learned and highly rehearsed, the value of hierarchy enjoys relative ease over competing egalitarian values. In six studies, we interfere with deliberate thinking and measure endorsement of hierarchy and egalitarianism. In Study 1, bar patrons' blood alcohol content was correlated with hierarchy preference. In Study 2, cognitive load increased the authority/hierarchy moral foundation. In Study 3, low-effort thought instructions increased hierarchy endorsement and reduced equality endorsement. In Study 4, ego depletion increased hierarchy endorsement and caused a trend toward reduced equality endorsement. In Study 5, low-effort thought instructions increased endorsement of hierarchical attitudes among those with a sense of low personal power. In Study 6, participants' thinking quickly allocated more resources to high-status groups. Across five operationalizations of impaired deliberative thought, hierarchy endorsement increased and egalitarianism receded. These data suggest hierarchy may persist in part because it has a psychological advantage. © 2015 by the Society for Personality and Social Psychology, Inc.

Improved Durand-equation for multiple application

International Nuclear Information System (INIS)

Weber, M.

1986-01-01

The applicability of Durand's equation could be improved for general use by applying suitable parameters representing the grain-size distribution. Thus, the Durand equation cannot only describe polydisperse (pseudo)-homogeneous or heterogeneous transportation, but also solid-fluid mixtures containing a certain amount of fine particles. Even non-Newtonian influences can be taken into account. The applicability of the extended Durand equation for polydisperse mixtures will be demonstrated by measurement data. With respect to this, the transition between pseudohomogeneous and heterogeneous transport has been considered on the basis of measured concentration profiles

Integrable hydrodynamics of Calogero-Sutherland model: bidirectional Benjamin-Ono equation

International Nuclear Information System (INIS)

Abanov, Alexander G; Bettelheim, Eldad; Wiegmann, Paul

2009-01-01

We develop a hydrodynamic description of the classical Calogero-Sutherland liquid: a Calogero-Sutherland model with an infinite number of particles and a non-vanishing density of particles. The hydrodynamic equations, being written for the density and velocity fields of the liquid, are shown to be a bidirectional analog of the Benjamin-Ono equation. The latter is known to describe internal waves of deep stratified fluids. We show that the bidirectional Benjamin-Ono equation appears as a real reduction of the modified KP hierarchy. We derive the chiral nonlinear equation which appears as a chiral reduction of the bidirectional equation. The conventional Benjamin-Ono equation is a degeneration of the chiral nonlinear equation at large density. We construct multi-phase solutions of the bidirectional Benjamin-Ono equations and of the chiral nonlinear equations

The gauge hierarchy problem

International Nuclear Information System (INIS)

Natale, A.A.; Shellard, R.C.

1981-01-01

The problem of gauge hierarchy in Grand Unified Theories using a toy model with O(N) symmetry is discussed. It is shown that there is no escape to the unnatural adjustment of coupling constants, made only after the computation of several orders in perturbation theory is performed. The propositions of some authors on ways to overcome the gauge hierarchy problem are commented. (Author) [pt

Relativistic dissipative hydrodynamic equations at the second order for multi-component systems with multiple conserved currents

International Nuclear Information System (INIS)

Monnai, Akihiko; Hirano, Tetsufumi

2010-01-01

We derive the second order hydrodynamic equations for the relativistic system of multi-components with multiple conserved currents by generalizing the Israel-Stewart theory and Grad's moment method. We find that, in addition to the conventional moment equations, extra moment equations associated with conserved currents should be introduced to consistently match the number of equations with that of unknowns and to satisfy the Onsager reciprocal relations. Consistent expansion of the entropy current leads to constitutive equations which involve the terms not appearing in the original Israel-Stewart theory even in the single component limit. We also find several terms which exhibit thermal diffusion such as Soret and Dufour effects. We finally compare our results with those of other existing formalisms.

Hierarchy is Detrimental for Human Cooperation

OpenAIRE

Cronin, Katherine A.; Acheson, Daniel J.; Hernández, Penélope; Sánchez, Angel

2016-01-01

Studies of animal behavior consistently demonstrate that the social environment impacts cooperation, yet the effect of social dynamics has been largely excluded from studies of human cooperation. Here, we introduce a novel approach inspired by nonhuman primate research to address how social hierarchies impact human cooperation. Participants competed to earn hierarchy positions and then could cooperate with another individual in the hierarchy by investing in a common effort. Cooperation was ac...

Group Decision Making with the Analytic Hierarchy Process in Benefit-Risk Assessment: A Tutorial

NARCIS (Netherlands)

Hummel, J. Marjan; Bridges, John; IJzerman, Maarten Joost

2014-01-01

The analytic hierarchy process (AHP) has been increasingly applied as a technique for multi-criteria decision analysis in healthcare. The AHP can aid decision makers in selecting the most valuable technology for patients, while taking into account multiple, and even conflicting, decision criteria.

Multiscale Analysis of Effects of Additive and Multiplicative Noise on Delay Differential Equations near a Bifurcation Point

International Nuclear Information System (INIS)

Klosek, M.M.

2004-01-01

We study effects of noisy and deterministic perturbations on oscillatory solutions to delay differential equations. We develop the multiscale technique and derive amplitude equations for noisy oscillations near a critical delay. We investigate effects of additive and multiplicative noise. We show that if the magnitudes of noise and deterministic perturbations are balanced, then the oscillatory behavior persists for long times being sustained by the noise. We illustrate the technique and its results on linear and logistic delay equations. (author)

Hierarchies in Coloured Petri Nets

DEFF Research Database (Denmark)

Huber, Peter; Jensen, Kurt; Shapiro, Robert M.

1991-01-01

constructs, and it illustrates them by means of two examples. The hierarchy constructs can be used for theoretical considerations, but their main use is to describe and analyse large real-world systems. All of the hierarchy constructs are supported by the editing and analysis facilities in the CPN Palette...

Maslow's Hierarchy of Needs Revisited.

Science.gov (United States)

Frame, Douglas

1996-01-01

Reviews Maslow's hierarchy of needs and characterization of the self-actualizing personality, suggesting that since few people meet his self-actualization criteria, an educational system designed to produce such personalities may fail, with teachers attending only to the hierarchy's lower stages (self-esteem and self-actualization) which dilutes…

Effects of host social hierarchy on disease persistence.

Science.gov (United States)

Davidson, Ross S; Marion, Glenn; Hutchings, Michael R

2008-08-07

The effects of social hierarchy on population dynamics and epidemiology are examined through a model which contains a number of fundamental features of hierarchical systems, but is simple enough to allow analytical insight. In order to allow for differences in birth rates, contact rates and movement rates among different sets of individuals the population is first divided into subgroups representing levels in the hierarchy. Movement, representing dominance challenges, is allowed between any two levels, giving a completely connected network. The model includes hierarchical effects by introducing a set of dominance parameters which affect birth rates in each social level and movement rates between social levels, dependent upon their rank. Although natural hierarchies vary greatly in form, the skewing of contact patterns, introduced here through non-uniform dominance parameters, has marked effects on the spread of disease. A simple homogeneous mixing differential equation model of a disease with SI dynamics in a population subject to simple birth and death process is presented and it is shown that the hierarchical model tends to this as certain parameter regions are approached. Outside of these parameter regions correlations within the system give rise to deviations from the simple theory. A Gaussian moment closure scheme is developed which extends the homogeneous model in order to take account of correlations arising from the hierarchical structure, and it is shown that the results are in reasonable agreement with simulations across a range of parameters. This approach helps to elucidate the origin of hierarchical effects and shows that it may be straightforward to relate the correlations in the model to measurable quantities which could be used to determine the importance of hierarchical corrections. Overall, hierarchical effects decrease the levels of disease present in a given population compared to a homogeneous unstructured model, but show higher levels of

CAUSAL INFERENCE WITH A GRAPHICAL HIERARCHY OF INTERVENTIONS.

Science.gov (United States)

Shpitser, Ilya; Tchetgen, Eric Tchetgen

2016-12-01

Identifying causal parameters from observational data is fraught with subtleties due to the issues of selection bias and confounding. In addition, more complex questions of interest, such as effects of treatment on the treated and mediated effects may not always be identified even in data where treatment assignment is known and under investigator control, or may be identified under one causal model but not another. Increasingly complex effects of interest, coupled with a diversity of causal models in use resulted in a fragmented view of identification. This fragmentation makes it unnecessarily difficult to determine if a given parameter is identified (and in what model), and what assumptions must hold for this to be the case. This, in turn, complicates the development of estimation theory and sensitivity analysis procedures. In this paper, we give a unifying view of a large class of causal effects of interest, including novel effects not previously considered, in terms of a hierarchy of interventions, and show that identification theory for this large class reduces to an identification theory of random variables under interventions from this hierarchy. Moreover, we show that one type of intervention in the hierarchy is naturally associated with queries identified under the Finest Fully Randomized Causally Interpretable Structure Tree Graph (FFRCISTG) model of Robins (via the extended g-formula), and another is naturally associated with queries identified under the Non-Parametric Structural Equation Model with Independent Errors (NPSEM-IE) of Pearl, via a more general functional we call the edge g-formula. Our results motivate the study of estimation theory for the edge g-formula, since we show it arises both in mediation analysis, and in settings where treatment assignment has unobserved causes, such as models associated with Pearl's front-door criterion.

Rethinking the waste hierarchy

Energy Technology Data Exchange (ETDEWEB)

Rasmussen, C; Vigsoe, D [eds.

2005-03-01

There is an increasing need to couple environmental and economic considerations within waste management. Consumers and companies alike generate ever more waste. The waste-policy challenges of the future lie in decoupling growth in waste generation from growth in consumption, and in setting priorities for the waste management. This report discusses the criteria for deciding priorities for waste management methods, and questions the current principles of EU waste policies. The basis for the discussion is the so-called waste hierarchy which has dominated the waste policy in the EU since the mid-1970s. The waste hierarchy ranks possible methods of waste management. According to the waste hierarchy, the very best solution is to reduce the amount of waste. After that, reuse is preferred to recycling which, in turn, is preferred to incineration. Disposal at a landfill is the least favourable solution. (BA)

Hierarchy stability for spontaneously broken theories

Energy Technology Data Exchange (ETDEWEB)

Galvan, J B; Perez-Mercader, J; Sanchez, F J

1987-04-16

By using Weisberger's method for the integration of heavy degrees of freedom in multiscale theories, we show that tree level hierarchies are not destabilized byquantum corrections in a two-scale, two scalar field theory model where the heavy sector undergoes spontaneous symmetry breaking. We see explicitly the role played by the one-loop heavy log corrections to the effective parameters in maintaining the original tree level hierarchy and in keeping the theory free of hierarchy problems.

Hierarchy stability for spontaneously broken theories

International Nuclear Information System (INIS)

Galvan, J.B.; Perez-Mercader, J.; Sanchez, F.J.

1987-01-01

By using Weisberger's method for the integration of heavy degrees of freedom in multiscale theories, we show that tree level hierarchies are not destabilized byquantum corrections in a two-scale, two scalar field theory model where the heavy sector undergoes spontaneous symmetry breaking. We see explicitly the role played by the one-loop heavy log corrections to the effective parameters in maintaining the original tree level hierarchy and in keeping the theory free of hierarchy problems. (orig.)

Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy

International Nuclear Information System (INIS)

Bergvelt, Maarten; Gekhtman, Michael; Kasman, Alex

2009-01-01

Pairs of nxn matrices whose commutator differ from the identity by a matrix of rank r are used to construct bispectral differential operators with rxr matrix coefficients satisfying the Lax equations of the Matrix KP hierarchy. Moreover, the bispectral involution on these operators has dynamical significance for the spin Calogero particles system whose phase space such pairs represent. In the case r = 1, this reproduces well-known results of Wilson and others from the 1990's relating (spinless) Calogero-Moser systems to the bispectrality of (scalar) differential operators

Dominance Hierarchies in Young Children

Science.gov (United States)

Edelman, Murray S.; Omark, Donald R.

1973-01-01

This study uses the ethological approach of seeking species characteristics and phylogenetic continuities in an investigation of human behavior. Among primates a striking consistency is the presence of some form of dominance hierarchy in many species. The present study examines peer group dominance hierarchies as they are perceived by children in…

PINGU sensitivity to neutrino mass hierarchy

International Nuclear Information System (INIS)

Groß, Andreas

2014-01-01

Determination of the neutrino mass hierarchy (NMH) is among the most fundamental questions in particle physics. Recent measurements of 1) a large mixing angle between the first and the third neutrino mass eigenstates and 2) the first observation of atmospheric neutrino oscillations at tens of GeV with neutrino telescopes, open the intriguing new possibility to exploit matter effects in neutrino oscillation to determine the neutrino mass hierarchy. A further extension of IceCube/DeepCore called PINGU (Precision IceCube Next Generation Upgrade) has been recently envisioned with the ultimate goal to measure neutrino mass hierarchy. PINGU would consist of additional IceCube-like strings of detectors deployed in the deepest and cleanest ice in the center of IceCube. More densely deployed instrumentation would provide a threshold substantially below 10 GeV and enhance the sensitivity to the mass hierarchy signal in atmospheric neutrinos. Here we discuss an estimate of the PINGU sensitivity to the mass hierarchy determined using an approximation with an Asimov dataset and an oscillation parameter fit

Resolution of ranking hierarchies in directed networks

Science.gov (United States)

Barucca, Paolo; Lillo, Fabrizio

2018-01-01

Identifying hierarchies and rankings of nodes in directed graphs is fundamental in many applications such as social network analysis, biology, economics, and finance. A recently proposed method identifies the hierarchy by finding the ordered partition of nodes which minimises a score function, termed agony. This function penalises the links violating the hierarchy in a way depending on the strength of the violation. To investigate the resolution of ranking hierarchies we introduce an ensemble of random graphs, the Ranked Stochastic Block Model. We find that agony may fail to identify hierarchies when the structure is not strong enough and the size of the classes is small with respect to the whole network. We analytically characterise the resolution threshold and we show that an iterated version of agony can partly overcome this resolution limit. PMID:29394278

Reactive Goal Decomposition Hierarchies for On-Board Autonomy

Science.gov (United States)

Hartmann, L.

2002-01-01

to state and environment and in general can terminate the execution of a decomposition and attempt a new decomposition at any level in the hierarchy. This goal decomposition system is suitable for workstation, microprocessor and fpga implementation and thus is able to support the full range of prototyping activities, from mission design in the laboratory to development of the fpga firmware for the flight system. This approach is based on previous artificial intelligence work including (1) Brooks' subsumption architecture for robot control, (2) Firby's Reactive Action Package System (RAPS) for mediating between high level automated planning and low level execution and (3) hierarchical task networks for automated planning. Reactive goal decomposition hierarchies can be used for a wide variety of on-board autonomy applications including automating low level operation sequences (such as scheduling prerequisite operations, e.g., heaters, warm-up periods, monitoring power constraints), coordinating multiple spacecraft as in formation flying and constellations, robot manipulator operations, rendez-vous, docking, servicing, assembly, on-orbit maintenance, planetary rover operations, solar system and interstellar probes, intelligent science data gathering and disaster early warning. Goal decomposition hierarchies can support high level fault tolerance. Given models of on-board resources and goals to accomplish, the decomposition hierarchy could allocate resources to goals taking into account existing faults and in real-time reallocating resources as new faults arise. Resources to be modeled include memory (e.g., ROM, FPGA configuration memory, processor memory, payload instrument memory), processors, on-board and interspacecraft network nodes and links, sensors, actuators (e.g., attitude determination and control, guidance and navigation) and payload instruments. A goal decomposition hierarchy could be defined to map mission goals and tasks to available on-board resources. As

Reflected‑Point‑Reactor Kinetics Model for Neutron Coincidence Counting: Comments on the Equation for the Leakage Self‑Multiplication

International Nuclear Information System (INIS)

Croft, S.; McElroy, RD.; Favalli, A.; Hauck, D.; Henzlova, D.; Henzl, V.; Santi, PA.

2015-01-01

Passive neutron correlation counting is widely used, for example by international inspection agencies, for the non‑destructive assay of spontaneously fissile nuclear materials for nuclear safeguards. The mass of special nuclear material present in an item is usually estimated from the observed neutron counting rates by using equations based on mathematically describing the object as an isolated multiplying point‑like source. Calibration using representative physical standards can often adequately compensate for this theoretical oversimplification through the introduction and use of effective‑interpretational‑model‑parameters meaning that useful assay results are obtained. In this work we extend the point‑model treatment by including a simple reflector around the fissioning material. Specifically we show how the leakage self‑multiplication equation mathematically connects the traditional bare source and the reflected source cases. In doing so we explicitly demonstrate that although the presence of a simple reflector changes the leakage self‑multiplication the traditional bare‑item point model multiplicity equations retain the same mathematical form. Making and explaining this connection is important because it helps to explain and justify the practical success and use of the traditional point‑model equations even when the assumptions used to generate the key functional dependences are violated. We are not aware that this point has been recognized previously.

Evaluating, Comparing, and Interpreting Protein Domain Hierarchies

Science.gov (United States)

2014-01-01

Abstract Arranging protein domain sequences hierarchically into evolutionarily divergent subgroups is important for investigating evolutionary history, for speeding up web-based similarity searches, for identifying sequence determinants of protein function, and for genome annotation. However, whether or not a particular hierarchy is optimal is often unclear, and independently constructed hierarchies for the same domain can often differ significantly. This article describes methods for statistically evaluating specific aspects of a hierarchy, for probing the criteria underlying its construction and for direct comparisons between hierarchies. Information theoretical notions are used to quantify the contributions of specific hierarchical features to the underlying statistical model. Such features include subhierarchies, sequence subgroups, individual sequences, and subgroup-associated signature patterns. Underlying properties are graphically displayed in plots of each specific feature's contributions, in heat maps of pattern residue conservation, in “contrast alignments,” and through cross-mapping of subgroups between hierarchies. Together, these approaches provide a deeper understanding of protein domain functional divergence, reveal uncertainties caused by inconsistent patterns of sequence conservation, and help resolve conflicts between competing hierarchies. PMID:24559108

The quadratic-form identity for constructing Hamiltonian structures of the NLS-MKdV hierarchy and multi-component Levi hierarchy

International Nuclear Information System (INIS)

Dong Huanhe; Wang Xiangrong

2008-01-01

The trace identity is extended to the quadratic-form identity. The Hamiltonian structures of the NLS-MKdV hierarchy, and integrable coupling of multi-component Levi hierarchy are obtained by the quadratic-form identity. The method can be used to produce the Hamiltonian structures of the other integrable couplings or multi-component hierarchies

Choosing of mode and calculation of multiple regression equation parameters in X-ray radiometric analysis

International Nuclear Information System (INIS)

Mamikonyan, S.V.; Berezkin, V.V.; Lyubimova, S.V.; Svetajlo, Yu.N.; Shchekin, K.I.

1978-01-01

A method to derive multiple regression equations for X-ray radiometric analysis is described. Te method is realized in the form of the REGRA program in an algorithmic language. The subprograms included in the program are describe. In analyzing cement for Mg, Al, Si, Ca and Fe contents as an example, the obtainment of working equations in the course of calculations by the program is shown to simpliy the realization of computing devices in instruments for X-ray radiometric analysis

Neutrino mass hierarchy and matter effects

OpenAIRE

Smirnov, Alexei Yu.

2013-01-01

Matter effects modify the mixing and the effective masses of neutrinos in a way which depends on the neutrino mass hierarchy. Consequently, for normal and inverted hierarchies the oscillations and flavor conversion results are different. Sensitivity to the mass hierarchy appears whenever the matter effects on the 1-3 mixing and mass splitting become substantial. This happens in supernovae in wide energy range and in the matter of the Earth. The Earth density profile is a multi-layer medium wh...

Hierarchies of belief and interim rationalizability

Directory of Open Access Journals (Sweden)

Jeffrey C. Ely

2006-03-01

Full Text Available In games with incomplete information, conventional hierarchies of belief are incomplete as descriptions of the players' information for the purposes of determining a player's behavior. We show by example that this is true for a variety of solution concepts. We then investigate what is essential about a player's information to identify behavior. We specialize to two player games and the solution concept of interim rationalizability. We construct the universal type space for rationalizability and characterize the types in terms of their beliefs. Infinite hierarchies of beliefs over conditional beliefs, which we call Delta-hierarchies, are what turn out to matter. We show that any two types in any two type spaces have the same rationalizable sets in all games if and only if they have the same Delta-hierarchies.

The problem of symmetry breaking hierarchy

International Nuclear Information System (INIS)

Natale, A.A.

1983-01-01

The problem of symmetry breaking hierarchy in grand unified theories is discussed, proving the impossibility to get a big hierarchy of interactions, in a natural way within the framework of perturbation theory. (L.C.) [pt

Is there a hierarchy of survival reflexes?

Science.gov (United States)

Macphail, Kieran

2013-10-01

A hierarchy of survival reflexes for prioritising assessment and treatment in patients with pain of insidious onset is hypothesised. The hierarchy asserts that some systems are more vital than others and that the central nervous system (CNS) prioritises systems based on their significance to survival. The hypothesis suggests that dysfunction in more important systems will cause compensation in less important systems. This paper presents studies examining these effects for each system, arguing that each section of the hierarchy may have effects on other systems within the hierarchy. This concept is untested empirically, highly speculative and substantial research is required to validate the suggested hierarchical prioritisation by the CNS. Nonetheless, the hierarchy does provide a theoretical framework to use to exclude contributing systems in patients with pain of insidious onset. Copyright © 2013 Elsevier Ltd. All rights reserved.

Hierarchy in directed random networks.

Science.gov (United States)

Mones, Enys

2013-02-01

In recent years, the theory and application of complex networks have been quickly developing in a markable way due to the increasing amount of data from real systems and the fruitful application of powerful methods used in statistical physics. Many important characteristics of social or biological systems can be described by the study of their underlying structure of interactions. Hierarchy is one of these features that can be formulated in the language of networks. In this paper we present some (qualitative) analytic results on the hierarchical properties of random network models with zero correlations and also investigate, mainly numerically, the effects of different types of correlations. The behavior of the hierarchy is different in the absence and the presence of giant components. We show that the hierarchical structure can be drastically different if there are one-point correlations in the network. We also show numerical results suggesting that the hierarchy does not change monotonically with the correlations and there is an optimal level of nonzero correlations maximizing the level of hierarchy.

Criteria for optimizing cortical hierarchies with continuous ranges

Directory of Open Access Journals (Sweden)

Antje Krumnack

2010-03-01

Full Text Available In a recent paper (Reid et al.; 2009, NeuroImage we introduced a method to calculate optimal hierarchies in the visual network that utilizes continuous, rather than discrete, hierarchical levels, and permits a range of acceptable values rather than attempting to fit fixed hierarchical distances. There, to obtain a hierarchy, the sum of deviations from the constraints that define the hierarchy was minimized using linear optimization. In the short time since publication of that paper we noticed that many colleagues misinterpreted the meaning of the term optimal hierarchy. In particular, a majority of them were under the impression that there was perhaps only one optimal hierarchy, but a substantial difficulty in finding that one. However, there is not only more than one optimal hierarchy but also more than one option for defining optimality. Continuing the line of this work we look at additional options for optimizing the visual hierarchy: minimizing the number of violated constraints and minimizing the maximal size of a constraint violation using linear optimization and mixed integer programming. The implementation of both optimization criteria is explained in detail. In addition, using constraint sets based on the data from Felleman and Van Essen, optimal hierarchies for the visual network are calculated for both optimization methods.

Multiple periodic solutions for a class of second-order nonlinear neutral delay equations

Directory of Open Access Journals (Sweden)

2006-01-01

Full Text Available By means of a variational structure and Z 2 -group index theory, we obtain multiple periodic solutions to a class of second-order nonlinear neutral delay equations of the form0, au>0$"> x ″ ( t − τ + λ ( t f ( t , x ( t , x ( t − τ , x ( t − 2 τ = x ( t , λ ( t > 0 , τ > 0 .

A classical-quantum coupling strategy for a hierarchy of one dimensional models for semiconductors

OpenAIRE

Jourdana, Clément; Pietra, Paola; Vauchelet, Nicolas

2014-01-01

We consider one dimensional coupled classical-quantum models for quantum semiconductor device simulations. The coupling occurs in the space variable : the domain of the device is divided into a region with strong quantum effects (quantum zone) and a region where quantum effects are negligible (classical zone). In the classical zone, transport in diffusive approximation is modeled through diffusive limits of the Boltzmann transport equation. This leads to a hierarchy of classical model. The qu...

The plasma transport equations derived by multiple time-scale expansions and turbulent transport. I. General theory

International Nuclear Information System (INIS)

Edenstrasser, J.W.

1995-01-01

A multiple time-scale derivative expansion scheme is applied to the dimensionless Fokker--Planck equation and to Maxwell's equations, where the parameter range of a typical fusion plasma was assumed. Within kinetic theory, the four time scales considered are those of Larmor gyration, particle transit, collisions, and classical transport. The corresponding magnetohydrodynamic (MHD) time scales are those of ion Larmor gyration, Alfven, MHD collision, and resistive diffusion. The solution of the zeroth-order equations results in the force-free equilibria and ideal Ohm's law. The solution of the first-order equations leads under the assumption of a weak collisional plasma to the ideal MHD equations. On the MHD-collision time scale, not only the full set of the MHD transport equations is obtained, but also turbulent terms, where the related transport quantities are one order in the expansion parameter larger than those of classical transport. Finally, at the resistive diffusion time scale the known transport equations are arrived at including, however, also turbulent contributions. copyright 1995 American Institute of Physics

Constrained KP models as integrable matrix hierarchies

International Nuclear Information System (INIS)

Aratyn, H.; Ferreira, L.A.; Gomes, J.F.; Zimerman, A.H.

1997-01-01

We formulate the constrained KP hierarchy (denoted by cKP K+1,M ) as an affine [cflx sl](M+K+1) matrix integrable hierarchy generalizing the Drinfeld endash Sokolov hierarchy. Using an algebraic approach, including the graded structure of the generalized Drinfeld endash Sokolov hierarchy, we are able to find several new universal results valid for the cKP hierarchy. In particular, our method yields a closed expression for the second bracket obtained through Dirac reduction of any untwisted affine Kac endash Moody current algebra. An explicit example is given for the case [cflx sl](M+K+1), for which a closed expression for the general recursion operator is also obtained. We show how isospectral flows are characterized and grouped according to the semisimple non-regular element E of sl(M+K+1) and the content of the center of the kernel of E. copyright 1997 American Institute of Physics

The Wright stuff: reimagining path analysis reveals novel components of the sex determination hierarchy in Drosophila melanogaster.

Science.gov (United States)

Fear, Justin M; Arbeitman, Michelle N; Salomon, Matthew P; Dalton, Justin E; Tower, John; Nuzhdin, Sergey V; McIntyre, Lauren M

2015-09-04

The Drosophila sex determination hierarchy is a classic example of a transcriptional regulatory hierarchy, with sex-specific isoforms regulating morphology and behavior. We use a structural equation modeling approach, leveraging natural genetic variation from two studies on Drosophila female head tissues--DSPR collection (596 F1-hybrids from crosses between DSPR sub-populations) and CEGS population (75 F1-hybrids from crosses between DGRP/Winters lines to a reference strain w1118)--to expand understanding of the sex hierarchy gene regulatory network (GRN). This approach is completely generalizable to any natural population, including humans. We expanded the sex hierarchy GRN adding novel links among genes, including a link from fruitless (fru) to Sex-lethal (Sxl) identified in both populations. This link is further supported by the presence of fru binding sites in the Sxl locus. 754 candidate genes were added to the pathway, including the splicing factors male-specific lethal 2 and Rm62 as downstream targets of Sxl which are well-supported links in males. Independent studies of doublesex and transformer mutants support many additions, including evidence for a link between the sex hierarchy and metabolism, via Insulin-like receptor. The genes added in the CEGS population were enriched for genes with sex-biased splicing and components of the spliceosome. A common goal of molecular biologists is to expand understanding about regulatory interactions among genes. Using natural alleles we can not only identify novel relationships, but using supervised approaches can order genes into a regulatory hierarchy. Combining these results with independent large effect mutation studies, allows clear candidates for detailed molecular follow-up to emerge.

Kramers-Moyal expansion for stochastic differential equations with single and multiple delays: Applications to financial physics and neurophysics

International Nuclear Information System (INIS)

Frank, T.D.

2007-01-01

We present a generalized Kramers-Moyal expansion for stochastic differential equations with single and multiple delays. In particular, we show that the delay Fokker-Planck equation derived earlier in the literature is a special case of the proposed Kramers-Moyal expansion. Applications for bond pricing and a self-inhibitory neuron model are discussed

Multiple solutions of steady-state Poisson–Nernst–Planck equations with steric effects

International Nuclear Information System (INIS)

Lin, Tai-Chia; Eisenberg, Bob

2015-01-01

Experiments measuring currents through single protein channels show unstable currents. Channels switch between ‘open’ or ‘closed’ states in a spontaneous stochastic process called gating. Currents are either (nearly) zero or at a definite level, characteristic of each type of protein, independent of time, once the channel is open. The steady state Poisson–Nernst–Planck equations with steric effects (PNP-steric equations) describe steady current through the open channel quite well, in a wide variety of conditions. Here we study the existence of multiple solutions of steady state PNP-steric equations to see if they themselves, without modification or augmentation, can describe two levels of current. We prove that there are two steady state solutions of PNP-steric equations for (a) three types of ion species (two types of cations and one type of anion) with a positive constant permanent charge, and (b) four types of ion species (two types of cations and their counter-ions) with a constant permanent charge but no sign condition. The excess currents (due to steric effects) associated with these two steady state solutions are derived and expressed as two distinct formulas. Our results indicate that PNP-steric equations may become a useful model to study spontaneous gating of ion channels. Spontaneous gating is thought to involve small structural changes in the channel protein that perhaps produce large changes in the profiles of free energy that determine ion flow. Gating is known to be modulated by external structures. Both can be included in future extensions of our present analysis. (paper)

The Ups and Downs of Hierarchy: the causes and consequences of hierarchy struggles and positional loss

NARCIS (Netherlands)

M.E. Schouten (Maartje)

2016-01-01

markdownabstractScholars have assumed that social hierarchies, the rank ordering of individuals with respect to a valued social dimension within a team, are stable over time. However, hierarchies change and the more changeable they are, the more likely they are to lead to conflicts and have other

Multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects

Directory of Open Access Journals (Sweden)

Tengfei Shen

2015-12-01

Full Text Available This paper deals with the multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects. By using critical point theory, a new result is obtained. An example is given to illustrate the main result.

Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?

Science.gov (United States)

Czégel, Dániel; Palla, Gergely

2015-12-10

Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or connections between the fundamental units of the studied system. Although a number of notable methods are already available, their vast majority is treating all directed acyclic graphs as already maximally hierarchical. Here we propose a hierarchy measure based on random walks on the network. The novelty of our approach is that directed trees corresponding to multi level pyramidal structures obtain higher hierarchy scores compared to directed chains and directed stars. Furthermore, in the thermodynamic limit the hierarchy measure of regular trees is converging to a well defined limit depending only on the branching number. When applied to real networks, our method is computationally very effective, as the result can be evaluated with arbitrary precision by subsequent multiplications of the transition matrix describing the random walk process. In addition, the tests on real world networks provided very intuitive results, e.g., the trophic levels obtained from our approach on a food web were highly consistent with former results from ecology.

Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?

Science.gov (United States)

Czégel, Dániel; Palla, Gergely

2015-01-01

Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or connections between the fundamental units of the studied system. Although a number of notable methods are already available, their vast majority is treating all directed acyclic graphs as already maximally hierarchical. Here we propose a hierarchy measure based on random walks on the network. The novelty of our approach is that directed trees corresponding to multi level pyramidal structures obtain higher hierarchy scores compared to directed chains and directed stars. Furthermore, in the thermodynamic limit the hierarchy measure of regular trees is converging to a well defined limit depending only on the branching number. When applied to real networks, our method is computationally very effective, as the result can be evaluated with arbitrary precision by subsequent multiplications of the transition matrix describing the random walk process. In addition, the tests on real world networks provided very intuitive results, e.g., the trophic levels obtained from our approach on a food web were highly consistent with former results from ecology. PMID:26657012

Hierarchy Bayesian model based services awareness of high-speed optical access networks

Science.gov (United States)

Bai, Hui-feng

2018-03-01

As the speed of optical access networks soars with ever increasing multiple services, the service-supporting ability of optical access networks suffers greatly from the shortage of service awareness. Aiming to solve this problem, a hierarchy Bayesian model based services awareness mechanism is proposed for high-speed optical access networks. This approach builds a so-called hierarchy Bayesian model, according to the structure of typical optical access networks. Moreover, the proposed scheme is able to conduct simple services awareness operation in each optical network unit (ONU) and to perform complex services awareness from the whole view of system in optical line terminal (OLT). Simulation results show that the proposed scheme is able to achieve better quality of services (QoS), in terms of packet loss rate and time delay.

Bidirectional control of social hierarchy by synaptic efficacy in medial prefrontal cortex.

Science.gov (United States)

Wang, Fei; Zhu, Jun; Zhu, Hong; Zhang, Qi; Lin, Zhanmin; Hu, Hailan

2011-11-04

Dominance hierarchy has a profound impact on animals' survival, health, and reproductive success, but its neural circuit mechanism is virtually unknown. We found that dominance ranking in mice is transitive, relatively stable, and highly correlates among multiple behavior measures. Recording from layer V pyramidal neurons of the medial prefrontal cortex (mPFC) showed higher strength of excitatory synaptic inputs in mice with higher ranking, as compared with their subordinate cage mates. Furthermore, molecular manipulations that resulted in an increase and decrease in the synaptic efficacy in dorsal mPFC neurons caused an upward and downward movement in the social rank, respectively. These results provide direct evidence for mPFC's involvement in social hierarchy and suggest that social rank is plastic and can be tuned by altering synaptic strength in mPFC pyramidal cells.

Neural basis of social status hierarchy across species.

Science.gov (United States)

Chiao, Joan Y

2010-12-01

Social status hierarchy is a ubiquitous principle of social organization across the animal kingdom. Recent findings in social neuroscience reveal distinct neural networks associated with the recognition and experience of social hierarchy in humans, as well as modulation of these networks by personality and culture. Additionally, allelic variation in the serotonin transporter gene is associated with prevalence of social hierarchy across species and cultures, suggesting the importance of the study of genetic factors underlying social hierarchy. Future studies are needed to determine how genetic and environmental factors shape neural systems involved in the production and maintenance of social hierarchy across ontogeny and phylogeny. Copyright © 2010 Elsevier Ltd. All rights reserved.

Modularization and epistatic hierarchy determine homeostatic actions of multiple blood pressure quantitative trait loci.

Science.gov (United States)

Chauvet, Cristina; Crespo, Kimberley; Ménard, Annie; Roy, Julie; Deng, Alan Y

2013-11-15

Hypertension, the most frequently diagnosed clinical condition world-wide, predisposes individuals to morbidity and mortality, yet its underlying pathological etiologies are poorly understood. So far, a large number of quantitative trait loci (QTLs) have been identified in both humans and animal models, but how they function together in determining overall blood pressure (BP) in physiological settings is unknown. Here, we systematically and comprehensively performed pair-wise comparisons of individual QTLs to create a global picture of their functionality in an inbred rat model. Rather than each of numerous QTLs contributing to infinitesimal BP increments, a modularized pattern arises: two epistatic 'blocks' constitute basic functional 'units' for nearly all QTLs, designated as epistatic module 1 (EM1) and EM2. This modularization dictates the magnitude and scope of BP effects. Any EM1 member can contribute to BP additively to that of EM2, but not to those of the same module. Members of each EM display epistatic hierarchy, which seems to reflect a related functional pathway. Rat homologues of 11 human BP QTLs belong to either EM1 or EM2. Unique insights emerge into the novel genetic mechanism and hierarchy determining BP in the Dahl salt-sensitive SS/Jr (DSS) rat model that implicate a portion of human QTLs. Elucidating the pathways underlying EM1 and EM2 may reveal the genetic regulation of BP.

A novel noncommutative KdV-type equation, its recursion operator, and solitons

Science.gov (United States)

Carillo, Sandra; Lo Schiavo, Mauro; Porten, Egmont; Schiebold, Cornelia

2018-04-01

A noncommutative KdV-type equation is introduced extending the Bäcklund chart in Carillo et al. [Symmetry Integrability Geom.: Methods Appl. 12, 087 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in Olver and Sokolov [Commun. Math. Phys. 193, 245 (1998), Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies, and an explicit solution class are derived.

Perceiving social inequity: when subordinate-group positioning on one dimension of social hierarchy enhances privilege recognition on another.

Science.gov (United States)

Rosette, Ashleigh Shelby; Tost, Leigh Plunkett

2013-08-01

Researchers have suggested that viewing social inequity as dominant-group privilege (rather than subordinate-group disadvantage) enhances dominant-group members' support for social policies aimed at lessening such inequity. However, because viewing inequity as dominant-group privilege can be damaging to dominant-group members' self-images, this perspective is frequently resisted. In the research reported here, we explored the circumstances that enhance the likelihood of dominant-group members' viewing inequity as privilege. Because social hierarchies have multiple vertical dimensions, individuals may have high status on one dimension but low status on another. We predicted that occupying a subordinate position on one dimension of social hierarchy could enhance perceptions of one's own privilege on a different dimension of hierarchy, but that this tendency would be diminished among individuals who felt they had achieved a particularly high level of success. Results from three studies that considered gender-based and race-based hierarchies in organizational settings supported our hypothesis.

Participatory hierarchies

DEFF Research Database (Denmark)

Kristiansen, Marianne; Bloch-Poulsen, Jørgen

2016-01-01

projects works in the interface between communication and organisation. Third, the methodological purpose is to show that handling of these participatory hierarchies ought to become a goal in OAR projects to be included along with producing practical and theoretical results. The article argues...

Method and System for Making OLAP Hierarchies Summarisable

DEFF Research Database (Denmark)

2002-01-01

Field of Invention: The present invention relates to computer databases, in particular to a method and system for transforming general OLAP hierarchies into summarizable hierarchies. This enables fast query response times for aggregation queries without excessive storage use even when the hierarc......Field of Invention: The present invention relates to computer databases, in particular to a method and system for transforming general OLAP hierarchies into summarizable hierarchies. This enables fast query response times for aggregation queries without excessive storage use even when...

Comments on gauge hierarchies

International Nuclear Information System (INIS)

Natale, A.A.

The problem of gauge hierarchy in a O(N) model is discussed. It is shown the existence of an upper bound for the hierarchy of order α- 1 / 2 , as proposed by Gildener. This same constraint appears when the breaking is made by the radiative corrections in a scheme elaborated by Weinberg. It is found that fine tunning or redefinition of coupling constants to improve hieracrchy, as proposed in several papers, cannot be done before the calculation of higher order contributions to the effective potential. (Author) [pt

The KP Hierarchy and Aspects of the Painlevé Property

Science.gov (United States)

Strampp, W.; Langer, C.

1990-12-01

We are concerned with the conjecture that the Painlevé property is a necessary condition for the integrability of nonlinear equations. Following a suggestion by lietratures (1) D. V. Chudnovsky, G. V. Chudnovsky and M. Tabor, Phys. Lett. 97A (1983), 268, and 2) A. K. Pogrebkov, Inverse Problems 5 (1989), L7), our investigations will be based on the Lax-pair which we use in Sato's sense (3) E. Date, M. Jimbo, M. Kashiwara and T. Miwa in Nonlinear Integrable Systems-Classical and Quantum Theory, ed. M. Jimbo and T. Miwa (World Scientific, Singapore, 1983), p. 39, 4) M. Jimbo and T. Miwa, Publ. RIMS, Kyoto Univ. 19 (1983), 943, 5) Y. Ohta, J. Satsuma, D. Takahashi and T. Tokihiro, Prog. Theor. Phys. Suppl. No. 94 (1988), 210). Leading orders, branch points and resonances are described for the Zakharov-Shabat equations of the KP-hierarchy. The symbolic manipulation system REDUCE, in particular its factorization algorithm for polynomials, is employed for finding the resonances. It is shown that the Painlevé structures of various nonlinear equations, which have been discussed a lot in the literature, follow from our results.

Lack of experience-based stratification in homing pigeon leadership hierarchies.

Science.gov (United States)

Watts, Isobel; Pettit, Benjamin; Nagy, Máté; de Perera, Theresa Burt; Biro, Dora

2016-01-01

In societies that make collective decisions through leadership, a fundamental question concerns the individual attributes that allow certain group members to assume leadership roles over others. Homing pigeons form transitive leadership hierarchies during flock flights, where flock members are ranked according to the average time differences with which they lead or follow others' movement. Here, we test systematically whether leadership ranks in navigational hierarchies are correlated with prior experience of a homing task. We constructed experimental flocks of pigeons with mixed navigational experience: half of the birds within each flock had been familiarized with a specific release site through multiple previous releases, while the other half had never been released from the same site. We measured the birds' hierarchical leadership ranks, then switched the same birds' roles at a second site to test whether the relative hierarchical positions of the birds in the two subsets would reverse in response to the reversal in levels of experience. We found that while across all releases the top hierarchical positions were occupied by experienced birds significantly more often than by inexperienced ones, the remaining experienced birds were not consistently clustered in the top half-in other words, the network did not become stratified. We discuss our results in light of the adaptive value of structuring leadership hierarchies according to 'merit' (here, navigational experience).

Probing Neutrino Mass Hierarchy with Supernova

International Nuclear Information System (INIS)

Chakraborty, Sovan

2013-01-01

The rise time of electron antineutrino lightcurve from a Galactic supernova (SN), observable at the IceCube Cherenkov detector, can provide signature of the neutrino mass hierarchy at “large” 1-3 leptonic mixing angle ϑ 13 . In the early accretion phase of the SN, the neutrino oscillations are nontrivial. Due to the matter suppression of collective effects at these early post bounce times, only the MSW resonances in the outer layers of the SN influence the neutrino flux. When the oscillations are taken into account, the signal in IceCube shows sufficiently fast rise time for the inverted mass hierarchy compared to the normal hierarchy. An investigation with an extensive set of stellar core-collapse simulations, provides both qualitative and quantitative robustness of these features. Thus opening another avenue to explore the neutrino mass hierarchy with the rise time of a supernova burst

Effective potential for spontaneously broken gauge theories and gauge hierarchies

International Nuclear Information System (INIS)

Hagiwara, T.; Ovrut, B.

1979-01-01

The Appelquist-Carazzone effective-field-theory method, where one uses effective light-field coupling constants dependent on the heavy-field sector, is explicitly shown to be valid for the discussion of the gauge-hierarchy problem in grand unified gauge models. Using the method of functionals we derive an expression for the one-loop approximation to the scalar-field effective potential for spontaneously broken theories in an arbitrary R/sub xi/ gauge. We argue that this potential generates, through its derivatives, valid zero-momentum, one-particle-irreducible vertices for any value of xi (not just the xi→infinity Landau gauge). The equation that the one-loop vacuum correction must satisfy is presented, and we solve this equation for a number of spontaneously broken theories including gauge theories with gauge groups U(1) and SO(3). We find that a one-loop vacuum shift in a massless, non-Goldstone direction occurs via the Coleman-Weinberg mechanism with an effective coupling constant dependent on the heavy-field sector

Hazardous Waste Landfill Siting using GIS Technique and Analytical Hierarchy Process

Directory of Open Access Journals (Sweden)

Ozeair Abessi

2010-07-01

Full Text Available Disposal of large amount of generated hazardous waste in power plants, has always received communities' and authori¬ties attentions. In this paper using site screening method and Analytical Hierarchy Process (AHP a sophisticated approach for siting hazardous waste landfill in large areas is presented. This approach demonstrates how the evaluation criteria such as physical, socio-economical, technical, environmental and their regulatory sub criteria can be introduced into an over layer technique to screen some limited appropriate zones in the area. Then, in order to find the optimal site amongst the primary screened site utilizing a Multiple Criteria Decision Making (MCDM method for hierarchy computations of the process is recommended. Using the introduced method an accurate siting procedure for environmental planning of the landfills in an area would be enabled. In the study this approach was utilized for disposal of hazardous wastes of Shahid Rajaee thermal power plant located in Qazvin province west central part of Iran. As a result of this study 10 suitable zones were screened in the area at first, then using analytical hierarchy process a site near the power plant were chosen as the optimal site for landfilling of the hazardous wastes in Qazvin province.

Light propagation in finite-sized photonic crystals: multiple scattering using an electric field integral equation

DEFF Research Database (Denmark)

Kristensen, Philip Trøst; Lodahl, Peter; Mørk, Jesper

2010-01-01

We present an accurate, stable, and efficient solution to the Lippmann–Schwinger equation for electromagnetic scattering in two dimensions. The method is well suited for multiple scattering problems and may be applied to problems with scatterers of arbitrary shape or non-homogenous background mat...

Two-reduction of the super-KP hierarchy

International Nuclear Information System (INIS)

McArthur, I.N.

1994-01-01

Recursion relations are established for the residues of fractional powers of a two-reduced super-KP operator making use of the Baker-Akhiezer function. These show the integrability of the two-reduced even (or bosonic) flows of the super-KP hierarchy. Similar recursion relations are also proven for the residues of operators associated with the odd (or fermionic) flows of the Mulase-Rabin super-KP hierarchy. Due to the presence of a spectral parameter and itts fermionic partner in the Baker-Akhiezer function, these recursion relations should be relevant to any attempt to prove or disprove a recent proposal that the integrable hierarchy underlying two-dimensional quantum supergravity is the Mulase-Rabin super-KP hierarchy. (orig.)

Singularities of Type-Q ABS Equations

Directory of Open Access Journals (Sweden)

James Atkinson

2011-07-01

Full Text Available The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS in their classification of discrete counterparts of KdV-type integrable partial differential equations. We ask what singularities are possible in the solutions of these equations, and examine the relationship between the singularities and the principal integrability feature of multidimensional consistency. These questions are considered in the global setting and therefore extend previous considerations of singularities which have been local. What emerges are some simple geometric criteria that determine the allowed singularities, and the interesting discovery that generically the presence of singularities leads to a breakdown in the global consistency of such systems despite their local consistency property. This failure to be globally consistent is quantified by introducing a natural notion of monodromy for isolated singularities.

Hierarchy from baryogenesis

International Nuclear Information System (INIS)

Senatore, Leonardo

2006-01-01

We study a recently proposed mechanism to solve the hierarchy problem in the context of the landscape, where the solution of the hierarchy problem is connected to the requirement of having baryons in our Universe via electroweak baryogenesis. The phase transition is triggered by the fermion condensation of a new gauge sector which becomes strong at a scale Λ determined by dimensional transmutation, and it is mediated to the standard model by a new singlet field. In a 'friendly' neighborhood of the landscape, where only the relevant operators are ''scanned'' among the vacua, baryogenesis is effective only if the Higgs mass m h is comparable to this low scale Λ, forcing m h ∼Λ, and solving the hierarchy problem. A new CP violating phase is needed coupling the new singlet and the Higgs field to new matter fields. We study the constraints on this model given by baryogenesis and by the electron electric dipole moment (EDM), and we briefly comment on gauge coupling unification and on dark matter relic abundance. We find that next generation experiments on the EDM will be sensitive to essentially the entire viable region of the parameter space, so that absence of a signal would effectively rule out the model

Bi-integrable and tri-integrable couplings of a soliton hierarchy associated with SO(4

Directory of Open Access Journals (Sweden)

Zhang Jian

2017-03-01

Full Text Available In our paper, the theory of bi-integrable and tri-integrable couplings is generalized to the discrete case. First, based on the six-dimensional real special orthogonal Lie algebra SO(4, we construct bi-integrable and tri-integrable couplings associated with SO(4 for a hierarchy from the enlarged matrix spectral problems and the enlarged zero curvature equations. Moreover, Hamiltonian structures of the obtained bi-integrable and tri-integrable couplings are constructed by the variational identities.

The extended bigraded Toda hierarchy

International Nuclear Information System (INIS)

Carlet, Guido

2006-01-01

We generalize the Toda lattice hierarchy by considering N + M dependent variables. We construct roots and logarithms of the Lax operator which are uniquely defined operators with coefficients that are ε-series of differential polynomials in the dependent variables, and we use them to provide a Lax pair definition of the extended bigraded Toda hierarchy, generalizing [4]. Using R-matrix theory we give the bi-Hamiltonian formulation of this hierarchy and we prove the existence of a tau function for its solutions. Finally we study the dispersionless limit and its connection with a class of Frobenius manifolds on the orbit space of the extended affine Weyl groups W-tilde (N) (A N+M-1 ) of the A series, defined by Dubrovin and Zhang (1998 Compos. Math. 111 167)

Existence and multiplicity of weak solutions for a class of degenerate nonlinear elliptic equations

Directory of Open Access Journals (Sweden)

Mihăilescu Mihai

2006-01-01

Full Text Available The goal of this paper is to study the existence and the multiplicity of non-trivial weak solutions for some degenerate nonlinear elliptic equations on the whole space . The solutions will be obtained in a subspace of the Sobolev space . The proofs rely essentially on the Mountain Pass theorem and on Ekeland's Variational principle.

Quantify entanglement by concurrence hierarchy

OpenAIRE

Fan, Heng; Matsumoto, Keiji; Imai, Hiroshi

2002-01-01

We define the concurrence hierarchy as d-1 independent invariants under local unitary transformations in d-level quantum system. The first one is the original concurrence defined by Wootters et al in 2-level quantum system and generalized to d-level pure quantum states case. We propose to use this concurrence hierarchy as measurement of entanglement. This measurement does not increase under local quantum operations and classical communication.

Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints

Science.gov (United States)

Manukure, Solomon

2018-04-01

We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.

Two New Reformulation Convexification Based Hierarchies for 0-1 MIPs

Directory of Open Access Journals (Sweden)

Hacene Ouzia

2015-01-01

Full Text Available First, we introduce two new reformulation convexification based hierarchies called RTC and RSC for which the rank d continuous relaxations are denoted by P^RTCd and P^RSCd, respectively. These two hierarchies are obtained using two different convexification schemes: term convexification in the case of the RTC hierarchy and standard convexification in the case of the RSC hierarchy. Secondly, we compare the strength of these two hierarchies. We will prove that (i the hierarchy RTC is equivalent to the RLT hierarchy of Sherali-Adams, (ii the hierarchy RTC dominates the hierarchy RSC, and (iii the hierarchy RSC is dominated by the Lift-and-Project hierarchy. Thirdly, for every rank d, we will prove that convTd∩Etd⊆P^RTCd⊆Td and convSd∩Esd⊆P^RSCd⊆Sd where the sets Td and Sd are convex, while Etd and Esd are two nonconvex sets with empty interior (all these sets depend on the convexification step. The first inclusions allow, in some cases, an explicit characterization (in the space of the original variables of the RLT relaxations. Finally, we will discuss weak version of both RTC and RSC hierarchies and we will emphasize some connections between them.

Existence and Multiplicity Results for Nonlinear Differential Equations Depending on a Parameter in Semipositone Case

Directory of Open Access Journals (Sweden)

Hailong Zhu

2012-01-01

Full Text Available The existence and multiplicity of solutions for second-order differential equations with a parameter are discussed in this paper. We are mainly concerned with the semipositone case. The analysis relies on the nonlinear alternative principle of Leray-Schauder and Krasnosel'skii's fixed point theorem in cones.

Special polynomials associated with rational solutions of some hierarchies

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.

2009-01-01

New special polynomials associated with rational solutions of the Painleve hierarchies are introduced. The Hirota relations for these special polynomials are found. Differential-difference hierarchies to find special polynomials are presented. These formulae allow us to search special polynomials associated with the hierarchies. It is shown that rational solutions of the Caudrey-Dodd-Gibbon, the Kaup-Kupershmidt and the modified hierarchy for these ones can be obtained using new special polynomials.

Nonholonomic deformation of generalized KdV-type equations

International Nuclear Information System (INIS)

Guha, Partha

2009-01-01

Karasu-Kalkani et al (2008 J. Math. Phys. 49 073516) recently derived a new sixth-order wave equation KdV6, which was shown by Kupershmidt (2008 Phys. Lett. 372A 2634) to have an infinite commuting hierarchy with a common infinite set of conserved densities. Incidentally, this equation was written for the first time by Calogero and is included in the book by Calogero and Degasperis (1982 Lecture Notes in Computer Science vol 144 (Amsterdam: North-Holland) p 516). In this paper, we give a geometric insight into the KdV6 equation. Using Kirillov's theory of coadjoint representation of the Virasoro algebra, we show how to obtain a large class of KdV6-type equations equivalent to the original equation. Using a semidirect product extension of the Virasoro algebra, we propose the nonholonomic deformation of the Ito equation. We also show that the Adler-Kostant-Symes scheme provides a geometrical method for constructing nonholonomic deformed integrable systems. Applying the Adler-Kostant-Symes scheme to loop algebra, we construct a new nonholonomic deformation of the coupled KdV equation.

Status hierarchy, attractiveness hierarchy and sex ratio : Three contextual factors explaining the status-aggression link among adolescents

NARCIS (Netherlands)

Zwaan, Michiel; Dijkstra, Jan; Veenstra, René

The moderating effects of three specific conditions (status hierarchy, attractiveness hierarchy and sex ratio) on the link between status (popularity) and physical and relational aggression were examined in a large sample of adolescent boys (N = 1,665) and girls (N = 1,637) (M age = 13.60). In line

When Do Types Induce the Same Belief Hierarchy?

Directory of Open Access Journals (Sweden)

Andrés Perea

2016-10-01

Full Text Available Type structures are a simple device to describe higher-order beliefs. However, how can we check whether two types generate the same belief hierarchy? This paper generalizes the concept of a type morphism and shows that one type structure is contained in another if and only if the former can be mapped into the other using a generalized type morphism. Hence, every generalized type morphism is a hierarchy morphism and vice versa. Importantly, generalized type morphisms do not make reference to belief hierarchies. We use our results to characterize the conditions under which types generate the same belief hierarchy.

A health hierarchy of effects model: a synthesis of advertising and health hierarchy conceptualizations.

Science.gov (United States)

Rouse, R A

1991-01-01

Work by both advertising and health researchers has independently yielded hierarchy of effects models which can be used to predict campaign success. Unfortunately, however, previous work has been criticized as "common sense" approaches which are more "assumed" than "proven." This analysis argues that much of the problem is due to the lack of precision often associated with over-simplified "uni-dimensional" models. Instead, this perspective synthesized a "two-dimensional" health hierarchy of effects model and outlines a pragmatic strategy for campaign measurement.

Improving Expression Power in Modeling OLAP Hierarchies

Science.gov (United States)

Malinowski, Elzbieta

Data warehouses and OLAP systems form an integral part of modern decision support systems. In order to exploit both systems to their full capabilities hierarchies must be clearly defined. Hierarchies are important in analytical applications, since they provide users with the possibility to represent data at different abstraction levels. However, even though there are different kinds of hierarchies in real-world applications and some are already implemented in commercial tools, there is still a lack of a well-accepted conceptual model that allows decision-making users express their analysis needs. In this paper, we show how the conceptual multidimensional model can be used to facilitate the representation of complex hierarchies in comparison to their representation in the relational model and commercial OLAP tool, using as an example Microsoft Analysis Services.

Symmetries of supersymmetric integrable hierarchies of KP type

International Nuclear Information System (INIS)

Nissimov, E.; Pacheva, S.

2002-01-01

This article is devoted to the systematic study of additional (non-isospectral) symmetries of constrained (reduced) supersymmetric integrable hierarchies of KP type--the so-called SKP (R;M B ,M F ) models. The latter are supersymmetric extensions of ordinary constrained KP hierarchies which contain as special cases basic integrable systems such as (m)KdV, AKNS, Fordy-Kulish, Yajima-Oikawa, etc. As a first main result it is shown that any SKP (R;M B ,M F ) hierarchy possesses two different mutually (anti-)commuting types of superloop superalgebra additional symmetries corresponding to the positive- and negative-grade parts of certain superloop superalgebras. The second main result is the systematic construction of the full algebra of additional Virasoro symmetries of SKP (R;M B ,M F ) hierarchies, which requires nontrivial modifications of the Virasoro flows known from the general case of unconstrained Manin-Radul super-KP hierarchies (the latter flows do not define symmetries for constrained SKP (R;M B ,M F ) hierarchies). As a third main result we provide systematic construction of the supersymmetric analogs of multi-component (matrix) KP hierarchies and show that the latter contain, among others, the supersymmetric version of the Davey-Stewartson system. Finally, we present an explicit derivation of the general Darboux-Baecklund solutions for the SKP (R;M B ,M F ) super-tau functions (supersymmetric 'soliton'-like solutions) which preserve the additional (non-isospectral) symmetries

Existence and multiplicity of weak solutions for a class of degenerate nonlinear elliptic equations

Directory of Open Access Journals (Sweden)

Mihai Mihăilescu

2006-02-01

Full Text Available The goal of this paper is to study the existence and the multiplicity of non-trivial weak solutions for some degenerate nonlinear elliptic equations on the whole space RN. The solutions will be obtained in a subspace of the Sobolev space W1/p(RN. The proofs rely essentially on the Mountain Pass theorem and on Ekeland's Variational principle.

Status Hierarchy, Attractiveness Hierarchy and Sex Ratio: Three Contextual Factors Explaining the Status-Aggression Link among Adolescents

Science.gov (United States)

Zwaan, Michiel; Dijkstra, Jan Kornelis; Veenstra, Rene

2013-01-01

The moderating effects of three specific conditions (status hierarchy, attractiveness hierarchy and sex ratio) on the link between status (popularity) and physical and relational aggression were examined in a large sample of adolescent boys ("N" = 1,665) and girls ("N" = 1,637) ("M" age = 13.60). In line with the…

On the multiple zeros of a real analytic function with applications to the averaging theory of differential equations

Science.gov (United States)

García, Isaac A.; Llibre, Jaume; Maza, Susanna

2018-06-01

In this work we consider real analytic functions , where , Ω is a bounded open subset of , is an interval containing the origin, are parameters, and ε is a small parameter. We study the branching of the zero-set of at multiple points when the parameter ε varies. We apply the obtained results to improve the classical averaging theory for computing T-periodic solutions of λ-families of analytic T-periodic ordinary differential equations defined on , using the displacement functions defined by these equations. We call the coefficients in the Taylor expansion of in powers of ε the averaged functions. The main contribution consists in analyzing the role that have the multiple zeros of the first non-zero averaged function. The outcome is that these multiple zeros can be of two different classes depending on whether the zeros belong or not to the analytic set defined by the real variety associated to the ideal generated by the averaged functions in the Noetheriang ring of all the real analytic functions at . We bound the maximum number of branches of isolated zeros that can bifurcate from each multiple zero z 0. Sometimes these bounds depend on the cardinalities of minimal bases of the former ideal. Several examples illustrate our results and they are compared with the classical theory, branching theory and also under the light of singularity theory of smooth maps. The examples range from polynomial vector fields to Abel differential equations and perturbed linear centers.

Modelling Dominance Hierarchies Under Winner and Loser Effects.

Science.gov (United States)

Kura, Klodeta; Broom, Mark; Kandler, Anne

2015-06-01

Animals that live in groups commonly form themselves into dominance hierarchies which are used to allocate important resources such as access to mating opportunities and food. In this paper, we develop a model of dominance hierarchy formation based upon the concept of winner and loser effects using a simulation-based model and consider the linearity of our hierarchy using existing and new statistical measures. Two models are analysed: when each individual in a group does not know the real ability of their opponents to win a fight and when they can estimate their opponents' ability every time they fight. This estimation may be accurate or fall within an error bound. For both models, we investigate if we can achieve hierarchy linearity, and if so, when it is established. We are particularly interested in the question of how many fights are necessary to establish a dominance hierarchy.

Should researchers use single indicators, best indicators, or multiple indicators in structural equation models?

Directory of Open Access Journals (Sweden)

Hayduk Leslie A

2012-10-01

Full Text Available Abstract Background Structural equation modeling developed as a statistical melding of path analysis and factor analysis that obscured a fundamental tension between a factor preference for multiple indicators and path modeling’s openness to fewer indicators. Discussion Multiple indicators hamper theory by unnecessarily restricting the number of modeled latents. Using the few best indicators – possibly even the single best indicator of each latent – encourages development of theoretically sophisticated models. Additional latent variables permit stronger statistical control of potential confounders, and encourage detailed investigation of mediating causal mechanisms. Summary We recommend the use of the few best indicators. One or two indicators are often sufficient, but three indicators may occasionally be helpful. More than three indicators are rarely warranted because additional redundant indicators provide less research benefit than single indicators of additional latent variables. Scales created from multiple indicators can introduce additional problems, and are prone to being less desirable than either single or multiple indicators.

Principles of synchronous digital hierarchy

CERN Document Server

Jain, Rajesh Kumar

2012-01-01

The book presents the current standards of digital multiplexing, called synchronous digital hierarchy, including analog multiplexing technologies. It is aimed at telecommunication professionals who want to develop an understanding of digital multiplexing and synchronous digital hierarchy in particular and the functioning of practical telecommunication systems in general. The text includes all relevant fundamentals and provides a handy reference for problem solving or defining operations and maintenance strategies. The author covers digital conversion and TDM principles, line coding and digital

Autonomous management of a recursive area hierarchy for large scale wireless sensor networks using multiple parents

Energy Technology Data Exchange (ETDEWEB)

Cree, Johnathan Vee [Washington State Univ., Pullman, WA (United States); Delgado-Frias, Jose [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

2016-03-01

Large scale wireless sensor networks have been proposed for applications ranging from anomaly detection in an environment to vehicle tracking. Many of these applications require the networks to be distributed across a large geographic area while supporting three to five year network lifetimes. In order to support these requirements large scale wireless sensor networks of duty-cycled devices need a method of efficient and effective autonomous configuration/maintenance. This method should gracefully handle the synchronization tasks duty-cycled networks. Further, an effective configuration solution needs to recognize that in-network data aggregation and analysis presents significant benefits to wireless sensor network and should configure the network in a way such that said higher level functions benefit from the logically imposed structure. NOA, the proposed configuration and maintenance protocol, provides a multi-parent hierarchical logical structure for the network that reduces the synchronization workload. It also provides higher level functions with significant inherent benefits such as but not limited to: removing network divisions that are created by single-parent hierarchies, guarantees for when data will be compared in the hierarchy, and redundancies for communication as well as in-network data aggregation/analysis/storage.

Solution of the gauge hierarchy problem

International Nuclear Information System (INIS)

Dimopoulos, S.; Georgi, H.

1982-01-01

We propose a novel solution to the gauge hierarchy problem in theories with softly broken supersymmetry. Quantum effects can resuscitate classically sick theories, producing the large scale from the small supersymmetry breaking scale. We use this mechanism to construct realistic SU(6) and SU(5) GUTs which do not suffer from gauge hierarchy or fine tuning problems. (orig.)

A quark interpretation of the combinatorial hierarchy

International Nuclear Information System (INIS)

Enqvist, Kari.

1979-01-01

We propose a physical interpretation of the second level of the combinatorial hierarchy in terms of three quarks, three antiquarks and the vacuum. This interpretation allows us to introduce a new quantum number, which measures electromagnetic mass splitting of the quarks. We extend our argument by analogue to baryons, and find some SU(3) and some new mass formulas for baryons. The generalization of our approach to other hierarchy levels is discussed. We present also an empirical mass formula for baryons, which seems to be loosely connected with the combinatorial hierarchy. (author)

Complete integrability of the difference evolution equations

International Nuclear Information System (INIS)

Gerdjikov, V.S.; Ivanov, M.I.; Kulish, P.P.

1980-01-01

The class of exactly solvable nonlinear difference evolution equations (DEE) related to the discrete analog of the one-dimensional Dirac problem L is studied. For this starting from L we construct a special linear non-local operator Λ and obtain the expansions of w and σ 3 deltaw over its eigenfunctions, w being the potential in L. This allows us to obtain compact expressions for the integrals of motion and to prove that these DEE are completely integrable Hamiltonian systems. Moreover, it is shown that there exists a hierarchy of Hamiltonian structures, generated by Λ, and the action-angle variables are explicity calculated. As particular cases the difference analog of the non-linear Schroedinger equation and the modified Korteweg-de-Vries equation are considered. The quantization of these Hamiltonian system through the use of the quantum inverse scattering method is briefly discussed [ru

Fokker-Planck-Rosenbluth-type equations for self-gravitating systems in the 1PN approximation

International Nuclear Information System (INIS)

Ramos-Caro, Javier; Gonzalez, Guillermo A

2008-01-01

We present two formulations of Fokker-Planck-Rosenbluth-type (FPR) equations for many-particle self-gravitating systems, with first-order relativistic corrections in the post-Newtonian approach (1PN). The first starts from a covariant Fokker-Planck equation for a simple gas, introduced recently by Chacon-Acosta and Kremer (2007 Phys. Rev. E 76 021201). The second derivation is based on the establishment of an 1PN-BBGKY hierarchy, developed systematically from the 1PN microscopic law of force and using the Klimontovich-Dupree (KD) method. We close the hierarchy by the introduction of a two-point correlation function that describes adequately the relaxation process. This picture reveals an aspect that is not considered in the first formulation: the contribution of ternary correlation patterns to the diffusion coefficients, as a consequence of the nature of 1PN interaction. Both formulations can be considered as a generalization of the equation derived by Rezania and Sobouti (2000 Astron. Astrophys. 354 1110), to stellar systems where the relativistic effects of gravitation play a significant role

W-algebra symmetries of generalised Drinfel'd-Sokolov hierarchies

International Nuclear Information System (INIS)

Spence, B.

1992-01-01

Using the zero curvature formulation, it is shown that W-algebra transformations are symmetries of corresponding generalised Drinfel'd-Sokolov hierarchies. This result is illustrated with the examples of the KdV and Boussinesque hierarchies, and the hierarchy associated to the Polyakov-Bershadsky W-algebra. (orig.)

Nonlinear dynamics in the relativistic field equation

International Nuclear Information System (INIS)

Tanaka, Yosuke; Mizuno, Yuji; Kado, Tatsuhiko; Zhao, Hua-An

2007-01-01

We have investigated relativistic equations and chaotic behaviors of the gravitational field with the use of general relativity and nonlinear dynamics. The space component of the Friedmann equation shows chaotic behaviors in case of the inflation (h=G-bar /G>0) and open (ζ=-1) universe. In other cases (h= 0 andx-bar 0 ) and the parameters (a, b, c and d); (2) the self-similarity of solutions in the x-x-bar plane and the x-ρ plane. We carried out the numerical calculations with the use of the microsoft EXCEL. The self-similarity and the hierarchy structure of the universe have been also discussed on the basis of E-infinity theory

Visual Hierarchy and Mind Motion in Advertising Design

Directory of Open Access Journals (Sweden)

Doaa Farouk Badawy Eldesouky

2013-06-01

Full Text Available Visual hierarchy is a significant concept in the field of advertising, a field that is dominated by effective communication, visual recognition and motion. Designers of advertisements have always been trying to organize the visual hierarchy throughout their advertising designs to aid the eye to recognize information in the desired order, to achieve the ultimate goals of clear perception and effectively delivering the advertising messages. However many assumptions and questions usually rise on how to create effective hierarchy throughout advertising designs and lead the eye and mind of the viewer in the most favorable way. This paper attempts to study visual hierarchy and mind motion in advertising designs and why it is important to develop visual paths when designing an advertisement. It explores the theory behind it, and how the very principles can be used to put these concepts into practice. The paper demonstrates some advertising samples applying visual hierarchy and mind motion in a representation of applying the basics and discussing the results.

Visual Hierarchy and Mind Motion in Advertising Design

Directory of Open Access Journals (Sweden)

Doaa Farouk Badawy Eldesouky

2013-06-01

Full Text Available Visual hierarchy is a significant concept in the field of advertising, a field that is dominated by effective communication, visual recognition and motion. Designers of advertisements have always been trying to organize the visual hierarchy throughout their advertising designs to aid the eye to recognize information in the desired order, to achieve the ultimate goals of clear perception and effectively delivering the advertising messages. However many assumptions and questions usually rise on how to create effective hierarchy throughout advertising designs and lead the eye and mind of the viewer in the most favorable way. This paper attempts to study visual hierarchy and mind motion in advertising designs and why it is important to develop visual paths when designing an advertisement. It explores the theory behind it, and how the very principles can be used to put these concepts into practice. The paper demonstrates some advertising samples applying visual hierarchy and mind motion in a representation of applying the basics and discussing the results. 

Recommended HSE-7 documents hierarchy

International Nuclear Information System (INIS)

Klein, R.B.; Jennrich, E.A.; Lund, D.M.; Danna, J.G.; Davis, K.D.; Rutz, A.C.

1990-01-01

This report recommends a hierarchy of waste management documents at Los Alamos National Laboratory (LANL or ''Laboratory''). The hierarchy addresses documents that are required to plan, implement, and document waste management programs at Los Alamos. These documents will enable the waste management group and the six sections contained within that group to satisfy requirements that are imposed upon them by the US Department of Energy (DOE), DOE Albuquerque Operations, US Environmental Protection Agency, various State of New Mexico agencies, and Laboratory management

Exploring maintenance policy selection using the Analytic Hierarchy Process; An application for naval ships

International Nuclear Information System (INIS)

Goossens, Adriaan J.M.; Basten, Rob J.I.

2015-01-01

In this paper we investigate maintenance policy selection (MPS) through the use of the Analytic Hierarchy Process (AHP). A maintenance policy is a policy that dictates which parameter triggers a maintenance action. In practice, selecting the right maintenance policy appears to be a difficult decision. We investigate MPS for naval ships, but our results have wider applicability. For our study we cooperate with the owner and operator of the ships, as well as with a shipbuilder and an original equipment manufacturer of naval ships. We apply a structured five step approach to obtain the relevant criteria that may make one policy preferable over another. The criteria are drawn from both literature and a series of interviews at several navy related companies and are structured into a hierarchy of criteria usable with the AHP. Additionally, we organize three workshops at the three different companies to test the AHP-based MPS approach in practice. We conclude that the AHP is well suited for maintenance policy selection in this broad setting, and that it provides a structured and detailed approach for MPS. Adding to that, it facilitates discussions during and after the sessions, creating a better understanding of the policy selection process. - Highlights: • We use the Analytic Hierarchy Process (AHP) for maintenance policy selection (MPS). • Using both interviews and case studies from the literature, we construct a hierarchy. • In sessions at 3 companies, we find that 1 hierarchy can be used for multiple assets. • The AHP creates a better understanding of the maintenance policy selection process. • Our work is on naval ships, but our approach and findings have wider applicability

A model of Yukawa hierarchies

International Nuclear Information System (INIS)

Elwood, J.K.; Irges, N.; Ramond, P.

1997-05-01

The authors present a model for the observed hierarchies among the Yukawa couplings of the standard model in the context of an effective low energy theory with an anomalous U(1) symmetry. This symmetry, a generic feature of superstring compactification, is a remnant of the Green-Schwarz anomaly cancellation mechanism. The gauge group is that of the standard model, augmented by X, the anomalous U(1), and two family-dependent phase symmetries Y (1) and Y (2) . The correct hierarchies are reproduced only when sin 2 θ w = 3/8 at the cut-off. To cancel anomalies, right-handed neutrinos and other standard model singlets must be introduced. Independently of the charges of the right-handed neutrinos, this model produces the same neutrino mixing matrix and an inverted hierarchy of neutrino masses. The heaviest is the electron neutrino with a mass ∼ 1 meV, and mixing of the order of λ c 3 with each of the other two neutrinos

Baecklund transformation for supersymmetric self-dual theories for semisimple gauge groups and a hierarchy of A1 solutions

International Nuclear Information System (INIS)

Devchand, C.

1994-01-01

We present a Baecklund transformation (a discrete symmetry transformation) for the self-duality equations for supersymmetric gauge theories in N-extended super-Minkowski space M 4vertical stroke 4N for an arbitrary semisimple gauge group. For the case of an A 1 gauge algebra we integrate the transformation starting with a given solution and iterating the process we construct a hierarchy of explicit solutions. (orig.)

High Agreement was Obtained Across Scores from Multiple Equated Scales for Social Anxiety Disorder using Item Response Theory.

Science.gov (United States)

Sunderland, Matthew; Batterham, Philip; Calear, Alison; Carragher, Natacha; Baillie, Andrew; Slade, Tim

2018-04-10

There is no standardized approach to the measurement of social anxiety. Researchers and clinicians are faced with numerous self-report scales with varying strengths, weaknesses, and psychometric properties. The lack of standardization makes it difficult to compare scores across populations that utilise different scales. Item response theory offers one solution to this problem via equating different scales using an anchor scale to set a standardized metric. This study is the first to equate several scales for social anxiety disorder. Data from two samples (n=3,175 and n=1,052), recruited from the Australian community using online advertisements, were utilised to equate a network of 11 self-report social anxiety scales via a fixed parameter item calibration method. Comparisons between actual and equated scores for most of the scales indicted a high level of agreement with mean differences <0.10 (equivalent to a mean difference of less than one point on the standardized metric). This study demonstrates that scores from multiple scales that measure social anxiety can be converted to a common scale. Re-scoring observed scores to a common scale provides opportunities to combine research from multiple studies and ultimately better assess social anxiety in treatment and research settings. Copyright © 2018. Published by Elsevier Inc.

A new multi-component hierarchy and its integrable expanding model

International Nuclear Information System (INIS)

Dong Huanhe; Liang Xiangqian

2008-01-01

A set of multi-component matrix Lie algebra is constructed, it follows that a type of new loop algebra is presented and multi-component integrable hierarchy is obtained. Furthermore, the loop algebra is expanded into a larger one and a type of integrable coupling system is worked out. As reduction of the hierarchy, some well-known hierarchy such as DNLS, KN, CLL hierarchy are established

Dark energy and the hierarchy problem

International Nuclear Information System (INIS)

Chen, Pisin

2007-01-01

The well-known hierarchy between the Planck scale (∼10 19 GeV) and the TeV scale, namely a ratio of ∼10 16 between the two, is coincidentally repeated in a inverted order between the TeV scale and the dark energy scale at ∼10 -3 eV implied by the observations. We argue that this is not a numerical coincidence. The same brane-world setups to address the first hierarchy problem may also in principle address this second hierarchy issue. Specifically, we consider supersymmetry in the bulk and its breaking on the brane and resort to the Casimir energy induced by the bulk graviton-gravitino mass-shift on the brane as the dark energy. For the ADD model we found that our notion is sensible only if the number of extra dimension n=2. We extend our study to the Randall-Sundrum model. Invoking the chirality-flip on the boundaries for SUSY-breaking, the zero-mode gravitino contribution to the Casimir energy does give rise to the double hierarchy. Unfortunately since the higher Kaluza-Klein modes acquire relative mass-shifts at the TeV level, the zero-mode contribution to Casimir energy is overshadowed

Numerical solution of plasma fluid equations using locally refined grids

International Nuclear Information System (INIS)

Colella, P.

1997-01-01

This paper describes a numerical method for the solution of plasma fluid equations on block-structured, locally refined grids. The plasma under consideration is typical of those used for the processing of semiconductors. The governing equations consist of a drift-diffusion model of the electrons and an isothermal model of the ions coupled by Poisson's equation. A discretization of the equations is given for a uniform spatial grid, and a time-split integration scheme is developed. The algorithm is then extended to accommodate locally refined grids. This extension involves the advancement of the discrete system on a hierarchy of levels, each of which represents a degree of refinement, together with synchronization steps to ensure consistency across levels. A brief discussion of a software implementation is followed by a presentation of numerical results

Why and when hierarchy impacts team effectiveness: A meta-analytic integration.

Science.gov (United States)

Greer, Lindred L; de Jong, Bart A; Schouten, Maartje E; Dannals, Jennifer E

2018-06-01

Hierarchy has the potential to both benefit and harm team effectiveness. In this article, we meta-analytically investigate different explanations for why and when hierarchy helps or hurts team effectiveness, drawing on results from 54 prior studies (N = 13,914 teams). Our findings show that, on net, hierarchy negatively impacts team effectiveness (performance: ρ = -.08; viability: ρ = -.11), and that this effect is mediated by increased conflict-enabling states. Additionally, we show that the negative relationship between hierarchy and team performance is exacerbated by aspects of the team structure (i.e., membership instability, skill differentiation) and the hierarchy itself (i.e., mutability), which make hierarchical teams prone to conflict. The predictions regarding the positive effect of hierarchy on team performance as mediated by coordination-enabling processes, and the moderating roles of several aspects of team tasks (i.e., interdependence, complexity) and the hierarchy (i.e., form) were not supported, with the exception that task ambiguity enhanced the positive effects of hierarchy. Given that our findings largely support dysfunctional views on hierarchy, future research is needed to understand when and why hierarchy may be more likely to live up to its purported functional benefits. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Stress amplifies memory for social hierarchy.

Science.gov (United States)

Cordero, María Isabel; Sandi, Carmen

2007-11-01

Individuals differ in their social status and societies in the extent of social status differences among their members. There is great interest in understanding the key factors that contribute to the establishment of social dominance structures. Given that stress can affect behavior and cognition, we hypothesized that, given equal opportunities to become either dominant or submissive, stress experienced by one of the individuals during their first encounter would determine the long-term establishment of a social hierarchy by acting as a two-stage rocket: (1) by influencing the rank achieved after a social encounter and (2) by facilitating and/or promoting a long-term memory for the specific hierarchy. Using a novel model for the assessment of long-term dominance hierarchies in rats, we present here the first evidence supporting such hypothesis. In control conditions, the social rank established through a first interaction and food competition test between two male rats is not maintained when animals are confronted 1 week later. However, if one of the rats is stressed just before their first encounter, the dominance hierarchy developed on day 1 is still clearly observed 1 week later, with the stressed animal becoming submissive (i.e., looser in competition tests) in both social interactions. Our findings also allow us to propose that stress potentiates a hierarchy-linked recognition memory between "specific" individuals through mechanisms that involve de novo protein synthesis. These results implicate stress among the key mechanisms contributing to create social imbalance and highlight memory mechanisms as key mediators of stress-induced long-term establishment of social rank.

Stress amplifies memory for social hierarchy

Directory of Open Access Journals (Sweden)

María I Cordero

2007-10-01

Full Text Available Individuals differ in their social status and societies in the extent of social status differences among their members. There is great interest in understanding the key factors that contribute to the establishment of social dominance structures. Given that stress can affect behavior and cognition, we hypothesized that, given equal opportunities to become either dominant or submissive, stress experienced by one of the individuals during their first encounter would determine the long-term establishment of a social hierarchy by acting as a two-stage rocket: (1 by influencing the rank achieved after a social encounter and (2 by facilitating and/or promoting a long-term memory for the specific hierarchy. Using a novel model for the assessment of long-term dominance hierarchies in rats, we present here the first evidence supporting such hypothesis. In control conditions, the social rank established through a first interaction and food competition test between two male rats is not maintained when animals are confronted 1 week later. However, if one of the rats is stressed just before their first encounter, the dominance hierarchy developed on day 1 is still clearly observed 1 week later, with the stressed animal becoming submissive (i.e., looser in competition tests in both social interactions. Our findings also allow us to propose that stress potentiates a hierarchy-linked recognition memory between “specific” individuals through mechanisms that involve de novo protein synthesis. These results implicate stress among the key mechanisms contributing to create social imbalance and highlight memory mechanisms as key mediators of stress-induced long-term establishment of social rank.

A Suggested Modification to Maslow's Need Hierarchy

Science.gov (United States)

Groves, David L.; And Others

1975-01-01

Since its development, Maslow's need hierarchy has been criticized and applauded. This investigation was undertaken to explore a modification of the upper levels of the need hierarchy based upon the application of power, competition, and achievement to self, as well as the concept of "other directed." (Author)

Gauge hierarchy, decoupling, and heavy particle effects

International Nuclear Information System (INIS)

Yao, York-Peng

1981-01-01

This chapter examines the problems of a large gauge hierarchy and decoupling in theories with spontaneously broken symmetry. Attempts to show, with regard to all orders in the loop expansion, that: once a proper identification is made of the light particles and of the heavy particles at the tree level, then such a division will be maintained order by order in the loop expansion without the necessity of fine tuning; there is a local renormalizable effective Lagrangian, composed of light fields only, which can be used to reproduce all the one light particle irreducible Green's functions; and a set of renormalization group equations can be written down, wherein one stays in the lower energy region to correlate the two sets of parameters in the full and the effective light theories. The appendix gives an algebraic rearrangement method which can be efficiently used to calculate the muon effects on the electron anomalous magnetic moment

Multi-component Wronskian solution to the Kadomtsev-Petviashvili equation

Science.gov (United States)

Xu, Tao; Sun, Fu-Wei; Zhang, Yi; Li, Juan

2014-01-01

It is known that the Kadomtsev-Petviashvili (KP) equation can be decomposed into the first two members of the coupled Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy by the binary non-linearization of Lax pairs. In this paper, we construct the N-th iterated Darboux transformation (DT) for the second- and third-order m-coupled AKNS systems. By using together the N-th iterated DT and Cramer's rule, we find that the KPII equation has the unreduced multi-component Wronskian solution and the KPI equation admits a reduced multi-component Wronskian solution. In particular, based on the unreduced and reduced two-component Wronskians, we obtain two families of fully-resonant line-soliton solutions which contain arbitrary numbers of asymptotic solitons as y → ∓∞ to the KPII equation, and the ordinary N-soliton solution to the KPI equation. In addition, we find that the KPI line solitons propagating in parallel can exhibit the bound state at the moment of collision.

The Evolutionary Origins of Hierarchy.

Science.gov (United States)

Mengistu, Henok; Huizinga, Joost; Mouret, Jean-Baptiste; Clune, Jeff

2016-06-01

Hierarchical organization-the recursive composition of sub-modules-is ubiquitous in biological networks, including neural, metabolic, ecological, and genetic regulatory networks, and in human-made systems, such as large organizations and the Internet. To date, most research on hierarchy in networks has been limited to quantifying this property. However, an open, important question in evolutionary biology is why hierarchical organization evolves in the first place. It has recently been shown that modularity evolves because of the presence of a cost for network connections. Here we investigate whether such connection costs also tend to cause a hierarchical organization of such modules. In computational simulations, we find that networks without a connection cost do not evolve to be hierarchical, even when the task has a hierarchical structure. However, with a connection cost, networks evolve to be both modular and hierarchical, and these networks exhibit higher overall performance and evolvability (i.e. faster adaptation to new environments). Additional analyses confirm that hierarchy independently improves adaptability after controlling for modularity. Overall, our results suggest that the same force-the cost of connections-promotes the evolution of both hierarchy and modularity, and that these properties are important drivers of network performance and adaptability. In addition to shedding light on the emergence of hierarchy across the many domains in which it appears, these findings will also accelerate future research into evolving more complex, intelligent computational brains in the fields of artificial intelligence and robotics.

The Evolutionary Origins of Hierarchy

Science.gov (United States)

Huizinga, Joost; Clune, Jeff

2016-01-01

Hierarchical organization—the recursive composition of sub-modules—is ubiquitous in biological networks, including neural, metabolic, ecological, and genetic regulatory networks, and in human-made systems, such as large organizations and the Internet. To date, most research on hierarchy in networks has been limited to quantifying this property. However, an open, important question in evolutionary biology is why hierarchical organization evolves in the first place. It has recently been shown that modularity evolves because of the presence of a cost for network connections. Here we investigate whether such connection costs also tend to cause a hierarchical organization of such modules. In computational simulations, we find that networks without a connection cost do not evolve to be hierarchical, even when the task has a hierarchical structure. However, with a connection cost, networks evolve to be both modular and hierarchical, and these networks exhibit higher overall performance and evolvability (i.e. faster adaptation to new environments). Additional analyses confirm that hierarchy independently improves adaptability after controlling for modularity. Overall, our results suggest that the same force–the cost of connections–promotes the evolution of both hierarchy and modularity, and that these properties are important drivers of network performance and adaptability. In addition to shedding light on the emergence of hierarchy across the many domains in which it appears, these findings will also accelerate future research into evolving more complex, intelligent computational brains in the fields of artificial intelligence and robotics. PMID:27280881

The Evolutionary Origins of Hierarchy.

Directory of Open Access Journals (Sweden)

Henok Mengistu

2016-06-01

Full Text Available Hierarchical organization-the recursive composition of sub-modules-is ubiquitous in biological networks, including neural, metabolic, ecological, and genetic regulatory networks, and in human-made systems, such as large organizations and the Internet. To date, most research on hierarchy in networks has been limited to quantifying this property. However, an open, important question in evolutionary biology is why hierarchical organization evolves in the first place. It has recently been shown that modularity evolves because of the presence of a cost for network connections. Here we investigate whether such connection costs also tend to cause a hierarchical organization of such modules. In computational simulations, we find that networks without a connection cost do not evolve to be hierarchical, even when the task has a hierarchical structure. However, with a connection cost, networks evolve to be both modular and hierarchical, and these networks exhibit higher overall performance and evolvability (i.e. faster adaptation to new environments. Additional analyses confirm that hierarchy independently improves adaptability after controlling for modularity. Overall, our results suggest that the same force-the cost of connections-promotes the evolution of both hierarchy and modularity, and that these properties are important drivers of network performance and adaptability. In addition to shedding light on the emergence of hierarchy across the many domains in which it appears, these findings will also accelerate future research into evolving more complex, intelligent computational brains in the fields of artificial intelligence and robotics.

Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method

International Nuclear Information System (INIS)

Fan Engui

2002-01-01

A new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system. Compared with most of the existing tanh methods, the Jacobi elliptic function method or other sophisticated methods, the proposed method not only gives new and more general solutions, but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters. The solutions obtained in this paper include (a) kink-shaped and bell-shaped soliton solutions, (b) rational solutions, (c) triangular periodic solutions and (d) Jacobi and Weierstrass doubly periodic wave solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. The efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper, KdV-MKdV, Ito's fifth MKdV, Hirota, Nizhnik-Novikov-Veselov, Broer-Kaup, generalized coupled Hirota-Satsuma, coupled Schroedinger-KdV, (2+1)-dimensional dispersive long wave, (2+1)-dimensional Davey-Stewartson equations. In addition, as an illustrative sample, the properties of the soliton solutions and Jacobi doubly periodic solutions for the Hirota equation are shown by some figures. The links among our proposed method, the tanh method, extended tanh method and the Jacobi elliptic function method are clarified generally. (author)

On the Hierarchy of Neutrino Masses

International Nuclear Information System (INIS)

Jezabek, M.; Urban, P.

2002-01-01

We present a model of neutrino masses combining the seesaw mechanism and strong Dirac mass hierarchy and at the same time exhibiting a significantly reduced hierarchy at the level of active neutrino masses. The heavy Majorana masses are assumed to be degenerate. The suppression of the hierarchy is due to a symmetric and unitary operator R whose role is discussed. The model gives realistic mixing and mass spectrum. The mixing of atmospheric neutrinos is attributed to the charged lepton sector whereas the mixing of solar neutrinos is due to the neutrino sector. Small U e3 is a consequence of the model. The masses of the active neutrinos are given by μ 3 ≅ √(Δm 2 O ) and μ 1 /μ 2 = ≅ tan 2 (θ O ). (author)

The Generalized Wronskian Solution to a Negative KdV-mKdV Equation

International Nuclear Information System (INIS)

Liu Yu-Qing; Chen Deng-Yuan; Hu Chao

2012-01-01

A negative KdV-mKdV hierarchy is presented through the KdV-mKdV operator. The generalized Wronskian solution to the negative KdV-mKdV equation is obtained. Some soliton-like solutions and a complexiton solution are presented explicitly as examples. (general)

Program information architecture/document hierarchy

International Nuclear Information System (INIS)

Woods, T.W.

1991-09-01

The Nuclear Waste Management System (NWMS) Management Systems Improvement Strategy (MSIS) (DOE 1990) requires that the information within the computer program and information management system be ordered into a precedence hierarchy for consistency. Therefore, the US Department of Energy (DOE). Office of Civilian Radioactive Waste Management (OCRWM) requested Westinghouse Hanford Company to develop a plan for NWMS program information which the MSIS calls a document hierarchy. This report provides the results of that effort and describes the management system as a ''program information architecture.'' 3 refs., 3 figs

Prediction of the neutrons subcritical multiplication using the diffusion hybrid equation with external neutron sources

Energy Technology Data Exchange (ETDEWEB)

Costa da Silva, Adilson; Carvalho da Silva, Fernando [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, 21941-914, Rio de Janeiro (Brazil); Senra Martinez, Aquilino, E-mail: aquilino@lmp.ufrj.br [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, 21941-914, Rio de Janeiro (Brazil)

2011-07-15

Highlights: > We proposed a new neutron diffusion hybrid equation with external neutron source. > A coarse mesh finite difference method for the adjoint flux and reactivity calculation was developed. > 1/M curve to predict the criticality condition is used. - Abstract: We used the neutron diffusion hybrid equation, in cartesian geometry with external neutron sources to predict the subcritical multiplication of neutrons in a pressurized water reactor, using a 1/M curve to predict the criticality condition. A Coarse Mesh Finite Difference Method was developed for the adjoint flux calculation and to obtain the reactivity values of the reactor. The results obtained were compared with benchmark values in order to validate the methodology presented in this paper.

Prediction of the neutrons subcritical multiplication using the diffusion hybrid equation with external neutron sources

International Nuclear Information System (INIS)

Costa da Silva, Adilson; Carvalho da Silva, Fernando; Senra Martinez, Aquilino

2011-01-01

Highlights: → We proposed a new neutron diffusion hybrid equation with external neutron source. → A coarse mesh finite difference method for the adjoint flux and reactivity calculation was developed. → 1/M curve to predict the criticality condition is used. - Abstract: We used the neutron diffusion hybrid equation, in cartesian geometry with external neutron sources to predict the subcritical multiplication of neutrons in a pressurized water reactor, using a 1/M curve to predict the criticality condition. A Coarse Mesh Finite Difference Method was developed for the adjoint flux calculation and to obtain the reactivity values of the reactor. The results obtained were compared with benchmark values in order to validate the methodology presented in this paper.

Riemann-Liouville integrals of fractional order and extended KP hierarchy

International Nuclear Information System (INIS)

Kamata, Masaru; Nakamula, Atsushi

2002-01-01

An attempt to formulate the extensions of the KP hierarchy by introducing fractional-order pseudo-differential operators is given. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered here. More general hierarchies constructed by the 1/Nth-order pseudo-differential operators, their integrability and the reduction procedure are also investigated. In addition to finding the new extensions of the KP hierarchy, a brief introduction to the Riemann-Liouville integral is provided to yield a candidate for the fractional-order pseudo-differential operators

Formal language theory: refining the Chomsky hierarchy

Science.gov (United States)

Jäger, Gerhard; Rogers, James

2012-01-01

The first part of this article gives a brief overview of the four levels of the Chomsky hierarchy, with a special emphasis on context-free and regular languages. It then recapitulates the arguments why neither regular nor context-free grammar is sufficiently expressive to capture all phenomena in the natural language syntax. In the second part, two refinements of the Chomsky hierarchy are reviewed, which are both relevant to the extant research in cognitive science: the mildly context-sensitive languages (which are located between context-free and context-sensitive languages), and the sub-regular hierarchy (which distinguishes several levels of complexity within the class of regular languages). PMID:22688632

Formal language theory: refining the Chomsky hierarchy.

Science.gov (United States)

Jäger, Gerhard; Rogers, James

2012-07-19

The first part of this article gives a brief overview of the four levels of the Chomsky hierarchy, with a special emphasis on context-free and regular languages. It then recapitulates the arguments why neither regular nor context-free grammar is sufficiently expressive to capture all phenomena in the natural language syntax. In the second part, two refinements of the Chomsky hierarchy are reviewed, which are both relevant to the extant research in cognitive science: the mildly context-sensitive languages (which are located between context-free and context-sensitive languages), and the sub-regular hierarchy (which distinguishes several levels of complexity within the class of regular languages).

Multiple periodic-soliton solutions of the (3+1)-dimensional generalised shallow water equation

Science.gov (United States)

Li, Ye-Zhou; Liu, Jian-Guo

2018-06-01

Based on the extended variable-coefficient homogeneous balance method and two new ansätz functions, we construct auto-Bäcklund transformation and multiple periodic-soliton solutions of (3 {+} 1)-dimensional generalised shallow water equations. Completely new periodic-soliton solutions including periodic cross-kink wave, periodic two-solitary wave and breather type of two-solitary wave are obtained. In addition, cross-kink three-soliton and cross-kink four-soliton solutions are derived. Furthermore, propagation characteristics and interactions of the obtained solutions are discussed and illustrated in figures.

SUSY-hierarchy of one-dimensional reflectionless potentials

International Nuclear Information System (INIS)

Maydanyuk, Sergei P.

2005-01-01

A class of one-dimensional reflectionless potentials is studied. It is found that all possible types of the reflectionless potentials can be combined into one SUSY-hierarchy with a constant potential. An approach for determination of a general form of the reflectionless potential on the basis of construction of such a hierarchy by the recurrent method is proposed. A general integral form of interdependence between superpotentials with neighboring numbers of this hierarchy, opening a possibility to find new reflectionless potentials, is found and has a simple analytical view. It is supposed that any possible type of the reflectionless potential can be expressed through finite number of elementary functions (unlike some presentations of the reflectionless potentials, which are constructed on the basis of soliton solutions or are shape invariant in one or many steps with involving scaling of parameters, and are expressed through series). An analysis of absolute transparency existence for the potential which has the inverse power dependence on space coordinate (and here tunneling is possible), i.e., which has the form V (x) = ± α/ vertical bar x-x 0 vertical bar n (where α and x 0 are constants, n is natural number), is fulfilled. It is shown that such a potential can be reflectionless at n = 2 only. A SUSY-hierarchy of the inverse power reflectionless potentials is constructed. Isospectral expansions of this hierarchy are analyzed

Deltons, peakons and other traveling-wave solutions of a Camassa-Holm hierarchy

International Nuclear Information System (INIS)

Peng Xiaochun; Dai Huihui

2009-01-01

In this letter, we study an integrable Camassa-Holm hierarchy whose high-frequency limit is the Camassa-Holm equation. Phase plane analysis is employed to investigate bounded traveling wave solutions. An important feature is that there exists a singular line on the phase plane. By considering the properties of the equilibrium points and the relative position of the singular line, we find that there are in total three types of phase planes. Those paths in phase planes which represented bounded solutions are discussed one-by-one. Besides solitary, peaked and periodic waves, the equations are shown to admit a new type of traveling waves, which concentrate all their energy in one point, and we name them deltons as they can be expressed as some constant multiplied by a delta function. There also exists a type of traveling waves we name periodic deltons, which concentrate their energy in periodic points. The explicit expressions for them and all the other traveling waves are given.

Peculiar symmetry structure of some known discrete nonautonomous equations

International Nuclear Information System (INIS)

Garifullin, R N; Habibullin, I T; Yamilov, R I

2015-01-01

We study the generalized symmetry structure of three known discrete nonautonomous equations. One of them is the semidiscrete dressing chain of Shabat. Two others are completely discrete equations defined on the square lattice. The first one is a discrete analogue of the dressing chain introduced by Levi and Yamilov. The second one is a nonautonomous generalization of the potential discrete KdV equation or, in other words, the H1 equation of the well-known Adler−Bobenko−Suris list. We demonstrate that these equations have generalized symmetries in both directions if and only if their coefficients, depending on the discrete variables, are periodic. The order of the simplest generalized symmetry in at least one direction depends on the period and may be arbitrarily high. We substantiate this picture by some theorems in the case of small periods. In case of an arbitrarily large period, we show that it is possible to construct two hierarchies of generalized symmetries and conservation laws. The same picture should take place in case of any nonautonomous equation of the Adler−Bobenko−Suris list. (paper)

A hierarchy of Ramsey-like cardinals

OpenAIRE

Holy, Peter; Schlicht, Philipp

2017-01-01

We introduce a hierarchy of large cardinals between weakly compact and measurable cardinals, that is closely related to the Ramsey-like cardinals introduced by Victoria Gitman, and is based on certain infinite filter games, however also has a range of equivalent characterizations in terms of elementary embeddings. The aim of this paper is to locate the Ramsey-like cardinals studied by Gitman, and other well-known large cardinal notions, in this hierarchy.

Hierarchy generation in compactified supersymmetric models

International Nuclear Information System (INIS)

Ross, G.G.

1988-01-01

The problem of generating a large hierarchy in compactified supersymmetric models is re-examined. It is shown how, even for the class of models for which Str M 2 is non-vanishing, a combination of non-perturbative effects and radiative corrections may lead to an exponentially large hierarchy. A corollary is that the couplings of the effective field theory in the visible sector should be small, i.e., perturbation theory should be applicable. (orig.)

The Toda lattice hierarchy and deformation of conformal field theories

International Nuclear Information System (INIS)

Fukuma, M.

1990-01-01

In this paper, the authors point out that the Toda lattice hierarchy known in soliton theory is relevant for the description of the deformations of conformal field theories while the KP hierarchy describes unperturbed conformal theories. It is shown that the holomorphic parts of the conserved currents in the perturbed system (the Toda lattice hierarchy) coincide with the conserved currents in the KP hierarchy and can be written in terms of the W-algebraic currents. Furthermore, their anti-holomorphic counterparts are obtained

Objective Bayesian analysis of neutrino masses and hierarchy

Science.gov (United States)

Heavens, Alan F.; Sellentin, Elena

2018-04-01

Given the precision of current neutrino data, priors still impact noticeably the constraints on neutrino masses and their hierarchy. To avoid our understanding of neutrinos being driven by prior assumptions, we construct a prior that is mathematically minimally informative. Using the constructed uninformative prior, we find that the normal hierarchy is favoured but with inconclusive posterior odds of 5.1:1. Better data is hence needed before the neutrino masses and their hierarchy can be well constrained. We find that the next decade of cosmological data should provide conclusive evidence if the normal hierarchy with negligible minimum mass is correct, and if the uncertainty in the sum of neutrino masses drops below 0.025 eV. On the other hand, if neutrinos obey the inverted hierarchy, achieving strong evidence will be difficult with the same uncertainties. Our uninformative prior was constructed from principles of the Objective Bayesian approach. The prior is called a reference prior and is minimally informative in the specific sense that the information gain after collection of data is maximised. The prior is computed for the combination of neutrino oscillation data and cosmological data and still applies if the data improve.

Quark mass hierarchies from the universal seesaw mechanism

International Nuclear Information System (INIS)

Davidson, A.; Michel, L.; Sage, M.L.; Wali, K.C.

1994-01-01

The paper is an extension of the previous work based on the idea of a universal seesaw mechanism to explain the hierarchies in the fermion mass spectrum. A model is proposed within the framework of left-right symmetry with a minimal Higgs system and an axial U(1) symmetry imposed to distinguish the generations. Previous work was confined, for mathematical simplifications, to the case of nonsingular mass matrices. In the present paper, singular matrices are considered. A systematic perturbative technique is developed to display the mass eigenvalues in terms of the vacuum expectation values of the assumed Higgs multiplets. The model successfully correlates the mass hierarchies among the quarks to the assumed hierarchies in the vacuum expectation values without appealing to a hierarchy in the Yukawa-type fermion--Higgs-boson couplings. By considering a general Higgs potential appropriate to the model, we study its minimization and prove that there exists an open subdomain in the parameter space where the orbit of the lowest minima of the potential corresponds to the kind of hierarchy in the vacuum expectation values needed for the success of the model

Hermitian versus anti-hermitian one-matrix models and their hierarchies

International Nuclear Information System (INIS)

Hollowood, T.; Miramontes, L.; Pasquinucci, A.; Nappi, C.

1992-01-01

Building on a recent work of C. Crnkovic, M. Douglas and G. Moore, a study of multi-critical multi-cut one-matrix models and their associated sl(2, C) integrable hierarchies, is further pursued. The double-scaling limits of hermitian matrix models with different scaling ansaetze, lead to the KdV hierarchy, to the modified KdV hierarchy and part of the non-linear Schroedinger hierarchy. Instead, the anti-hermitian matrix model, in the 2-arc sector, results in the Zakharov-Shabat hierarchy, which contains both KdV and mKdV as reductions. For all the hierarchies it is found that the Virasoro constraints act on the associated τ-functions. Whereas it is known that the ZS and KdV models lead to the Virasoro constraints of an sl(2, C) vacuum, we find that the mKdV model leads to the Virasoro constraints of a highest-weight state with arbitrary conformal dimension. (orig.)

Neutrino mass hierarchy determination for θ13 = 0

International Nuclear Information System (INIS)

Gandhi, Raj; Ghoshal, Pomita; Goswami, Srubabati; Sankar, S. Uma

2010-01-01

We examine the possibility of determining the neutrino mass hierarchy in the limit θ 13 = 0 using atmospheric neutrinos as the source. In this limit, θ 13 driven matter effects are absent so independent measurements of Δ 31 and Δ 32 can, in principle, lead to hierarchy determination. Since their difference is Δ 21 , one needs an experimental arrangement where Δ 21 L/E > or approx. 1 can be achieved. This can be satisfied by atmospheric neutrinos which have a large range of L and E. Still, we find that hierarchy determination in the θ 13 = 0 limit with atmospheric neutrinos is not a realistic possibility, even in conjunction with a beam experiment like T2K or NOνA. We discuss why, and also reiterate the general conditions for hierarchy determination if θ 13 = 0.

On the origins of hierarchy in complex networks

Science.gov (United States)

Corominas-Murtra, Bernat; Goñi, Joaquín; Solé, Ricard V.; Rodríguez-Caso, Carlos

2013-01-01

Hierarchy seems to pervade complexity in both living and artificial systems. Despite its relevance, no general theory that captures all features of hierarchy and its origins has been proposed yet. Here we present a formal approach resulting from the convergence of theoretical morphology and network theory that allows constructing a 3D morphospace of hierarchies and hence comparing the hierarchical organization of ecological, cellular, technological, and social networks. Embedded within large voids in the morphospace of all possible hierarchies, four major groups are identified. Two of them match the expected from random networks with similar connectivity, thus suggesting that nonadaptive factors are at work. Ecological and gene networks define the other two, indicating that their topological order is the result of functional constraints. These results are consistent with an exploration of the morphospace, using in silico evolved networks. PMID:23898177

Cohesion and Hierarchy in Physically Abusive Families

Directory of Open Access Journals (Sweden)

Clarissa De Antoni

2009-06-01

Full Text Available This paper investigates cohesion (emotional bonding and hierarchy (powerstructure in families with abuse against their children. Twenty low-incomefamilies participated. Father, mother and child’s perspective of family relations(cohesion and hierarchy were evaluated by the Family System Test(FAST. The relationship between father-child, mother-child, couple, andamong siblings were evaluated at typical and conflictive situations. Resultsshow a significance regarding to cohesion in typical and conflictive situationfor father-child and mother-child dyads in all perspectives (by father, mother,and child. There is no significant differences regarding to hierarchy. Theseresults suggest that the families see the intrafamilial violence as a constant,since they cannot differentiate between both situations.

The Hierarchy of Segment Reports

Directory of Open Access Journals (Sweden)

Danilo Dorović

2015-05-01

Full Text Available The article presents an attempt to find the connection between reports created for managers responsible for different business segments. With this purpose, the hierarchy of the business reporting segments is proposed. This can lead to better understanding of the expenses under common responsibility of more than one manager since these expenses should be in more than one report. The structure of cost defined per business segment hierarchy with the aim of new, unusual but relevant cost structure for management can be established. Both could potentially bring new information benefits for management in the context of profit reporting.

The sl (2 n|2 n) (1) super-Toda lattices and the heavenly equations as continuum limit

International Nuclear Information System (INIS)

Kuznetsova, Zhanna; Popowicz, Ziemowit; Toppan, Francesco.

2005-04-01

The n → ∞ continuum limit of super-Toda models associated with the affine sl (2 n|2 n) (1) (super)algebra series produces (2 + 1)-dimensional integrable equations in the S 1 versus R 2 spacetimes. The equations of motion of the (super)Toda hierarchies depend not only on the chosen (super)algebras but also on the specific presentation of their Cartan matrices. Four distinct series of integrable hierarchies in relation with symmetric-versus-antisymmetric, null-versus-non null presentations of the corresponding Cartan matrices are investigated. In the continuum limit we derive four classes of integrable equations of heavenly type, generalizing the results previously obtained in the literature. The systems are manifestly N = 1 supersymmetric and, for specific choices of the Cartan matrix preserving the complex structure, admit a hidden N = 2 supersymmetry. The coset reduction of the (super)-heavenly equation to the I versus R (2) (S 1 /Z 2 ) versus R 2 spacetime (with I a line segment) is illustrated. Finally, integrable N = 2,4 super symmetrically extended models in (1 + 1) dimensions are constructed through dimensional reduction of the previous systems. (author)

Multiple periodic solutions to a class of second-order nonlinear mixed-type functional differential equations

Directory of Open Access Journals (Sweden)

Xiao-Bao Shu

2005-01-01

Full Text Available By means of variational structure and Z2 group index theory, we obtain multiple periodic solutions to a class of second-order mixed-type differential equations x''(t−τ+f(t,x(t,x(t−τ,x(t−2τ=0 and x''(t−τ+λ(tf1(t,x(t,x(t−τ,x(t−2τ=x(t−τ.

Boolean Operations, Joins, and the Extended Low Hierarchy

OpenAIRE

Hemaspaandra, Lane A.; Jiang, Zhigen; Rothe, Joerg; Watanabe, Osamu

1999-01-01

We prove that the join of two sets may actually fall into a lower level of the extended low hierarchy than either of the sets. In particular, there exist sets that are not in the second level of the extended low hierarchy, EL_2, yet their join is in EL_2. That is, in terms of extended lowness, the join operator can lower complexity. Since in a strong intuitive sense the join does not lower complexity, our result suggests that the extended low hierarchy is unnatural as a complexity measure. We...

A general equation to obtain multiple cut-off scores on a test from multinomial logistic regression.

Science.gov (United States)

Bersabé, Rosa; Rivas, Teresa

2010-05-01

The authors derive a general equation to compute multiple cut-offs on a total test score in order to classify individuals into more than two ordinal categories. The equation is derived from the multinomial logistic regression (MLR) model, which is an extension of the binary logistic regression (BLR) model to accommodate polytomous outcome variables. From this analytical procedure, cut-off scores are established at the test score (the predictor variable) at which an individual is as likely to be in category j as in category j+1 of an ordinal outcome variable. The application of the complete procedure is illustrated by an example with data from an actual study on eating disorders. In this example, two cut-off scores on the Eating Attitudes Test (EAT-26) scores are obtained in order to classify individuals into three ordinal categories: asymptomatic, symptomatic and eating disorder. Diagnoses were made from the responses to a self-report (Q-EDD) that operationalises DSM-IV criteria for eating disorders. Alternatives to the MLR model to set multiple cut-off scores are discussed.

Self-organizing dominance hierarchies in a wild primate population

OpenAIRE

Franz, Mathias; McLean, Emily; Tung, Jenny; Altmann, Jeanne; Alberts, Susan C.

2015-01-01

Linear dominance hierarchies, which are common in social animals, can profoundly influence access to limited resources, reproductive opportunities and health. In spite of their importance, the mechanisms that govern the dynamics of such hierarchies remain unclear. Two hypotheses explain how linear hierarchies might emerge and change over time. The ‘prior attributes hypothesis’ posits that individual differences in fighting ability directly determine dominance ranks. By contrast, the ‘social d...

A unified expressing model of the AKNS hierarchy and the KN hierarchy, as well as its integrable coupling system

International Nuclear Information System (INIS)

Guo Fukui; Zhang Yufeng

2004-01-01

A new subalgebra of loop algebra A-tilde 1 is first constructed. Then a new Lax pair is presented, whose compatibility gives rise to a new Liouville integrable system(called a major result), possessing bi-Hamiltonian structures. It is remarkable that two symplectic operators obtained in this paper are directly constructed in terms of the recurrence relations. As reduction cases of the new integrable system obtained, the famous AKNS hierarchy and the KN hierarchy are obtained, respectively. Second, we prove a conjugate operator of a recurrence operator is a hereditary symmetry. Finally, we construct a high dimension loop algebra G-bar to obtain an integrable coupling system of the major result by making use of Tu scheme. In addition, we find the major result obtained is a unified expressing integrable model of both the AKNS and KN hierarchies, of course, we may also regard the major result as an expanding integrable model of the AKNS and KN hierarchies. Thus, we succeed to find an example of expanding integrable models being Liouville integrable

Selection of power market structure using the analytic hierarchy process

International Nuclear Information System (INIS)

Subhes Bhattacharyya; Prasanta Kumar Dey

2003-01-01

Selection of a power market structure from the available alternatives is an important activity within an overall power sector reform program. The evaluation criteria for selection are both subjective as well as objective in nature and the selection of alternatives is characterised by their conflicting nature. This study demonstrates a methodology for power market structure selection using the analytic hierarchy process, a multiple attribute decision- making technique, to model the selection methodology with the active participation of relevant stakeholders in a workshop environment. The methodology is applied to a hypothetical case of a State Electricity Board reform in India. (author)

Eye Movement Evidence for Hierarchy Effects on Memory Representation of Discourses.

Directory of Open Access Journals (Sweden)

Yingying Wu

Full Text Available In this study, we applied the text-change paradigm to investigate whether and how discourse hierarchy affected the memory representation of a discourse. Three kinds of three-sentence discourses were constructed. In the hierarchy-high condition and the hierarchy-low condition, the three sentences of the discourses were hierarchically organized and the last sentence of each discourse was located at the high level and the low level of the discourse hierarchy, respectively. In the linear condition, the three sentences of the discourses were linearly organized. Critical words were always located at the last sentence of the discourses. These discourses were successively presented twice and the critical words were changed to semantically related words in the second presentation. The results showed that during the early processing stage, the critical words were read for longer times when they were changed in the hierarchy-high and the linear conditions, but not in the hierarchy-low condition. During the late processing stage, the changed-critical words were again found to induce longer reading times only when they were in the hierarchy-high condition. These results suggest that words in a discourse have better memory representation when they are located at the higher rather than at the lower level of the discourse hierarchy. Global discourse hierarchy is established as an important factor in constructing the mental representation of a discourse.

Eye Movement Evidence for Hierarchy Effects on Memory Representation of Discourses.

Science.gov (United States)

Wu, Yingying; Yang, Xiaohong; Yang, Yufang

2016-01-01

In this study, we applied the text-change paradigm to investigate whether and how discourse hierarchy affected the memory representation of a discourse. Three kinds of three-sentence discourses were constructed. In the hierarchy-high condition and the hierarchy-low condition, the three sentences of the discourses were hierarchically organized and the last sentence of each discourse was located at the high level and the low level of the discourse hierarchy, respectively. In the linear condition, the three sentences of the discourses were linearly organized. Critical words were always located at the last sentence of the discourses. These discourses were successively presented twice and the critical words were changed to semantically related words in the second presentation. The results showed that during the early processing stage, the critical words were read for longer times when they were changed in the hierarchy-high and the linear conditions, but not in the hierarchy-low condition. During the late processing stage, the changed-critical words were again found to induce longer reading times only when they were in the hierarchy-high condition. These results suggest that words in a discourse have better memory representation when they are located at the higher rather than at the lower level of the discourse hierarchy. Global discourse hierarchy is established as an important factor in constructing the mental representation of a discourse.

Hierarchy and social status in Budongo chimpanzees.

Science.gov (United States)

Newton-Fisher, Nicholas E

2004-04-01

The status hierarchy is fundamental in the lives of male chimpanzees. This study describes the dominance interactions and social status among adult male chimpanzees of the Sonso community in the Budongo Forest Reserve, Uganda, during the period that they were first studied (1994 and 1995). Social dominance is typically measured using the behaviour of either the subordinate or the dominant individual, but a relationship is dependent on the behaviour of both parties and this study explicitly used both subordinate and dominant behaviours to investigate the status hierarchy. Among adult males of the Sonso community, agonistic interactions occurred at a low rate and pant-grunts were rare, but males could be ranked into separate hierarchies of agonistic dominance and pant-grunting (labelled 'respect') using ratios of behaviour performed/behaviour received. These hierarchies were combined to form a single hierarchy of social status that divided the males among five distinct status levels. The highest status level was held by an alliance between two males who replaced the previous alpha male during the first part of the study. Neither male in this alliance partnership pant-grunted to the other, although the reason for cooperative behaviour was unclear. Although the nominally beta male was treated as such by other adult males, he achieved surprisingly little mating success. Budongo Forest chimpanzees do not warrant the sometimes-expressed view that they are non-aggressive and peaceable and the broad pattern of their status interactions matches with that seen in other chimpanzee populations.

Plasticity within stem cell hierarchies in mammalian epithelia.

Science.gov (United States)

Tetteh, Paul W; Farin, Henner F; Clevers, Hans

2015-02-01

Tissue homeostasis and regeneration are fueled by resident stem cells that have the capacity to self-renew, and to generate all the differentiated cell types that characterize a particular tissue. Classical models of such cellular hierarchies propose that commitment and differentiation occur unidirectionally, with the arrows 'pointing away' from the stem cell. Recent studies, all based on genetic lineage tracing, describe various strategies employed by epithelial stem cell hierarchies to replace damaged or lost cells. While transdifferentiation from one tissue type into another ('metaplasia') appears to be generally forbidden in nonpathological contexts, plasticity within an individual tissue stem cell hierarchy may be much more common than previously appreciated. In this review, we discuss recent examples of such plasticity in selected mammalian epithelia, highlighting the different modes of regeneration and their implications for our understanding of cellular hierarchy and tissue self-renewal. Copyright © 2014 Elsevier Ltd. All rights reserved.

Ansatz for dynamical hierarchies

DEFF Research Database (Denmark)

Rasmussen, S.; Baas, N.A.; Mayer, B.

2001-01-01

Complex, robust functionalities can be generated naturally in at least two ways: by the assembly of structures and by the evolution of structures. This work is concerned with spontaneous formation of structures. We define the notion of dynamical hierarchies in natural systems and show...... the importance of this particular kind of organization for living systems. We then define a framework that enables us to formulate, investigate, and manipulate such dynamical hierarchies. This framework allows us to simultaneously investigate different levels of description together with them interrelationship...... three. Formulating this system as a simple two-dimensional molecular dynamics (MD) lattice gas allows us within one dynamical system to demonstrate the successive emergence of two higher levels (three levels all together) of robust structures with associated properties. Second, we demonstrate how...

The Impact of Formal Hierarchies on Enterprise Social Networking Behavior

DEFF Research Database (Denmark)

Behrendt, Sebastian; Klier, Julia; Klier, Mathias

2015-01-01

With more and more companies using enterprise social networks (ESN) for employee communication and collaboration, the influence of ESN on organizational hierarchies has been subject of countless discussions in practice-oriented media and first academic studies. Conversely, the question whether...... and how formal organizational hierarchies influence ESN usage behavior has not yet been addressed. Drawing on a rich data set comprising 2.5 years of relationship building via direct messages, confirmed contact requests, and group messages, we are able to show that formal hierarchies have an important...... impact on social networking behavior. By applying means of social network analysis and supported by statements from interviews, we illustrate how deeply formal hierarchy impacts the three examined types of relationships. Our results motivate academics to further study the interrelation between hierarchy...

Hierarchy among Automata on Linear Orderings

OpenAIRE

Bruyère , Véronique; Carton , Olivier

2005-01-01

In a preceding paper, automata and rational expressions have been introduced for words indexed by linear orderings, together with a Kleene-like theorem. We here pursue this work by proposing a hierarchy among the rational sets. Each class of the hierarchy is defined by a subset of the rational operations that can be used. We then characterize any class by an appropriate class of automata, leading to a Kleene theorem inside the class. A characterization by particular classes of orderings is al...

Shrinking population and the urban hierarchy

OpenAIRE

Kim, Ho Yeon

2012-01-01

This paper examines whether population shrinkage leads to changes in the urban hierarchy in terms of relative sizes of cities and their functions onomic geography. We work backwards in a racetrack economy with eight cities in a long-run equilibrium. Initial distribution of population is chosen to satisfy both the rank-size rule and central place hierarchy. We have a short-run equilibrium in which firms choose prices and consumers choose consumption taking the number of workers in each region ...

Inequality Matters : Classroom Status Hierarchy and Adolescents' Bullying

NARCIS (Netherlands)

Garandeau, Claire F.; Lee, Ihno A.; Salmivalli, Christina

2014-01-01

The natural emergence of status hierarchies in adolescent peer groups has long been assumed to help prevent future intragroup aggression. However, clear evidence of this beneficial influence is lacking. In fact, few studies have examined between-group differences in the degree of status hierarchy

Reappraising the functional implications of the primate visual anatomical hierarchy.

Science.gov (United States)

Hegdé, Jay; Felleman, Daniel J

2007-10-01

The primate visual system has been shown to be organized into an anatomical hierarchy by the application of a few principled criteria. It has been widely assumed that cortical visual processing is also hierarchical, with the anatomical hierarchy providing a defined substrate for clear levels of hierarchical function. A large body of empirical evidence seemed to support this assumption, including the general observations that functional properties of visual neurons grow progressively more complex at progressively higher levels of the anatomical hierarchy. However, a growing body of evidence, including recent direct experimental comparisons of functional properties at two or more levels of the anatomical hierarchy, indicates that visual processing neither is hierarchical nor parallels the anatomical hierarchy. Recent results also indicate that some of the pathways of visual information flow are not hierarchical, so that the anatomical hierarchy cannot be taken as a strict flowchart of visual information either. Thus, while the sustaining strength of the notion of hierarchical processing may be that it is rather simple, its fatal flaw is that it is overly simplistic.

Wronskian type solutions for the vector k-constrained KP hierarchy

International Nuclear Information System (INIS)

Zhang Youjin.

1995-07-01

Motivated by a relation of the 1-constrained Kadomtsev-Petviashvili (KP) hierarchy with the 2 component KP hierarchy, the tau-conditions of the vector k-constrained KP hierarchy are constructed by using an analogue of the Baker-Akhiezer (m + 1)-point function. These tau functions are expressed in terms of Wronskian type determinants. (author). 20 refs

〈査読付論文〉The Necessity to Advance Disclosing Fair Value by the Hierarchy: Evidence from Literature Review about Fair Value Hierarchy Information

OpenAIRE

ZHANG, JIAO

2016-01-01

[Abstract]This paper aims to discuss the necessity to advance disclosing fair value by hierarchy in Japan by reviewing the literature about fair value hierarchy information in the U.S.　In Japan, ASBJ published the Exposure Draft "Accounting Standards on Fair Value Measurement and Disclosure" in 2010 which specifies that the fair value should be reported by hierarchy.　However, it has not published as formal standard until March 2016.　Furthermore, some commenters suggested that the hierarchy an...

Three semi-direct sum Lie algebras and three discrete integrable couplings associated with the modified K dV lattice equation

International Nuclear Information System (INIS)

Yu Zhang; Zhang Yufeng

2009-01-01

Three semi-direct sum Lie algebras are constructed, which is an efficient and new way to obtain discrete integrable couplings. As its applications, three discrete integrable couplings associated with the modified K dV lattice equation are worked out. The approach can be used to produce other discrete integrable couplings of the discrete hierarchies of soliton equations.

Gender-specific hierarchy in nuage localization of PIWI-interacting RNA factors in Drosophila

Directory of Open Access Journals (Sweden)

Mikiko C Siomi

2011-08-01

Full Text Available PIWI-interacting RNAs (piRNAs are germline-specific small non-coding RNAs that form piRNA-induced silencing complexes (piRISCs by associating with PIWI proteins, a subclade of the Argonaute proteins predominantly expressed in the germline. piRISCs protect the integrity of the germline genome from invasive transposable DNA elements by silencing them. Multiple piRNA biogenesis factors have been identified in Drosophila. The majority of piRNA factors are localized in the nuage, electron-dense non-membranous cytoplasmic structures located in the perinuclear regions of germ cells. Thus, piRNA biogenesis is thought to occur in the nuage in germ cells. Immunofluorescence analyses of ovaries from piRNA factor mutants have revealed a localization hierarchy of piRNA factors in female nuage. However, whether this hierarchy is female-specific or can also be applied in male gonads remains undetermined. Here, we show by immunostaining of both ovaries and testes from piRNA factor mutants that the molecular hierarchy of piRNA factors shows gender-specificity, especially for Krimper (Krimp, a Tudor-domain containing protein of unknown function(s: Krimp is dispensable for PIWI protein Aubergine (Aub nuage localization in ovaries but Krimp and Aub require each other for their proper nuage localization in testes. This suggests that the functional requirement of Krimp in piRNA biogenesis may be different in male and female gonads.

The Development of Hierarchy of Effects Model in Advertising

Directory of Open Access Journals (Sweden)

Bambang Sukma Wijaya

2012-04-01

Full Text Available This paper aims to review the hierarchy of effects models in advertising, especially the well-known model, AIDA (Attention, Interest, Desire, and Action. Since its introduction by Lewis (1900 and generally attributed in the marketing and advertising literature by Strong (1925, the concept of AIDA’s hierarchy of effects model has been used by many researchers, both academicians and practitioners. The model is used to measure the effect of an advertisement. However, the development of information technology has radically changed the way of how people communicate and socialize; as well as a paradigm shift from product-oriented marketing to consumer-oriented marketing or people-oriented marketing. Therefore, the variables in the hierarchy of effects model needs to be updated in respond to the latest developments in the notice of public power as consumer audience. Based on deep literature review and reflective method, this paper introduces a new developed concept of hierarchy of effects model that was adopted from AIDA’s hierarchy of effects model, namely: AISDALSLove (At-tention, Interest, Search, Desire, Action, Like/dislike, Share, and Love/hate.

Do experiments suggest a hierarchy problem?

International Nuclear Information System (INIS)

Vissani, F.

1997-09-01

The hierarchy problem of the scalar sector of the standard model is reformulated, emphasizing the role of experimental facts that may suggest the existence of a new physics large mass scale, for instance indications of the instability of the matter, or indications in favor of massive neutrinos. In the see-saw model for the neutrino masses a hierarchy problem arises if the mass of the right-handed neutrinos is larger than approximatively 10 7 GeV: this problem, and its possible solutions, are discussed. (author)

Comparing the Hierarchy of Keywords in On-Line News Portals.

Science.gov (United States)

Tibély, Gergely; Sousa-Rodrigues, David; Pollner, Péter; Palla, Gergely

2016-01-01

Hierarchical organization is prevalent in networks representing a wide range of systems in nature and society. An important example is given by the tag hierarchies extracted from large on-line data repositories such as scientific publication archives, file sharing portals, blogs, on-line news portals, etc. The tagging of the stored objects with informative keywords in such repositories has become very common, and in most cases the tags on a given item are free words chosen by the authors independently. Therefore, the relations among keywords appearing in an on-line data repository are unknown in general. However, in most cases the topics and concepts described by these keywords are forming a latent hierarchy, with the more general topics and categories at the top, and more specialized ones at the bottom. There are several algorithms available for deducing this hierarchy from the statistical features of the keywords. In the present work we apply a recent, co-occurrence-based tag hierarchy extraction method to sets of keywords obtained from four different on-line news portals. The resulting hierarchies show substantial differences not just in the topics rendered as important (being at the top of the hierarchy) or of less interest (categorized low in the hierarchy), but also in the underlying network structure. This reveals discrepancies between the plausible keyword association frameworks in the studied news portals.

Comparing the Hierarchy of Keywords in On-Line News Portals.

Directory of Open Access Journals (Sweden)

Gergely Tibély

Full Text Available Hierarchical organization is prevalent in networks representing a wide range of systems in nature and society. An important example is given by the tag hierarchies extracted from large on-line data repositories such as scientific publication archives, file sharing portals, blogs, on-line news portals, etc. The tagging of the stored objects with informative keywords in such repositories has become very common, and in most cases the tags on a given item are free words chosen by the authors independently. Therefore, the relations among keywords appearing in an on-line data repository are unknown in general. However, in most cases the topics and concepts described by these keywords are forming a latent hierarchy, with the more general topics and categories at the top, and more specialized ones at the bottom. There are several algorithms available for deducing this hierarchy from the statistical features of the keywords. In the present work we apply a recent, co-occurrence-based tag hierarchy extraction method to sets of keywords obtained from four different on-line news portals. The resulting hierarchies show substantial differences not just in the topics rendered as important (being at the top of the hierarchy or of less interest (categorized low in the hierarchy, but also in the underlying network structure. This reveals discrepancies between the plausible keyword association frameworks in the studied news portals.

A generative model for scientific concept hierarchies.

Science.gov (United States)

Datta, Srayan; Adar, Eytan

2018-01-01

In many scientific disciplines, each new 'product' of research (method, finding, artifact, etc.) is often built upon previous findings-leading to extension and branching of scientific concepts over time. We aim to understand the evolution of scientific concepts by placing them in phylogenetic hierarchies where scientific keyphrases from a large, longitudinal academic corpora are used as a proxy of scientific concepts. These hierarchies exhibit various important properties, including power-law degree distribution, power-law component size distribution, existence of a giant component and less probability of extending an older concept. We present a generative model based on preferential attachment to simulate the graphical and temporal properties of these hierarchies which helps us understand the underlying process behind scientific concept evolution and may be useful in simulating and predicting scientific evolution.

A generative model for scientific concept hierarchies

Science.gov (United States)

Adar, Eytan

2018-01-01

In many scientific disciplines, each new ‘product’ of research (method, finding, artifact, etc.) is often built upon previous findings–leading to extension and branching of scientific concepts over time. We aim to understand the evolution of scientific concepts by placing them in phylogenetic hierarchies where scientific keyphrases from a large, longitudinal academic corpora are used as a proxy of scientific concepts. These hierarchies exhibit various important properties, including power-law degree distribution, power-law component size distribution, existence of a giant component and less probability of extending an older concept. We present a generative model based on preferential attachment to simulate the graphical and temporal properties of these hierarchies which helps us understand the underlying process behind scientific concept evolution and may be useful in simulating and predicting scientific evolution. PMID:29474409

Implications of nonzero θ13 for the neutrino mass hierarchy

International Nuclear Information System (INIS)

Ernst, D J; Cogswell, B K; Burroughs, H R; Escamilla-Roa, J; Latimer, D C

2012-01-01

The Daya Bay, RENO, and Double Chooz experiments have discovered a large non-zero value for θ 13 . We present a global analysis that includes these three experiments, Chooz, the Super-K atmospheric data, and the ν μ → ν e T2K and MINOS experiments that are sensitive to the hierarchy and the sign of θ 13 . We report preliminary results in which we fix the mixing parameters other than θ 13 to those from a recent global analysis. Given there is no evidence for a non-zero CP violation, we assume δ = 0. T2K and MINOS lie in a region of L/E where there is a hierarchy degeneracy in the limit of θ 13 → 0 and no matter interaction. For nonzero θ 13 , the symmetry is partially broken, but a degeneracy under the simultaneous exchange of both hierarchy and the sign of θ 13 remains. Matter effects break this symmetry such that the positions of the peaks in the oscillation probabilities maintain the two-fold symmetry, while the magnitude of the oscillations is sensitive to the hierarchy. This renders T2K and NOvA, with different baselines and different matter effects, better able in combination to distinguish the hierarchy and the sign of θ 13 . The present T2K and MINOS data do not distinguish between hierarchies or the sign of θ 13 , but the large value of θ 13 yields effects from atmospheric data that do. We find for normal hierarchy, positive θ 13 , sin 2 2θ 13 = 0.090 ± 0.020 and is 0.2% probable it is the correct combination; for normal hierarchy, negative θ 13 , sin 2 2θ 13 = 0.108 ± 0.023 and is 2.2% probable; for inverse hierarchy, positive θ 13 , sin 2 2θ 13 = 0.110±0.022 and is 7.1% probable; for inverse hierarchy, negative θ 13 , sin 2 2θ 13 = 0.113 ± 0.022 and is 90.5% probable, results that are inconsistent with two similar analyses.

Hierarchy Measure for Complex Networks

Science.gov (United States)

Mones, Enys; Vicsek, Lilla; Vicsek, Tamás

2012-01-01

Nature, technology and society are full of complexity arising from the intricate web of the interactions among the units of the related systems (e.g., proteins, computers, people). Consequently, one of the most successful recent approaches to capturing the fundamental features of the structure and dynamics of complex systems has been the investigation of the networks associated with the above units (nodes) together with their relations (edges). Most complex systems have an inherently hierarchical organization and, correspondingly, the networks behind them also exhibit hierarchical features. Indeed, several papers have been devoted to describing this essential aspect of networks, however, without resulting in a widely accepted, converging concept concerning the quantitative characterization of the level of their hierarchy. Here we develop an approach and propose a quantity (measure) which is simple enough to be widely applicable, reveals a number of universal features of the organization of real-world networks and, as we demonstrate, is capable of capturing the essential features of the structure and the degree of hierarchy in a complex network. The measure we introduce is based on a generalization of the m-reach centrality, which we first extend to directed/partially directed graphs. Then, we define the global reaching centrality (GRC), which is the difference between the maximum and the average value of the generalized reach centralities over the network. We investigate the behavior of the GRC considering both a synthetic model with an adjustable level of hierarchy and real networks. Results for real networks show that our hierarchy measure is related to the controllability of the given system. We also propose a visualization procedure for large complex networks that can be used to obtain an overall qualitative picture about the nature of their hierarchical structure. PMID:22470477

The AGL equation from the dipole picture

International Nuclear Information System (INIS)

Gay Ducati, M.B.; Goncalves, V.P.

1999-01-01

The AGL equation includes all multiple pomeron exchanges in the double logarithmic approximation (DLA) limit, leading to a unitarized gluon distribution in the small x regime. This equation was originally obtained using the Glauber-Mueller approach. We demonstrate in this paper that the AGL equation and, consequently, the GLR equation, can also be obtained from the dipole picture in the double logarithmic limit, using an evolution equation, recently proposed, which includes all multiple pomeron exchanges in the leading logarithmic approximation. Our conclusion is that the AGL equation is a good candidate for a unitarized evolution equation at small x in the DLA limit

Fermion mass hierarchies in theories of technicolor

International Nuclear Information System (INIS)

Peskin, M.E.

1981-01-01

Models in which light fermion masses result from dynamical symmetry breaking often produce these masses in a hierarchial pattern. The author exhibits two scenarios for obtaining such hierarchies and illustrates each with a simple model of mass generation. In the first scenario, the light fermion masses are separated by powers of a weak coupling constant; in the second scenario, they are separated by a ratio of large mass scales

The analytic hierarchy process as a support for decision making

Directory of Open Access Journals (Sweden)

Filipović Milanka

2007-01-01

Full Text Available The first part of this text deals with a convention site selection as one of the most lucrative areas in the tourism industry. The second part gives a further description of a method for decision making - the analytic hierarchy process. The basic characteristics: hierarchy constructions and pair wise comparison on the given level of the hierarchy are allured. The third part offers an example of application. This example is solved using the Super - Decision software, which is developed as a computer support for the analytic hierarchy process. This indicates that the AHP approach is a useful tool to help support a decision of convention site selection. .

Modelling and nonlinear shock waves for binary gas mixtures by the discrete Boltzmann equation with multiple collisions

International Nuclear Information System (INIS)

Bianchi, M.P.

1991-01-01

The discrete Boltzmann equation is a mathematical model in the kinetic theory of gases which defines the time and space evolution of a system of gas particles with a finite number of selected velocities. Discrete kinetic theory is an interesting field of research in mathematical physics and applied mathematics for several reasons. One of the relevant fields of application of the discrete Boltzmann equation is the analysis of nonlinear shock wave phenomena. Here, a new multiple collision regular plane model for binary gas mixtures is proposed within the discrete theory of gases and applied to the analysis of the classical problems of shock wave propagation

Critical constraints on chiral hierarchies

International Nuclear Information System (INIS)

Chivukula, R.S.; Golden, M.; Simmons, E.H.

1993-01-01

Critical dynamics constrains models of dynamical electroweak symmetry breaking in which the scale of high-energy physics is far above 1 TeV. A big hierarchy requires the high-energy theory to have a second-order chiral phase transition, near which the theory is described by a low-energy effective Lagrangian with composite ''Higgs'' scalars. As scalar theories with more than one Φ 4 coupling can have a Coleman-Weinberg instability and a first-order transition, such dynamical EWSB models cannot always support a large hierarchy. If the large-N c Nambu--Jona-Lasinio model is a good approximation to the top-condensate and strong extended technicolor models, they will not produce acceptable EWSB

Gauge theories, duality relations and the tensor hierarchy

NARCIS (Netherlands)

Bergshoeff, Eric A.; Hartong, Jelle; Hohm, Olaf; Huebscher, Mechthild; Ortin, Tomas; Hübscher, Mechthild

We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of

Formal Derivation of Lotka-Volterra-Haken Amplitude Equations of Task-Related Brain Activity in Multiple, Consecutively Performed Tasks