On coherent-state representations of quantum mechanics: Wave mechanics in phase space
DEFF Research Database (Denmark)
Møller, Klaus Braagaard; Jørgensen, Thomas Godsk; Torres-Vega, Gabino
1997-01-01
In this article we argue that the state-vector phase-space representation recently proposed by Torres-Vega and co-workers [introduced in J. Chem. Phys. 98, 3103 (1993)] coincides with the totality of coherent-state representations for the Heisenberg-Weyl group. This fact leads to ambiguities when...
On the phase space representations. 1
International Nuclear Information System (INIS)
Polubarinov, I.V.
1978-01-01
The Dirac representation theory deals usually with the amplitude formalism of the quantum theory. An introduction is given into a theory of some other representations, which are applicable in the density matrix formalism and can naturally be called phase space representations (PSR). They use terms of phase space variables (x and p simultaneously) and give a description, close to the classical phase space description. Definitions and algebraic properties are given in quantum mechanics for such PSRs as the Wigner representation, coherent state representation and others. Completeness relations of a matrix type are used as a starting point. The case of quantum field theory is also outlined
International Nuclear Information System (INIS)
Davis, J. E.; Eddy, M. J.; Sutton, T. M.; Altomari, T. J.
2007-01-01
Solid modeling computer software systems provide for the design of three-dimensional solid models used in the design and analysis of physical components. The current state-of-the-art in solid modeling representation uses a boundary representation format in which geometry and topology are used to form three-dimensional boundaries of the solid. The geometry representation used in these systems is cubic B-spline curves and surfaces - a network of cubic B-spline functions in three-dimensional Cartesian coordinate space. Many Monte Carlo codes, however, use a geometry representation in which geometry units are specified by intersections and unions of half-spaces. This paper describes an algorithm for converting from a boundary representation to a half-space representation. (authors)
Study on a phase space representation of quantum theory
International Nuclear Information System (INIS)
Ranaivoson, R.T.R; Raoelina Andriambololona; Hanitriarivo, R.; Raboanary, R.
2013-01-01
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current formulation of quantum mechanics which is based on the use of Hilbert space and linear operators theory. Phase space representation of quantum states and wave functions in phase space are introduced using properties of a set of functions called harmonic Gaussian functions. Then, new operators called dispersion operators are defined and identified as the operators which admit as eigenstates the basis states of the phase space representation. Generalization of the approach for multidimensional cases is shown. Examples of applications are given.
DEFF Research Database (Denmark)
Møller, Klaus Braagaard; Jørgensen, Thomas Godsk; Dahl, Jens Peder
1996-01-01
For some applications the overall phase of a quantum state is crucial. For the so-called displaced squeezed number state (DSN), which is a generalization of the well-known squeezed coherent state, we obtain the position space representation with the correct overall phase, from the dynamics...... in a harmonic potential. The importance of the overall phase is demonstrated in the context of characteristic or moment generating functions. For two special cases the characteristic function is shown to be computable from the inner product of two different DSNs....
On phase-space representations of quantum mechanics using
Indian Academy of Sciences (India)
space representations of quantum mechanics using Glauber coherent states. DIÓGENES CAMPOS. Research Article Volume 87 Issue 2 August ... Keywords. Phase-space quantum mechanics, coherent states, Husimi function, Wigner function ...
Phase space representations for spin23
International Nuclear Information System (INIS)
Polubarinov, I.V.
1991-01-01
General properties of spin matrices and density ones are considered for any spin s. For spin 2 3 phase space representations are constructed. Representations, similar to the Bell one, for the correlator of projections of two spins 2 3 in the singlet state are found. Quantum analogs of the Bell inequality are obtained. 14 refs
Santos, Léonard; Thirel, Guillaume; Perrin, Charles
2018-04-01
In many conceptual rainfall-runoff models, the water balance differential equations are not explicitly formulated. These differential equations are solved sequentially by splitting the equations into terms that can be solved analytically with a technique called operator splitting. As a result, only the solutions of the split equations are used to present the different models. This article provides a methodology to make the governing water balance equations of a bucket-type rainfall-runoff model explicit and to solve them continuously. This is done by setting up a comprehensive state-space representation of the model. By representing it in this way, the operator splitting, which makes the structural analysis of the model more complex, could be removed. In this state-space representation, the lag functions (unit hydrographs), which are frequent in rainfall-runoff models and make the resolution of the representation difficult, are first replaced by a so-called Nash cascade and then solved with a robust numerical integration technique. To illustrate this methodology, the GR4J model is taken as an example. The substitution of the unit hydrographs with a Nash cascade, even if it modifies the model behaviour when solved using operator splitting, does not modify it when the state-space representation is solved using an implicit integration technique. Indeed, the flow time series simulated by the new representation of the model are very similar to those simulated by the classic model. The use of a robust numerical technique that approximates a continuous-time model also improves the lag parameter consistency across time steps and provides a more time-consistent model with time-independent parameters.
The Koslowski-Sahlmann representation: quantum configuration space
Campiglia, Miguel; Varadarajan, Madhavan
2014-09-01
The Koslowski-Sahlmann (KS) representation is a generalization of the representation underlying the discrete spatial geometry of loop quantum gravity (LQG), to accommodate states labelled by smooth spatial geometries. As shown recently, the KS representation supports, in addition to the action of the holonomy and flux operators, the action of operators which are the quantum counterparts of certain connection dependent functions known as ‘background exponentials’. Here we show that the KS representation displays the following properties which are the exact counterparts of LQG ones: (i) the abelian * algebra of SU(2) holonomies and ‘U(1)’ background exponentials can be completed to a C* algebra, (ii) the space of semianalytic SU(2) connections is topologically dense in the spectrum of this algebra, (iii) there exists a measure on this spectrum for which the KS Hilbert space is realized as the space of square integrable functions on the spectrum, (iv) the spectrum admits a characterization as a projective limit of finite numbers of copies of SU(2) and U(1), (v) the algebra underlying the KS representation is constructed from cylindrical functions and their derivations in exactly the same way as the LQG (holonomy-flux) algebra except that the KS cylindrical functions depend on the holonomies and the background exponentials, this extra dependence being responsible for the differences between the KS and LQG algebras. While these results are obtained for compact spaces, they are expected to be of use for the construction of the KS representation in the asymptotically flat case.
Phase space density representations in fluid dynamics
International Nuclear Information System (INIS)
Ramshaw, J.D.
1989-01-01
Phase space density representations of inviscid fluid dynamics were recently discussed by Abarbanel and Rouhi. Here it is shown that such representations may be simply derived and interpreted by means of the Liouville equation corresponding to the dynamical system of ordinary differential equations that describes fluid particle trajectories. The Hamiltonian and Poisson bracket for the phase space density then emerge as immediate consequences of the corresponding structure of the dynamics. For barotropic fluids, this approach leads by direct construction to the formulation presented by Abarbanel and Rouhi. Extensions of this formulation to inhomogeneous incompressible fluids and to fluids in which the state equation involves an additional transported scalar variable are constructed by augmenting the single-particle dynamics and phase space to include the relevant additional variable
Quantum holonomy theory and Hilbert space representations
Energy Technology Data Exchange (ETDEWEB)
Aastrup, Johannes [Mathematisches Institut, Universitaet Hannover (Germany); Moeller Grimstrup, Jesper [QHT Gruppen, Copenhagen Area (Denmark)
2016-11-15
We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy-diffeomorphisms form a non-commutative C*-algebra. A proof that the state that generates the representation exist is left for later publications. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Directory of Open Access Journals (Sweden)
L. Santos
2018-04-01
Full Text Available In many conceptual rainfall–runoff models, the water balance differential equations are not explicitly formulated. These differential equations are solved sequentially by splitting the equations into terms that can be solved analytically with a technique called operator splitting. As a result, only the solutions of the split equations are used to present the different models. This article provides a methodology to make the governing water balance equations of a bucket-type rainfall–runoff model explicit and to solve them continuously. This is done by setting up a comprehensive state-space representation of the model. By representing it in this way, the operator splitting, which makes the structural analysis of the model more complex, could be removed. In this state-space representation, the lag functions (unit hydrographs, which are frequent in rainfall–runoff models and make the resolution of the representation difficult, are first replaced by a so-called Nash cascade and then solved with a robust numerical integration technique. To illustrate this methodology, the GR4J model is taken as an example. The substitution of the unit hydrographs with a Nash cascade, even if it modifies the model behaviour when solved using operator splitting, does not modify it when the state-space representation is solved using an implicit integration technique. Indeed, the flow time series simulated by the new representation of the model are very similar to those simulated by the classic model. The use of a robust numerical technique that approximates a continuous-time model also improves the lag parameter consistency across time steps and provides a more time-consistent model with time-independent parameters.
State-space representation of the reactor dynamics equations
International Nuclear Information System (INIS)
Bernard, J.A.
1995-01-01
This paper describes a novel formulation of the reactor space-independent kinetics equations. The intent is to present these equations in a form that is both compatible with modern control theory and mathematically rigorous. It is desired to write the kinetics equations in the standard state variable representation, x = Ax, where x is the state vector and A is the system matrix and, at the same time, avoid mathematical compromises such as the linearization of an equation about a particular operating point. The advantage to this proposed formulation is that it may allow the lateral transfer of existing control concepts, some that have been developed for other fields, to the operation of nuclear reactors. For example, sliding mode control has been developed to allow robots to function in a robust manner in the presence of changes in the system model. This is necessary because a robot is expected to be capable of picking up an object of unknown mass and moving that object along a specified trajectory. The variability of the object's mass introduces an uncertainty into the system model that is used to deduce the appropriate control action. Thus, the robot controller must be made robust against such variations. Sliding mode control is one means of accomplishing this. A reactor controller might benefit from the same concept if its objective were to cause the reactor power to move along a demanded trajectory despite the presence of some uncertainty in the net amount of reactivity that is present
Semiclassical propagation: Hilbert space vs. Wigner representation
Gottwald, Fabian; Ivanov, Sergei D.
2018-03-01
A unified viewpoint on the van Vleck and Herman-Kluk propagators in Hilbert space and their recently developed counterparts in Wigner representation is presented. Based on this viewpoint, the Wigner Herman-Kluk propagator is conceptually the most general one. Nonetheless, the respective semiclassical expressions for expectation values in terms of the density matrix and the Wigner function are mathematically proven here to coincide. The only remaining difference is a mere technical flexibility of the Wigner version in choosing the Gaussians' width for the underlying coherent states beyond minimal uncertainty. This flexibility is investigated numerically on prototypical potentials and it turns out to provide neither qualitative nor quantitative improvements. Given the aforementioned generality, utilizing the Wigner representation for semiclassical propagation thus leads to the same performance as employing the respective most-developed (Hilbert-space) methods for the density matrix.
Statistical representation of quantum states
Energy Technology Data Exchange (ETDEWEB)
Montina, A [Dipartimento di Fisica, Universita di Firenze, Via Sansone 1, 50019 Sesto Fiorentino (Italy)
2007-05-15
In the standard interpretation of quantum mechanics, the state is described by an abstract wave function in the representation space. Conversely, in a realistic interpretation, the quantum state is replaced by a probability distribution of physical quantities. Bohm mechanics is a consistent example of realistic theory, where the wave function and the particle positions are classically defined quantities. Recently, we proved that the probability distribution in a realistic theory cannot be a quadratic function of the quantum state, in contrast to the apparently obvious suggestion given by the Born rule for transition probabilities. Here, we provide a simplified version of this proof.
A group property for the coherent state representation of fermionic squeezing operators
Fan, Hong-yi; Li, Chao
2004-06-01
For the two-mode fermionic squeezing operators we find that their coherent state projection operator representation make up a loyal representation, which is homomorphic to an SO(4) group, though the fermionic coherent states are not mutual orthogonal. Thus the result of successively operating with many fermionic squeezing operators on a state can be equivalent to a single operation. The fermionic squeezing operators are mappings of orthogonal transformations in Grassmann number pseudo-classical space in the fermionic coherent state representation.
A group property for the coherent state representation of fermionic squeezing operators
International Nuclear Information System (INIS)
Fan Hongyi; Li Chao
2004-01-01
For the two-mode fermionic squeezing operators we find that their coherent state projection operator representation make up a loyal representation, which is homomorphic to an SO(4) group, though the fermionic coherent states are not mutual orthogonal. Thus the result of successively operating with many fermionic squeezing operators on a state can be equivalent to a single operation. The fermionic squeezing operators are mappings of orthogonal transformations in Grassmann number pseudo-classical space in the fermionic coherent state representation
Directory of Open Access Journals (Sweden)
Esfandiar, H.
2013-05-01
Full Text Available In this paper, based on the VoigtKelvin constitutive model, nonlinear dynamic modelling and state space representation of a viscoelastic beam acting as a flexible robotic manipulator is investigated. Complete nonlinear dynamic modelling of a viscoelastic beam without premature linearisation of dynamic equations is developed. The adopted method is capable of reproducing nonlinear dynamic effects, such as beam stiffening due to centrifugal and Coriolis forces induced by rotation of the joints. Structural damping effects on the models dynamic behaviour are also shown. A reliable model for a viscoelastic beam is subsequently presented. The governing equations of motion are derived using Hamiltons principle, and using the finite difference method, nonlinear partial differential equations are reduced to ordinary differential equations. For the purpose of flexible manipulator control, the standard form of state space equations for the viscoelastic link and the actuator is obtained. Simulation results indicate substantial improvements in dynamic behaviour, and a parameter sensitivity study is carried out to investigate the effect of structural damping on the vibration amplitude.
Coordinate, Momentum and Dispersion operators in Phase space representation
International Nuclear Information System (INIS)
Rakotoson, H.; Raoelina Andriambololona; Ranaivoson, R.T.R.; Raboanary, R.
2017-07-01
The aim of this paper is to present a study on the representations of coordinate, momentum and dispersion operators in the framework of a phase space representation of quantum mechanics that we have introduced and studied in previous works. We begin in the introduction section with a recall about the concept of representation of operators on wave function spaces. Then, we show that in the case of the phase space representation the coordinate and momentum operators can be represented either with differential operators or with matrices. The explicit expressions of both the differential operators and matrices representations are established. Multidimensional generalization of the obtained results are performed and phase space representation of dispersion operators are given.
Representations of coherent states in non-orthogonal bases
International Nuclear Information System (INIS)
Ali, S Twareque; Roknizadeh, R; Tavassoly, M K
2004-01-01
Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of bases in the underlying Hilbert space. This observation leads to an interesting duality between pairs of generalized coherent states, bringing into play a Gelfand triple of (rigged) Hilbert spaces. Moreover, it is shown that in each dual pair of families of nonlinear coherent states, at least one family is related to a (generally) non-unitary projective representation of the Weyl-Heisenberg group, which can then be thought of as characterizing the dual pair
Unilateral vestibular loss impairs external space representation.
Directory of Open Access Journals (Sweden)
Liliane Borel
Full Text Available The vestibular system is responsible for a wide range of postural and oculomotor functions and maintains an internal, updated representation of the position and movement of the head in space. In this study, we assessed whether unilateral vestibular loss affects external space representation. Patients with Menière's disease and healthy participants were instructed to point to memorized targets in near (peripersonal and far (extrapersonal spaces in the absence or presence of a visual background. These individuals were also required to estimate their body pointing direction. Menière's disease patients were tested before unilateral vestibular neurotomy and during the recovery period (one week and one month after the operation, and healthy participants were tested at similar times. Unilateral vestibular loss impaired the representation of both the external space and the body pointing direction: in the dark, the configuration of perceived targets was shifted toward the lesioned side and compressed toward the contralesioned hemifield, with higher pointing error in the near space. Performance varied according to the time elapsed after neurotomy: deficits were stronger during the early stages, while gradual compensation occurred subsequently. These findings provide the first demonstration of the critical role of vestibular signals in the representation of external space and of body pointing direction in the early stages after unilateral vestibular loss.
Rapisarda, P.; Trentelman, H.L.; Minh, H.B.
We illustrate an algorithm that starting from the image representation of a strictly bounded-real system computes a minimal balanced state variable, from which a minimal balanced state realization is readily obtained. The algorithm stems from an iterative procedure to compute a storage function,
[The fragmentation of representational space in schizophrenia].
Plagnol, A; Oïta, M; Montreuil, M; Granger, B; Lubart, T
2003-01-01
Existent neurocognitive models of schizophrenia converge towards a core of impairments involving working memory, context processing, action planning, controlled and intentional processing. However, the emergence of this core remains itself difficult to explain and more specific hypotheses do not explain the heterogeneity of schizophrenia. To overcome these limits, we propose a new paradigm based on representational theory from cognitive science. Some recent developments of this theory enable us to describe a subjective universe as a representational space which is displayed from memory. We outline a conceptual framework to construct such a representational space from analogical -representations that can be activated in working memory and are connected to a network of symbolic structures. These connections are notably made through an analytic process of the analogical fragments, which involves the attentional focus. This framework allows us to define rigorously some defense processes in response to traumatic tensions that are expressed on the representational space. The fragmentation of representational space is a consequence of a defensive denial based on an impairment of the analytic process. The fragmentation forms some parasitic areas in memory which are excluded from the main part of the representational space and disturb information processing. The key clinical concepts of paranoid syndromes can be defined in this conceptual framework: mental automatism, delusional intuition, acute destructuration, psychotic dissociation, and autistic withdrawal. We show that these syndromes imply each other, which in return increases the fragmentation of the representational space. Some new concepts emerge naturally in this framework, such as the concept of "suture" which is defined as a link between a parasitic area and the main representational space. Schizophrenia appears as a borderline case of fragmentation of the representational space. This conceptual framework is
An evaluation of space time cube representation of spatiotemporal patterns.
Kristensson, Per Ola; Dahlbäck, Nils; Anundi, Daniel; Björnstad, Marius; Gillberg, Hanna; Haraldsson, Jonas; Mårtensson, Ingrid; Nordvall, Mathias; Ståhl, Josefine
2009-01-01
Space time cube representation is an information visualization technique where spatiotemporal data points are mapped into a cube. Information visualization researchers have previously argued that space time cube representation is beneficial in revealing complex spatiotemporal patterns in a data set to users. The argument is based on the fact that both time and spatial information are displayed simultaneously to users, an effect difficult to achieve in other representations. However, to our knowledge the actual usefulness of space time cube representation in conveying complex spatiotemporal patterns to users has not been empirically validated. To fill this gap, we report on a between-subjects experiment comparing novice users' error rates and response times when answering a set of questions using either space time cube or a baseline 2D representation. For some simple questions, the error rates were lower when using the baseline representation. For complex questions where the participants needed an overall understanding of the spatiotemporal structure of the data set, the space time cube representation resulted in on average twice as fast response times with no difference in error rates compared to the baseline. These results provide an empirical foundation for the hypothesis that space time cube representation benefits users analyzing complex spatiotemporal patterns.
On the state space of the dipole ghost
International Nuclear Information System (INIS)
Binegar, B.
1984-01-01
A particular representation of SO(4, 2) is identified with the state space of the free dipole ghost. This representation is then given an explicit realization as the solution space of a 4th-order wave equation on a spacetime locally isomorphic to Minkowski space. A discrete basis for this solution space is given, as well as an explicit expression for its SO(4, 2) invariant inner product. The connection between the modes of dipole field and those of the massless scalar field is clarified, and a recent conjecture concerning the restriction of the dipole representation to the Poincare subgroup is confirmed. A particular coordinate transformation then reveals the theory of the dipole ghost in Minkowski space. Finally, it is shown that the solution space of the dipole equation is not unitarizable in a Poincare invariant manner. (orig.)
κ-Minkowski representations on Hilbert spaces
International Nuclear Information System (INIS)
Agostini, Alessandra
2007-01-01
The algebra of functions on κ-Minkowski noncommutative space-time is studied as algebra of operators on Hilbert spaces. The representations of this algebra are constructed and classified. This new approach leads to a natural construction of integration in κ-Minkowski space-time in terms of the usual trace of operators
Distributed Graph-Based State Space Generation
Blom, Stefan; Kant, Gijs; Rensink, Arend; De Lara, J.; Varro, D.
LTSMIN provides a framework in which state space generation can be distributed easily over many cores on a single compute node, as well as over multiple compute nodes. The tool works on the basis of a vector representation of the states; the individual cores are assigned the task of computing all
Phase-space representation of non-classical behaviour of scalar wave-fields
International Nuclear Information System (INIS)
Canas-Cardona, Gustavo; Castaneda, Roman; Vinck-Posada, Herbert
2011-01-01
The modelling of optical fields by using radiant and virtual point sources for the spatial coherence wavelets in the phase-space representation evidences some effects, conventionally attributed to non-classical correlations of light, although such type of correlations are not explicitly included in the model. Specifically, a light state is produced that has similar morphology to the Wigner Distribution Function of the well-known quantum Schroedinger cat and squeezed states.
Representations of G+++ and the role of space-time
International Nuclear Information System (INIS)
Kleinschmidt, A.; West, P.
2004-01-01
We consider the decomposition of the adjoint and fundamental representations of very extended Kac-Moody algebras G+++ with respect to their regular A type subalgebra which, in the corresponding non-linear realisation, is associated with gravity. We find that for many very extended algebras almost all the A type representations that occur in the decomposition of the fundamental representations also occur in the adjoint representation of G+++ . In particular, for E 8 +++ , this applies to all its fundamental representations. However, there are some important examples, such as A N-3 +++ , where this is not true and indeed the adjoint representation contains no generator that can be identified with a space-time translation. We comment on the significance of these results for how space-time can occur in the non-linear realisation based on G+++ . Finally we show that there is a correspondence between the A representations that occur in the fundamental representation associated with the very extended node and the adjoint representation of G+++ which is consistent with the interpretation of the former as charges associated with brane solutions. (author)
Representation Discovery using Harmonic Analysis
Mahadevan, Sridhar
2008-01-01
Representations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particu
Loop space representation of quantum general relativity and the group of loops
International Nuclear Information System (INIS)
Gambini, R.
1991-01-01
The action of the constraints of quantum general relativity on a general state in the loop representation is coded in terms of loop derivatives. These differential operators are related to the infinitesimal generators of the group of loops and generalize the area derivative first considered by Mandelstam. A new sector of solutions of the physical states space of nonperturbative quantum general relativity is found. (orig.)
Riesz Representation Theorem on Bilinear Spaces of Truncated Laurent Series
Directory of Open Access Journals (Sweden)
Sabarinsyah
2017-06-01
Full Text Available In this study a generalization of the Riesz representation theorem on non-degenerate bilinear spaces, particularly on spaces of truncated Laurent series, was developed. It was shown that any linear functional on a non-degenerate bilinear space is representable by a unique element of the space if and only if its kernel is closed. Moreover an explicit equivalent condition can be identiﬁed for the closedness property of the kernel when the bilinear space is a space of truncated Laurent series.
International Nuclear Information System (INIS)
Raoelina Andriambololona; Ranaivoson, R.T.R.; Rakotoson, H.; Solofoarisina, W.C.
2015-04-01
We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work. We begin with a brief recall about the so called phase space representation. We give the definition of linear canonical transformation with the transformation law of coordinate and momentum operators. We establish successively the transformation laws of mean values, dispersions, basis state and wave functions.Then we introduce the concept of isodispersion linear canonical transformation.
Representation of heading direction in far and near head space
Poljac, E.; Berg, A.V. van den
2003-01-01
Manipulation of objects around the head requires an accurate and stable internal representation of their locations in space, also during movements such as that of the eye or head. For far space, the representation of visual stimuli for goal-directed arm movements relies on retinal updating, if eye
State space in BRST-quantization and Kugo-Ojima quartets
International Nuclear Information System (INIS)
Rybkin, G.N.
1989-01-01
The structure of the state space in the BRST-quantization is considered and the connection between different approaches to the proof of the positive definiteness of the metric on the physical state space is established. The correspondence between different expressions for the BRST-charge, quadratic in fields, is obtained. The relation between different representations of the BRST-algebra is found. 22 refs
Spectral representations of neutron-star equations of state
International Nuclear Information System (INIS)
Lindblom, Lee
2010-01-01
Methods are developed for constructing spectral representations of cold (barotropic) neutron-star equations of state. These representations are faithful in the sense that every physical equation of state has a representation of this type and conversely every such representation satisfies the minimal thermodynamic stability criteria required of any physical equation of state. These spectral representations are also efficient, in the sense that only a few spectral coefficients are generally required to represent neutron-star equations of state quiet accurately. This accuracy and efficiency is illustrated by constructing spectral fits to a large collection of 'realistic' neutron-star equations of state.
Relativistic resonances as non-orthogonal states in Hilbert space
Blum, W
2003-01-01
We analyze the energy-momentum properties of relativistic short-lived particles with the result that they are characterized by two 4-vectors: in addition to the familiar energy-momentum vector (timelike) there is an energy-momentum 'spread vector' (spacelike). The wave functions in space and time for unstable particles are constructed. For the relativistic properties of unstable states we refer to Wigner's method of Poincare group representations that are induced by representations of the space-time translation and rotation groups. If stable particles, unstable particles and resonances are treated as elementary objects that are not fundamentally different one has to take into account that they will not generally be orthogonal to each other in their state space. The scalar product between a stable and an unstable state with otherwise identical properties is calculated in a particular Lorentz frame. The spin of an unstable particle is not infinitely sharp but has a 'spin spread' giving rise to 'spin neighbors'....
The problem of general Radon representation for an arbitrary Hausdorff space
Zakharov, V. K.; Mikhalev, A. V.
1999-10-01
After the fundamental work of Riesz, Radon and Hausdorff in the period 1909-1914, the following problem of general Radon representation emerged: for any Hausdorff space find the space of linear functionals that are integrally representable by Radon measures. In the early 1950s, a partial solution of this problem (the bijective version) for locally compact spaces was obtained by Halmos, Hewitt, Edwards, Bourbaki and others. For bounded Radon measures on a Tychonoff space, the problem of isomorphic Radon representation was solved in 1956 by Prokhorov. In this paper we give a possible solution of the problem of general Radon representation. To do this, we use the family of metasemicontinuous functions with compact support and the class of thin functionals. We present bijective and isomorphic versions of the solution (Theorems 1 and 2 of §2.5). To get the isomorphic version, we introduce the family of Radon bimeasures.
The problem of general Radon representation for an arbitrary Hausdorff space
Energy Technology Data Exchange (ETDEWEB)
Zakharov, V K [St Petersburg State University of Technology and Design (Russian Federation); Mikhalev, A V [M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
1999-10-31
After the fundamental work of Riesz, Radon and Hausdorff in the period 1909-1914, the following problem of general Radon representation emerged: for any Hausdorff space find the space of linear functionals that are integrally representable by Radon measures. In the early 1950s, a partial solution of this problem (the bijective version) for locally compact spaces was obtained by Halmos, Hewitt, Edwards, Bourbaki and others. For bounded Radon measures on a Tychonoff space, the problem of isomorphic Radon representation was solved in 1956 by Prokhorov. In this paper we give a possible solution of the problem of general Radon representation. To do this, we use the family of metasemicontinuous functions with compact support and the class of thin functionals. We present bijective and isomorphic versions of the solution (Theorems 1 and 2 of paragraph 2.5). To get the isomorphic version, we introduce the family of Radon bimeasures.
The problem of general Radon representation for an arbitrary Hausdorff space
International Nuclear Information System (INIS)
Zakharov, V K; Mikhalev, A V
1999-01-01
After the fundamental work of Riesz, Radon and Hausdorff in the period 1909-1914, the following problem of general Radon representation emerged: for any Hausdorff space find the space of linear functionals that are integrally representable by Radon measures. In the early 1950s, a partial solution of this problem (the bijective version) for locally compact spaces was obtained by Halmos, Hewitt, Edwards, Bourbaki and others. For bounded Radon measures on a Tychonoff space, the problem of isomorphic Radon representation was solved in 1956 by Prokhorov. In this paper we give a possible solution of the problem of general Radon representation. To do this, we use the family of metasemicontinuous functions with compact support and the class of thin functionals. We present bijective and isomorphic versions of the solution (Theorems 1 and 2 of paragraph 2.5). To get the isomorphic version, we introduce the family of Radon bimeasures
Changes in the representation of space and time while listening to music.
Schäfer, Thomas; Fachner, Jörg; Smukalla, Mario
2013-01-01
Music is known to alter people's ordinary experience of space and time. Not only does this challenge the concept of invariant space and time tacitly assumed in psychology but it may also help us understand how music works and how music can be understood as an embodied experience. Yet research about these alterations is in its infancy. This review is intended to delineate a future research agenda. We review experimental evidence and subjective reports of the influence of music on the representation of space and time and present prominent approaches to explaining these effects. We discuss the role of absorption and altered states of consciousness and their associated changes in attention and neurophysiological processes, as well as prominent models of human time processing and time experience. After integrating the reviewed research, we conclude that research on the influence of music on the representation of space and time is still quite inconclusive but that integrating the different approaches could lead to a better understanding of the observed effects. We also provide a working model that integrates a large part of the evidence and theories. Several suggestions for further research in both music psychology and cognitive psychology are outlined.
Changes in the representation of space and time while listening to music
Schäfer, Thomas; Fachner, Jörg; Smukalla, Mario
2013-01-01
Music is known to alter people's ordinary experience of space and time. Not only does this challenge the concept of invariant space and time tacitly assumed in psychology but it may also help us understand how music works and how music can be understood as an embodied experience. Yet research about these alterations is in its infancy. This review is intended to delineate a future research agenda. We review experimental evidence and subjective reports of the influence of music on the representation of space and time and present prominent approaches to explaining these effects. We discuss the role of absorption and altered states of consciousness and their associated changes in attention and neurophysiological processes, as well as prominent models of human time processing and time experience. After integrating the reviewed research, we conclude that research on the influence of music on the representation of space and time is still quite inconclusive but that integrating the different approaches could lead to a better understanding of the observed effects. We also provide a working model that integrates a large part of the evidence and theories. Several suggestions for further research in both music psychology and cognitive psychology are outlined. PMID:23964254
Symplectic Group Representation of the Two-Mode Squeezing Operator in the Coherent State Basis
Fan, Hong-Yi; Chen, Jun-Hua
2003-11-01
We find that the coherent state projection operator representation of the two-mode squeezing operator constitutes a loyal group representation of symplectic group, which is a remarkable property of the coherent state. As a consequence, the resultant effect of successively applying two-mode squeezing operators are equivalent to a single squeezing in the two-mode Fock space. Generalization of this property to the 2n-mode case is also discussed. The project supported by National Natural Science Foundation of China under Grant No. 10575057
A Learning State-Space Model for Image Retrieval
Directory of Open Access Journals (Sweden)
Lee Greg C
2007-01-01
Full Text Available This paper proposes an approach based on a state-space model for learning the user concepts in image retrieval. We first design a scheme of region-based image representation based on concept units, which are integrated with different types of feature spaces and with different region scales of image segmentation. The design of the concept units aims at describing similar characteristics at a certain perspective among relevant images. We present the details of our proposed approach based on a state-space model for interactive image retrieval, including likelihood and transition models, and we also describe some experiments that show the efficacy of our proposed model. This work demonstrates the feasibility of using a state-space model to estimate the user intuition in image retrieval.
On a microscopic representation of space-time
International Nuclear Information System (INIS)
Dahm, R.
2012-01-01
We start from a noncompact Lie algebra isomorphic to the Dirac algebra and relate this Lie algebra in a brief review to low-energy hadron physics described by the compact group SU(4). This step permits an overall physical identification of the operator actions. Then we discuss the geometrical origin of this noncompact Lie algebra and “reduce” the geometry in order to introduce in each of these steps coordinate definitions which can be related to an algebraic representation in terms of the spontaneous symmetry breakdown along the Lie algebra chain su*(4) → usp(4) → su(2) × u(1). Standard techniques of Lie algebra decomposition(s) as well as the (physical) operator identification give rise to interesting physical aspects and lead to a rank-1 Riemannian space which provides an analytic representation and leads to a 5-dimensional hyperbolic space H 5 with SO(5, 1) isometries. The action of the (compact) symplectic group decomposes this (globally) hyperbolic space into H 2 ⊕ H 3 with SO(2, 1) and SO(3, 1) isometries, respectively, which we relate to electromagnetic (dynamically broken SU(2) isospin) and Lorentz transformations. Last not least, we attribute this symmetry pattern to the algebraic representation of a projective geometry over the division algebra H and subsequent coordinate restrictions.
Bayne, Michael G; Scher, Jeremy A; Ellis, Benjamin H; Chakraborty, Arindam
2018-05-21
Electron-hole or quasiparticle representation plays a central role in describing electronic excitations in many-electron systems. For charge-neutral excitation, the electron-hole interaction kernel is the quantity of interest for calculating important excitation properties such as optical gap, optical spectra, electron-hole recombination and electron-hole binding energies. The electron-hole interaction kernel can be formally derived from the density-density correlation function using both Green's function and TDDFT formalism. The accurate determination of the electron-hole interaction kernel remains a significant challenge for precise calculations of optical properties in the GW+BSE formalism. From the TDDFT perspective, the electron-hole interaction kernel has been viewed as a path to systematic development of frequency-dependent exchange-correlation functionals. Traditional approaches, such as MBPT formalism, use unoccupied states (which are defined with respect to Fermi vacuum) to construct the electron-hole interaction kernel. However, the inclusion of unoccupied states has long been recognized as the leading computational bottleneck that limits the application of this approach for larger finite systems. In this work, an alternative derivation that avoids using unoccupied states to construct the electron-hole interaction kernel is presented. The central idea of this approach is to use explicitly correlated geminal functions for treating electron-electron correlation for both ground and excited state wave functions. Using this ansatz, it is derived using both diagrammatic and algebraic techniques that the electron-hole interaction kernel can be expressed only in terms of linked closed-loop diagrams. It is proved that the cancellation of unlinked diagrams is a consequence of linked-cluster theorem in real-space representation. The electron-hole interaction kernel derived in this work was used to calculate excitation energies in many-electron systems and results
Fock space representation of differential calculus on the noncommutative quantum space
International Nuclear Information System (INIS)
Mishra, A.K.; Rajasekaran, G.
1997-01-01
A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of the new algebra for the statistics of quanta are analyzed and discussed. The concept of statistical transmutation between bosons and fermions is introduced. copyright 1997 American Institute of Physics
Do Monkeys Think in Metaphors? Representations of Space and Time in Monkeys and Humans
Merritt, Dustin J.; Casasanto, Daniel; Brannon, Elizabeth M.
2010-01-01
Research on the relationship between the representation of space and time has produced two contrasting proposals. ATOM posits that space and time are represented via a common magnitude system, suggesting a symmetrical relationship between space and time. According to metaphor theory, however, representations of time depend on representations of…
Changes in the representation of space and time while listening to music
Directory of Open Access Journals (Sweden)
Thomas eSchäfer
2013-08-01
Full Text Available Music is known to alter people’s ordinary experience of space and time. Not only does this challenge the concept of invariant space and time tacitly assumed in psychology but it may also help us understand how music works and how music can be understood as an embodied experience. Yet research about these alterations is in its infancy. This review is intended to delineate a future research agenda. We review experimental evidence and subjective reports of the influence of music on the representation of space and time and present prominent approaches to explaining these effects. We discuss the role of absorption and altered states of consciousness and their associated changes in attention and neurophysiological processes, as well as prominent models of human time processing and time experience. After integrating the reviewed research, we conclude that research on the influence of music on the representation of space and time is still quite inconclusive but that integrating the different approaches could lead to a better understanding of the observed effects. We also provide a working model that integrates a large part of the evidence and theories. Several suggestions for further research in both music psychology and cognitive psychology are outlined.
The quantum state vector in phase space and Gabor's windowed Fourier transform
International Nuclear Information System (INIS)
Bracken, A J; Watson, P
2010-01-01
Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in the state vector and anti-linear in a fixed 'window state vector'. Here aspects of this construction are explored, and a connection is established with Gabor's 'windowed Fourier transform'. The amplitudes that arise for simple quantum states from various choices of windows are presented as illustrations. Generalized Bargmann representations of the state vector appear as special cases, associated with Gaussian windows. For every choice of window, amplitudes lie in a corresponding linear subspace of square-integrable functions on phase space. A generalized Born interpretation of amplitudes is described, with both the Wigner function and a generalized Husimi function appearing as quantities linear in an amplitude and anti-linear in its complex conjugate. Schroedinger's time-dependent and time-independent equations are represented on phase space amplitudes, and their solutions described in simple cases.
Representations of space based on haptic input
Zuidhoek, S.
2005-01-01
The present thesis focused on the representations of grasping space based on haptic input. We aimed at identifying their characteristics, and the underlying neurocognitive processes and mechanisms. To this end, we studied the systematic distortions in performance on several orientation perception
Explicit state representation and the ATLAS event data model: theory and practice
International Nuclear Information System (INIS)
Nowak, M; Snyder, S; Cranmer, K; Malon, D; Gemmeren, P v; Schaffer, A; Binet, S
2008-01-01
In anticipation of data taking, ATLAS has undertaken a program of work to develop an explicit state representation of the experiment's complex transient event data model. This effort has provided both an opportunity to consider explicitly the structure, organization, and content of the ATLAS persistent event store before writing tens of petabytes of data (replacing simple streaming, which uses the persistent store as a core dump of transient memory), and a locus for support of event data model evolution, including significant refactoring, beyond the automatic schema evolution capabilities of underlying persistence technologies. ATLAS has encountered the need for such non-trivial schema evolution on several occasions already. This paper describes the state representation strategy (transient/persistent separation) and its implementation, including both the payoffs that ATLAS has seen (significant and sometimes surprising space and performance improvements, the extra layer notwithstanding, and extremely general schema evolution support) and the costs (additional and relatively pervasive additional infrastructure development and maintenance). The paper further discusses how these costs are mitigated, and how ATLAS is able to implement this strategy without losing the ability to take advantage of the (improving!) automatic schema evolution capabilities of underlying technology layers when appropriate. Implications of state representations for direct ROOT browsability, and current strategies for associating physics analysis views with such state representations, are also described
A Model of Representational Spaces in Human Cortex.
Guntupalli, J Swaroop; Hanke, Michael; Halchenko, Yaroslav O; Connolly, Andrew C; Ramadge, Peter J; Haxby, James V
2016-06-01
Current models of the functional architecture of human cortex emphasize areas that capture coarse-scale features of cortical topography but provide no account for population responses that encode information in fine-scale patterns of activity. Here, we present a linear model of shared representational spaces in human cortex that captures fine-scale distinctions among population responses with response-tuning basis functions that are common across brains and models cortical patterns of neural responses with individual-specific topographic basis functions. We derive a common model space for the whole cortex using a new algorithm, searchlight hyperalignment, and complex, dynamic stimuli that provide a broad sampling of visual, auditory, and social percepts. The model aligns representations across brains in occipital, temporal, parietal, and prefrontal cortices, as shown by between-subject multivariate pattern classification and intersubject correlation of representational geometry, indicating that structural principles for shared neural representations apply across widely divergent domains of information. The model provides a rigorous account for individual variability of well-known coarse-scale topographies, such as retinotopy and category selectivity, and goes further to account for fine-scale patterns that are multiplexed with coarse-scale topographies and carry finer distinctions. © The Author 2016. Published by Oxford University Press.
Grey-box state-space identification of nonlinear mechanical vibrations
Noël, J. P.; Schoukens, J.
2018-05-01
The present paper deals with the identification of nonlinear mechanical vibrations. A grey-box, or semi-physical, nonlinear state-space representation is introduced, expressing the nonlinear basis functions using a limited number of measured output variables. This representation assumes that the observed nonlinearities are localised in physical space, which is a generic case in mechanics. A two-step identification procedure is derived for the grey-box model parameters, integrating nonlinear subspace initialisation and weighted least-squares optimisation. The complete procedure is applied to an electrical circuit mimicking the behaviour of a single-input, single-output (SISO) nonlinear mechanical system and to a single-input, multiple-output (SIMO) geometrically nonlinear beam structure.
Holographic representation of space-variant systems: system theory.
Marks Ii, R J; Krile, T F
1976-09-01
System theory for holographic representation of linear space-variant systems is derived. The utility of the resulting piecewise isoplanatic approximation (PIA) is illustrated by example application to the invariant system, ideal magnifier, and Fourier transformer. A method previously employed to holographically represent a space-variant system, the discrete approximation, is shown to be a special case of the PIA.
Directory of Open Access Journals (Sweden)
Gurvan Le Clec’H
2016-11-01
Full Text Available In this article, we present a simple agent which learns an internal representation of space without a priori knowledge of its environment, body, or sensors. The learned environment is seen as an internal space representation. This representation is isomorphic to the group of transformations applied to the environment. The model solves certain theoretical and practical issues encountered in previous work in sensorimotor contingency theory. Considering the mathematical description of the internal representation, analysis of its properties and simulations, we prove that this internal representation is equivalent to knowledge of space.
A State-Space Estimation of the Lee-Carter Mortality Model and Implications for Annuity Pricing
Man Chung Fung; Gareth W. Peters; Pavel V. Shevchenko
2015-01-01
In this article we investigate a state-space representation of the Lee-Carter model which is a benchmark stochastic mortality model for forecasting age-specific death rates. Existing relevant literature focuses mainly on mortality forecasting or pricing of longevity derivatives, while the full implications and methods of using the state-space representation of the Lee-Carter model in pricing retirement income products is yet to be examined. The main contribution of this article is twofold. Fi...
Grms or graphical representation of model spaces. Vol. I Basics
International Nuclear Information System (INIS)
Duch, W.
1986-01-01
This book presents a novel approach to the many-body problem in quantum chemistry, nuclear shell-theory and solid-state theory. Many-particle model spaces are visualized using graphs, each path of a graph labeling a single basis function or a subspace of functions. Spaces of a very high dimension are represented by small graphs. Model spaces have structure that is reflected in the architecture of the corresponding graphs, that in turn is reflected in the structure of the matrices corresponding to operators acting in these spaces. Insight into this structure leads to formulation of very efficient computer algorithms. Calculation of matrix elements is reduced to comparison of paths in a graph, without ever looking at the functions themselves. Using only very rudimentary mathematical tools graphical rules of matrix element calculation in abelian cases are derived, in particular segmentation rules obtained in the unitary group approached are rederived. The graphs are solutions of Diophantine equations of the type appearing in different branches of applied mathematics. Graphical representation of model spaces should find as many applications as has been found for diagramatical methods in perturbation theory
The unitary space of particle internal states
International Nuclear Information System (INIS)
Perjes, Z.
1978-09-01
A relativistic theory of particle internal properties has been developed. Suppressing space-time information, internal wave functions and -observables are constructed in a 3-complex-dimensional space. The quantum numbers of a spinning point particle in this unitary space correspond with those of a low-mass hadron. Unitary space physics is linked with space-time notions via the Penrose theory of twistors, where new flavors may be represented by many-twistor systems. It is shown here that a four-twistor particle fits into the unitary space picture as a system of two points with equal masses and oppositely pointing unitary spins. Quantum states fall into the ISU(3) irreducible representations discovered by Sparling and the author. Full details of the computation involving SU(3) recoupling techniques are given. (author)
Unknown quantum states: The quantum de Finetti representation
International Nuclear Information System (INIS)
Caves, Carlton M.; Fuchs, Christopher A.; Schack, Ruediger
2002-01-01
We present an elementary proof of the quantum de Finetti representation theorem, a quantum analog of de Finetti's classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanced mathematics and does not share the same potential for generalization. The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. The quantum de Finetti theorem, in a closely analogous fashion, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an ''unknown quantum state'' in quantum-state tomography. This result is especially important for information-based interpretations of quantum mechanics, where quantum states, like probabilities, are taken to be states of knowledge rather than states of nature. We further demonstrate that the theorem fails for real Hilbert spaces and discuss the significance of this point
International Nuclear Information System (INIS)
Chuan-Mei, Xie; Shao-Long, Wan; Hong-Yi, Fan
2010-01-01
Based on the displacement-squeezing related squeezed coherent state representation |z) g and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula (Huygens–Fresnel integration transformation describing optical diffraction). The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz - rz * in the |z) g representation, while |z) g in phase space is graphically denoted by an ellipse. (classical areas of phenomenology)
Braids as a representation space of SU(5)
Cartin, Daniel
2015-06-01
The standard model of particle physics provides very accurate predictions of phenomena occurring at the sub-atomic level, but the reason for the choice of symmetry group and the large number of particles considered elementary is still unknown. Along the lines of previous preon models positing a substructure to explain these aspects, Bilson-Thompson showed how the first family of elementary particles is realized as the crossings of braids made of three strands, with charges resulting from twists of those strands with certain conditions; in this topological model, there are only two distinct neutrino states. Modeling the particles as braids implies these braids must be the representation space of a Lie algebra, giving the symmetries of the standard model. In this paper, this representation is made explicit, obtaining the raising operators associated with the Lie algebra of SU(5), one of the earliest grand unified theories. Because the braids form a group, the action of these operators are braids themselves, leading to their identification as gauge bosons. Possible choices for the other two families are also given. Although this realization of particles as braids is lacking a dynamical framework, it is very suggestive, especially when considered as a natural method of adding matter to loop quantum gravity.
Towards a multilevel cognitive probabilistic representation of space
Tapus, Adriana; Vasudevan, Shrihari; Siegwart, Roland
2005-03-01
This paper addresses the problem of perception and representation of space for a mobile agent. A probabilistic hierarchical framework is suggested as a solution to this problem. The method proposed is a combination of probabilistic belief with "Object Graph Models" (OGM). The world is viewed from a topological optic, in terms of objects and relationships between them. The hierarchical representation that we propose permits an efficient and reliable modeling of the information that the mobile agent would perceive from its environment. The integration of both navigational and interactional capabilities through efficient representation is also addressed. Experiments on a set of images taken from the real world that validate the approach are reported. This framework draws on the general understanding of human cognition and perception and contributes towards the overall efforts to build cognitive robot companions.
State-space representation of instationary two-dimensional airfoil aerodynamics
Energy Technology Data Exchange (ETDEWEB)
Meyer, Marcus; Matthies, Hermann G. [Institute of Scientific Computing, Technical University Braunschweig, Hans-Sommer-Str. 65, Braunschweig 38106 (Germany)
2004-03-01
In the aero-elastic analysis of wind turbines the need to include a model of the local, two-dimensional instationary aerodynamic loads, commonly referred to as dynamic stall model, has become obvious in the last years. In this contribution an alternative choice for such a model is described, based on the DLR model. Its derivation is governed by the flow physics, thus enabling interpolation between different profile geometries. An advantage of the proposed model is its state-space form, i.e. a system of differential equations, which facilitates the important tasks of aeroelastic stability and sensitivity investigations. The model is validated with numerical calculations.
Wigner function and Schroedinger equation in phase-space representation
International Nuclear Information System (INIS)
Chruscinski, Dariusz; Mlodawski, Krzysztof
2005-01-01
We discuss a family of quasidistributions (s-ordered Wigner functions of Agarwal and Wolf [Phys. Rev. D 2, 2161 (1970); Phys. Rev. D 2, 2187 (1970); Phys. Rev. D 2, 2206 (1970)]) and its connection to the so-called phase space representation of the Schroedinger equation. It turns out that although Wigner functions satisfy the Schroedinger equation in phase space, they have a completely different interpretation
Deformed two-photon squeezed states in noncommutative space
International Nuclear Information System (INIS)
Zhang Jianzu
2004-01-01
Recent studies on nonperturbation aspects of noncommutative quantum mechanics explored a new type of boson commutation relations at the deformed level, described by deformed annihilation-creation operators in noncommutative space. This correlated boson commutator correlates different degrees of freedom, and shows an essential influence on dynamics. This Letter devotes to the development of formalism of deformed two-photon squeezed states in noncommutative space. General representations of deformed annihilation-creation operators and the consistency condition for the electromagnetic wave with a single mode of frequency in noncommunicative space are obtained. Two-photon squeezed states are studied. One finds that variances of the dimensionless Hermitian quadratures of the annihilation operator in one degree of freedom include variances in the other degree of freedom. Such correlations show the new feature of spatial noncommutativity and allow a deeper understanding of the correlated boson commutator
Configuration spaces geometry, topology and representation theory
Cohen, Frederick; Concini, Corrado; Feichtner, Eva; Gaiffi, Giovanni; Salvetti, Mario
2016-01-01
This book collects the scientific contributions of a group of leading experts who took part in the INdAM Meeting held in Cortona in September 2014. With combinatorial techniques as the central theme, it focuses on recent developments in configuration spaces from various perspectives. It also discusses their applications in areas ranging from representation theory, toric geometry and geometric group theory to applied algebraic topology.
SARAJEVO LOST IN TRANSITION? Ideologies and Their Representational Spaces
Directory of Open Access Journals (Sweden)
Nermina Zagora
2014-03-01
Full Text Available This study aims to investigate three characteristic representational typologies in Sarajevo, in regard to Henri Lefebvre's theory of “Production of Space.” Representational typologies are considered as a tool in the hands of power holders capable of influencing, motivating or manipulating wider population. The comparative analysis of the deterministic link between the social system and architecture will be examined in order to highlight the universal qualities of architecture capable of outliving the liminal momentum of transitions from one socio-political system to another.
Decoding Decoders: Finding Optimal Representation Spaces for Unsupervised Similarity Tasks
Zhelezniak, Vitalii; Busbridge, Dan; Shen, April; Smith, Samuel L.; Hammerla, Nils Y.
2018-01-01
Experimental evidence indicates that simple models outperform complex deep networks on many unsupervised similarity tasks. We provide a simple yet rigorous explanation for this behaviour by introducing the concept of an optimal representation space, in which semantically close symbols are mapped to representations that are close under a similarity measure induced by the model's objective function. In addition, we present a straightforward procedure that, without any retraining or architectura...
Vector coherent state representations and their inner products
International Nuclear Information System (INIS)
Rowe, D J
2012-01-01
Several advances have extended the power and versatility of coherent state theory to the extent that it has become a vital tool in the representation theory of Lie groups and their Lie algebras. Representative applications are reviewed and some new developments are introduced. The examples given are chosen to illustrate special features of the scalar and vector coherent state constructions and how they work in practical situations. Comparisons are made with Mackey's theory of induced representations. For simplicity, we focus on square integrable (discrete series) unitary representations although many of the techniques apply more generally, with minor adjustment. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (review)
Fan, Hong-Yi; Chen, Jun-Hua
2002-08-01
We find that the coherent state projection operator representation of symplectic transformation constitutes a loyal group representation of symplectic group. The result of successively applying squeezing operators on number state can be easily derived. The project supported by National Natural Science Foundation of China under Grant No. 10575057 and the President Foundation of the Chinese Academy of Sciences
English, Michael C.; Maybery, Murray T.; Visser, Troy A.
2017-01-01
Neurotypical individuals display a leftward attentional bias, called pseudoneglect, for physical space (e.g. landmark task) and mental representations of space (e.g. mental number line bisection). However, leftward bias is reduced in autistic individuals viewing faces, and neurotypical individuals with autistic traits viewing "greyscale"…
Inequivalent coherent state representations in group field theory
Kegeles, Alexander; Oriti, Daniele; Tomlin, Casey
2018-06-01
In this paper we propose an algebraic formulation of group field theory and consider non-Fock representations based on coherent states. We show that we can construct representations with an infinite number of degrees of freedom on compact manifolds. We also show that these representations break translation symmetry. Since such representations can be regarded as quantum gravitational systems with an infinite number of fundamental pre-geometric building blocks, they may be more suitable for the description of effective geometrical phases of the theory.
Women And Visual Representations Of Space In Two Chinese Film Adaptations Of Hamlet
Directory of Open Access Journals (Sweden)
CHEANG WAI FONG
2014-12-01
Full Text Available This paper studies two Chinese film adaptations of Shakespeare’s Hamlet, Xiaogang Feng’s The Banquet (2006 and Sherwood Hu’s Prince of the Himalayas (2006, by focusing on their visual representations of spaces allotted to women. Its thesis is that even though on the original Shakespearean stage details of various spaces might not be as vividly represented as in modern film productions, spaces are still crucial dramatic elements imbued with powerful significations. By analyzing the two Chinese film adaptations alongside the original Hamlet text, the paper attempts to reinterpret their different representations of spaces in relation to their different historical-cultural gender notions.
Non-commutative flux representation for loop quantum gravity
Baratin, A.; Dittrich, B.; Oriti, D.; Tambornino, J.
2011-09-01
The Hilbert space of loop quantum gravity is usually described in terms of cylindrical functionals of the gauge connection, the electric fluxes acting as non-commuting derivation operators. It has long been believed that this non-commutativity prevents a dual flux (or triad) representation of loop quantum gravity to exist. We show here, instead, that such a representation can be explicitly defined, by means of a non-commutative Fourier transform defined on the loop gravity state space. In this dual representation, flux operators act by sstarf-multiplication and holonomy operators act by translation. We describe the gauge invariant dual states and discuss their geometrical meaning. Finally, we apply the construction to the simpler case of a U(1) gauge group and compare the resulting flux representation with the triad representation used in loop quantum cosmology.
International Nuclear Information System (INIS)
Díaz, Guzmán; Gómez-Aleixandre, Javier; Coto, José
2016-01-01
Highlights: • State space representations for simulating wind power plant output are proposed. • The representation of wind speed in state space allows structural analysis. • The joint model incorporates the temporal and spatial dependence structure. • The models are easily integrable into a backward/forward sweep algorithm. • Results evidence the remarkable differences between joint and marginal models. - Abstract: This paper proposes the use of state space models to generate scenarios for the analysis of wind power plant (WPP) generation capabilities. The proposal is rooted on the advantages that state space models present for dealing with stochastic processes; mainly their structural definition and the use of Kalman filter to naturally tackle some involved operations. The specification proposed in this paper comprises a structured representation of individual Box–Jenkins models, with indications about further improvements that can be easily performed. These marginal models are combined to form a joint model in which the dependence structure is easily handled. Indications about the procedure to calibrate and check the model, as well as a validation of its statistical appropriateness, are provided. Application of the proposed state space models provides insight on the need to properly specify the structural dependence between wind speeds. In this paper the joint and marginal models are smoothly integrated into a backward–forward sweep algorithm to determine the performance indicators (voltages and powers) of a WPP through simulation. As a result, visibly heavy tails emerge in the generated power probability distribution through the use of the joint model—incorporating a detailed description of the dependence structure—in contrast with the normally distributed power yielded by the margin-based model.
International Nuclear Information System (INIS)
Weigert, S.
1999-01-01
To reconstruct a mixed or pure quantum state of a spin s is possible through coherent states: its density matrix is fixed by the probabilities to measure the value s along 4s(s+1) appropriately chosen directions in space. Thus, after inverting the experimental data, the statistical operator is parametrized entirely by expectation values. On this basis, a symbolic calculus for quantum spins is developed, the e xpectation-value representation . It resembles the Moyal representation for SU(2) but two important differences exist. On the one hand, the symbols take values on a discrete set of points in phase space only. On the other hand, no quasi-probabilities - that is, phase-space distributions with negative values - are encountered in this approach. (Author)
Vector space representation of array antenna pattern synthesis problems
DEFF Research Database (Denmark)
Wu, Jian; Roederer, A.G
1991-01-01
and to visualize the optimization process. The vector space approach described provides a very powerful representation of the array pattern synthesis problems. It is not only general, since many parameters are represented under one model, but also helps to visualize the problem. The proposed approach provides...
A representation independent propagator. Pt. 1. Compact Lie groups
International Nuclear Information System (INIS)
Tome, W.A.
1995-01-01
Conventional path integral expressions for propagators are representation dependent. Rather than having to adapt each propagator to the representation in question, it is shown that for compact Lie groups it is possible to introduce a propagator that is representation independent. For a given set of kinematical variables this propagator is a single function independent of any particular choice of fiducial vector, which monetheless, correctly propagates each element of the coherent state representation associated with these kinematical variables. Although the configuration space is in general curved, nevertheless the lattice phase-space path integral for the representation independent propagator has the form appropriate to flat space. To illustrate the general theory a representation independent propagator is explicitly constructed for the Lie group SU(2). (orig.)
Directory of Open Access Journals (Sweden)
Lau M. Andersen
2018-05-01
Full Text Available An important aim of an analysis pipeline for magnetoencephalographic (MEG data is that it allows for the researcher spending maximal effort on making the statistical comparisons that will answer his or her questions. The example question being answered here is whether the so-called beta rebound differs between novel and repeated stimulations. Two analyses are presented: going from individual sensor space representations to, respectively, an across-group sensor space representation and an across-group source space representation. The data analyzed are neural responses to tactile stimulations of the right index finger in a group of 20 healthy participants acquired from an Elekta Neuromag System. The processing steps covered for the first analysis are MaxFiltering the raw data, defining, preprocessing and epoching the data, cleaning the data, finding and removing independent components related to eye blinks, eye movements and heart beats, calculating participants' individual evoked responses by averaging over epoched data and subsequently removing the average response from single epochs, calculating a time-frequency representation and baselining it with non-stimulation trials and finally calculating a grand average, an across-group sensor space representation. The second analysis starts from the grand average sensor space representation and after identification of the beta rebound the neural origin is imaged using beamformer source reconstruction. This analysis covers reading in co-registered magnetic resonance images, segmenting the data, creating a volume conductor, creating a forward model, cutting out MEG data of interest in the time and frequency domains, getting Fourier transforms and estimating source activity with a beamformer model where power is expressed relative to MEG data measured during periods of non-stimulation. Finally, morphing the source estimates onto a common template and performing group-level statistics on the data are
International Nuclear Information System (INIS)
Uren, Kenneth Richard; Schoor, George van
2013-01-01
This second paper in a two part series presents the application of a developed state space model extraction methodology applied to a Brayton cycle-based PCU (power conversion unit) of a PBMR (pebble bed modular reactor). The goal is to investigate if the state space extraction methodology can cope with larger and more complex thermohydraulic systems. In Part I the state space model extraction methodology for the purpose of control was described in detail and a state space representation was extracted for a U-tube system to illustrate the concept. In this paper a 25th order nonlinear state space representation in terms of the different energy domains is extracted. This state space representation is solved and the responses of a number of important states are compared with results obtained from a PBMR PCU Flownex ® model. Flownex ® is a validated thermo fluid simulation software package. The results show that the state space model closely resembles the dynamics of the PBMR PCU. This kind of model may be used for nonlinear MIMO (multi-input, multi-output) type of control strategies. However, there is still a need for linear state space models since many control system design and analysis techniques require a linear state space model. This issue is also addressed in this paper by showing how a linear state space model can be derived from the extracted nonlinear state space model. The linearised state space model is also validated by comparing the state space model to an existing linear Simulink ® model of the PBMR PCU system. - Highlights: • State space model extraction of a pebble bed modular reactor PCU (power conversion unit). • A 25th order nonlinear time varying state space model is obtained. • Linearisation of a nonlinear state space model for use in power output control. • Non-minimum phase characteristic that is challenging in terms of control. • Models derived are useful for MIMO control strategies
New Three-Mode Squeezing Operators Gained via Tripartite Entangled State Representation
International Nuclear Information System (INIS)
Jiang Nianquan; Fan Hongyi
2008-01-01
We show that the Agarwal-Simon representation of single-mode squeezed states can be generalized to find new form of three-mode squeezed states. We use the tripartite entangled state representations |p,y,z> and |x,u,v> to realize this goal.
Real-space quadrature: A convenient, efficient representation for multipole expansions
International Nuclear Information System (INIS)
Rogers, David M.
2015-01-01
Multipoles are central to the theory and modeling of polarizable and nonpolarizable molecular electrostatics. This has made a representation in terms of point charges a highly sought after goal, since rotation of multipoles is a bottleneck in molecular dynamics implementations. All known point charge representations are orders of magnitude less efficient than spherical harmonics due to either using too many fixed charge locations or due to nonlinear fitting of fewer charge locations. We present the first complete solution to this problem—completely replacing spherical harmonic basis functions by a dramatically simpler set of weights associated to fixed, discrete points on a sphere. This representation is shown to be space optimal. It reduces the spherical harmonic decomposition of Poisson’s operator to pairwise summations over the point set. As a corollary, we also shows exact quadrature-based formulas for contraction over trace-free supersymmetric 3D tensors. Moreover, multiplication of spherical harmonic basis functions translates to a direct product in this representation
Response to the Comment by G. Emch on projective group representations in quaternionic Hilbert space
International Nuclear Information System (INIS)
Adler, S.L.
1996-01-01
We discuss the differing definitions of complex and quaternionic projective group representations employed by us and by Emch. The definition of Emch (termed here a strong projective representation) is too restrictive to accommodate quaternionic Hilbert space embeddings of complex projective representations. Our definition (termed here a weak projective representation) encompasses such embeddings, and leads to a detailed theory of quaternionic, as well as complex, projective group representations. copyright 1996 American Institute of Physics
Measuring the representational space of music with fMRI: a case study with Sting.
Levitin, Daniel J; Grafton, Scott T
2016-12-01
Functional brain imaging has revealed much about the neuroanatomical substrates of higher cognition, including music, language, learning, and memory. The technique lends itself to studying of groups of individuals. In contrast, the nature of expert performance is typically studied through the examination of exceptional individuals using behavioral case studies and retrospective biography. Here, we combined fMRI and the study of an individual who is a world-class expert musician and composer in order to better understand the neural underpinnings of his music perception and cognition, in particular, his mental representations for music. We used state of the art multivoxel pattern analysis (MVPA) and representational dissimilarity analysis (RDA) in a fixed set of brain regions to test three exploratory hypotheses with the musician Sting: (1) Composing would recruit neutral structures that are both unique and distinguishable from other creative acts, such as composing prose or visual art; (2) listening and imagining music would recruit similar neural regions, indicating that musical memory shares anatomical substrates with music listening; (3) the MVPA and RDA results would help us to map the representational space for music, revealing which musical pieces and genres are perceived to be similar in the musician's mental models for music. Our hypotheses were confirmed. The act of composing, and even of imagining elements of the composed piece separately, such as melody and rhythm, activated a similar cluster of brain regions, and were distinct from prose and visual art. Listened and imagined music showed high similarity, and in addition, notable similarity/dissimilarity patterns emerged among the various pieces used as stimuli: Muzak and Top 100/Pop songs were far from all other musical styles in Mahalanobis distance (Euclidean representational space), whereas jazz, R&B, tango and rock were comparatively close. Closer inspection revealed principaled explanations for the
Directory of Open Access Journals (Sweden)
Nataliya Chukhrova
2017-05-01
Full Text Available This paper gives a detailed overview of the current state of research in relation to the use of state space models and the Kalman-filter in the field of stochastic claims reserving. Most of these state space representations are matrix-based, which complicates their applications. Therefore, to facilitate the implementation of state space models in practice, we present a scalar state space model for cumulative payments, which is an extension of the well-known chain ladder (CL method. The presented model is distribution-free, forms a basis for determining the entire unobservable lower and upper run-off triangles and can easily be applied in practice using the Kalman-filter for prediction, filtering and smoothing of cumulative payments. In addition, the model provides an easy way to find outliers in the data and to determine outlier effects. Finally, an empirical comparison of the scalar state space model, promising prior state space models and some popular stochastic claims reserving methods is performed.
Energy Technology Data Exchange (ETDEWEB)
Sikora, W
1974-10-15
A description of magnetic structures based on the use of representations of space groups is given. Representations of the space groups were established for each compound on the basis of experimental data by the method of projection operators. The compounds contained in the list are collected according to crystal systems, alphabetically within each system. The description of each compound consists of the four parts. The first part contain the chemical symbol of the compound, the second its space group. The next part contains the chemical symbol of the magnetic atom and its positions in Wychoff notation with the number of equivalent positions in the crystal unit cell. The main description of a compound magnetic structure is given in the fourth part. It contains: K vector defined in the reciprocal space, the representation according to which a magnetic structure is transformed and the axial vector function S which describes the magnetic structure.
Quantum de Finetti theorem in phase-space representation
International Nuclear Information System (INIS)
Leverrier, Anthony; Cerf, Nicolas J.
2009-01-01
The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ xn . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).
International Nuclear Information System (INIS)
Li Qianshu; Lue Liqiang; Wei Gongmin
2004-01-01
This paper discusses the relationship between the Wigner function, along with other related quasiprobability distribution functions, and the probability density distribution function constructed from the wave function of the Schroedinger equation in quantum phase space, as formulated by Torres-Vega and Frederick (TF). At the same time, a general approach in solving the wave function of the Schroedinger equation of TF quantum phase space theory is proposed. The relationship of the wave functions between the TF quantum phase space representation and the coordinate or momentum representation is thus revealed
State space model extraction of thermohydraulic systems – Part I: A linear graph approach
International Nuclear Information System (INIS)
Uren, K.R.; Schoor, G. van
2013-01-01
Thermohydraulic simulation codes are increasingly making use of graphical design interfaces. The user can quickly and easily design a thermohydraulic system by placing symbols on the screen resembling system components. These components can then be connected to form a system representation. Such system models may then be used to obtain detailed simulations of the physical system. Usually this kind of simulation models are too complex and not ideal for control system design. Therefore, a need exists for automated techniques to extract lumped parameter models useful for control system design. The goal of this first paper, in a two part series, is to propose a method that utilises a graphical representation of a thermohydraulic system, and a lumped parameter modelling approach, to extract state space models. In this methodology each physical domain of the thermohydraulic system is represented by a linear graph. These linear graphs capture the interaction between all components within and across energy domains – hydraulic, thermal and mechanical. These linear graphs are analysed using a graph-theoretic approach to derive reduced order state space models. These models capture the dominant dynamics of the thermohydraulic system and are ideal for control system design purposes. The proposed state space model extraction method is demonstrated by considering a U-tube system. A non-linear state space model is extracted representing both the hydraulic and thermal domain dynamics of the system. The simulated state space model is compared with a Flownex ® model of the U-tube. Flownex ® is a validated systems thermal-fluid simulation software package. - Highlights: • A state space model extraction methodology based on graph-theoretic concepts. • An energy-based approach to consider multi-domain systems in a common framework. • Allow extraction of transparent (white-box) state space models automatically. • Reduced order models containing only independent state
A new representation for ground states and its Legendre transforms
International Nuclear Information System (INIS)
Cedillo, A.
1994-01-01
The ground-state energy of an electronic system is a functional of the number of electrons (N) and the external potential (v): E = E(N,V), this is the energy representation for ground states. In 1982, Nalewajski defined the Legendre transforms of this representation, taking advantage of the strict concavity of E with respect to their variables (concave respect v and convex respect N), and he also constructed a scheme for the reduction of derivatives of his representations. Unfortunately, N and the electronic density (p) were the independent variables of one of these representations, but p depends explicitly on N. In this work, this problem is avoided using the energy per particle (ε) as the basic variables, and the Legendre transformations can be defined. A procedure for the reduction of derivatives is generated for the new four representations and, in contrast to the Nalewajski's procedure, it only includes derivatives of the four representations. Finally, the reduction of derivatives is used to test some relationships between the hardness and softness kernels
Amputation and prosthesis implantation shape body and peripersonal space representations
Canzoneri, Elisa; Marzolla, Marilena; Amoresano, Amedeo; Verni, Gennaro; Serino, Andrea
2013-01-01
Little is known about whether and how multimodal representations of the body (BRs) and of the space around the body (Peripersonal Space, PPS) adapt to amputation and prosthesis implantation. In order to investigate this issue, we tested BR in a group of upper limb amputees by means of a tactile distance perception task and PPS by means of an audio-tactile interaction task. Subjects performed the tasks with stimulation either on the healthy limb or the stump of the amputated limb, while wearin...
Representation theory of 2-groups on finite dimensional 2-vector spaces
Elgueta, Josep
2004-01-01
In this paper, the 2-category $\\mathfrak{Rep}_{{\\bf 2Mat}_{\\mathbb{C}}}(\\mathbb{G})$ of (weak) representations of an arbitrary (weak) 2-group $\\mathbb{G}$ on (some version of) Kapranov and Voevodsky's 2-category of (complex) 2-vector spaces is studied. In particular, the set of equivalence classes of representations is computed in terms of the invariants $\\pi_0(\\mathbb{G})$, $\\pi_1(\\mathbb{G})$ and $[\\alpha]\\in H^3(\\pi_0(\\mathbb{G}),\\pi_1(\\mathbb{G}))$ classifying $\\mathbb{G}$. Also the categ...
Directory of Open Access Journals (Sweden)
Sandra Valeria Ursino
2012-01-01
Full Text Available In this article, we present some of the results and argumentative lines used in the analysis of the field work carried out in the neighborhoods of Porst, Danubio and Villa Inflamable, in the Dock Sud area, located in the district of Avellaneda, province de Buenos Aires, during 2010 and 2011. Within this framework, we observed and recorded the inhabitants' usual routes around the neighborhood, which is environmentally polluted but which has also been symbolically appropriated. Along these lines then, our general aim was to learn about social representations, representation spaces and the spatial practices of the inhabitants of the most affected neighborhoods of Dock Sud due to the area's environmental issues. To this end, there was a reconstruction of the subjects' practices in the neighborhood, of the hegemonic discourse about the pollution in this place and, finally, the population's conflict and struggle practices
García-Vela, A.
2000-05-01
A definition of a quantum-type phase-space distribution is proposed in order to represent the initial state of the system in a classical dynamics simulation. The central idea is to define an initial quantum phase-space state of the system as the direct product of the coordinate and momentum representations of the quantum initial state. The phase-space distribution is then obtained as the square modulus of this phase-space state. The resulting phase-space distribution closely resembles the quantum nature of the system initial state. The initial conditions are sampled with the distribution, using a grid technique in phase space. With this type of sampling the distribution of initial conditions reproduces more faithfully the shape of the original phase-space distribution. The method is applied to generate initial conditions describing the three-dimensional state of the Ar-HCl cluster prepared by ultraviolet excitation. The photodissociation dynamics is simulated by classical trajectories, and the results are compared with those of a wave packet calculation. The classical and quantum descriptions are found in good agreement for those dynamical events less subject to quantum effects. The classical result fails to reproduce the quantum mechanical one for the more strongly quantum features of the dynamics. The properties and applicability of the phase-space distribution and the sampling technique proposed are discussed.
Linear and nonlinear optical signals in probability and phase-space representations
International Nuclear Information System (INIS)
Man'ko, Margarita A
2006-01-01
Review of different representations of signals including the phase-space representations and tomographic representations is presented. The signals under consideration are either linear or nonlinear ones. The linear signals satisfy linear quantumlike Schroedinger and von Neumann equations. Nonlinear signals satisfy nonlinear Schroedinger equations as well as Gross-Pitaevskii equation describing solitons in Bose-Einstein condensate. The Ville-Wigner distributions for solitons are considered in comparison with tomographic-probability densities describing solitons completely. different kinds of tomographies - symplectic tomography, optical tomography and Fresnel tomography are reviewed. New kind of map of the signals onto probability distributions of discrete photon number-like variable is discussed. Mutual relations between different transformations of signal functions are established in explicit form. Such characteristics of the signal-probability distribution as entropy is discussed
Generation of symmetry coordinates for crystals using multiplier representations of the space groups
DEFF Research Database (Denmark)
Hansen, Flemming Yssing
1978-01-01
Symmetry coordinates play an important role in the normal-mode calculations of crystals. It is therefore of great importance to have a general method, which may be applied for any crystal at any wave vector, to generate these. The multiplier representations of the space groups as given by Kovalev...... and the projection-operator technique provide a basis for such a method. The method is illustrated for the nonsymmorphic D36 space group, and the theoretical background for the representations of space groups in general is reviewed and illustrated on the example above. It is desirable to perform the projection...... of symmetry coordinates in such a way that they may be used for as many wave vectors as possible. We discuss how to achieve this goal. The detailed illustrations should make it simple to apply the theory in any other case....
Quantum Mechanics in the Gaussian wave-packet phase space representation: Dynamics
International Nuclear Information System (INIS)
Mizrahi, S.S.
1985-01-01
The Heisenberg and Liouville dynamical equations are mapped using the Wave-Packet Phase Space Representation. A semiclassical perturbative expansion is introduced - the Quasi-Causal Approximation - for the Green function and an expression for transition probabilities is derived up to the first order. (Author) [pt
Unstable quantum states and rigged Hilbert spaces
International Nuclear Information System (INIS)
Gorini, V.; Parravicini, G.
1978-10-01
Rigged Hilbert space techniques are applied to the quantum mechanical treatment of unstable states in nonrelativistic scattering theory. A method is discussed which is based on representations of decay amplitudes in terms of expansions over complete sets of generalized eigenvectors of the interacting Hamiltonian, corresponding to complex eigenvalues. These expansions contain both a discrete and a continuum contribution. The former corresponds to eigenvalues located at the second sheet poles of the S matrix, and yields the exponential terms in the survival amplitude. The latter arises from generalized eigenvectors associated to complex eigenvalues on background contours in the complex plane, and gives the corrections to the exponential law. 27 references
On massless representations of the Q-deformed Poincare algebra
International Nuclear Information System (INIS)
Ogievetsky, O.; Pillin, M.; Schmidke, W.B.; Wess, J.
1993-01-01
This talk is devoted to the construction of massless representations of the q-deformed Poincare algebra. In section 2 we give Hilbert space representations of the SL q (2, C)-covariant quantum space. We then show in the next section how the generators of the q-Poincare algebra can be expressed in terms of operators which live in the light cone. The q-deformed massless one-particle states are considered in section 4. (orig.)
The Role of Familiarity for Representations in Norm-Based Face Space.
Faerber, Stella J; Kaufmann, Jürgen M; Leder, Helmut; Martin, Eva Maria; Schweinberger, Stefan R
2016-01-01
According to the norm-based version of the multidimensional face space model (nMDFS, Valentine, 1991), any given face and its corresponding anti-face (which deviates from the norm in exactly opposite direction as the original face) should be equidistant to a hypothetical prototype face (norm), such that by definition face and anti-face should bear the same level of perceived typicality. However, it has been argued that familiarity affects perceived typicality and that representations of familiar faces are qualitatively different (e.g., more robust and image-independent) from those for unfamiliar faces. Here we investigated the role of face familiarity for rated typicality, using two frequently used operationalisations of typicality (deviation-based: DEV), and distinctiveness (face in the crowd: FITC) for faces of celebrities and their corresponding anti-faces. We further assessed attractiveness, likeability and trustworthiness ratings of the stimuli, which are potentially related to typicality. For unfamiliar faces and their corresponding anti-faces, in line with the predictions of the nMDFS, our results demonstrate comparable levels of perceived typicality (DEV). In contrast, familiar faces were perceived much less typical than their anti-faces. Furthermore, familiar faces were rated higher than their anti-faces in distinctiveness, attractiveness, likability and trustworthiness. These findings suggest that familiarity strongly affects the distribution of facial representations in norm-based face space. Overall, our study suggests (1) that familiarity needs to be considered in studies of mental representations of faces, and (2) that familiarity, general distance-to-norm and more specific vector directions in face space make different and interactive contributions to different types of facial evaluations.
The Role of Familiarity for Representations in Norm-Based Face Space.
Directory of Open Access Journals (Sweden)
Stella J Faerber
Full Text Available According to the norm-based version of the multidimensional face space model (nMDFS, Valentine, 1991, any given face and its corresponding anti-face (which deviates from the norm in exactly opposite direction as the original face should be equidistant to a hypothetical prototype face (norm, such that by definition face and anti-face should bear the same level of perceived typicality. However, it has been argued that familiarity affects perceived typicality and that representations of familiar faces are qualitatively different (e.g., more robust and image-independent from those for unfamiliar faces. Here we investigated the role of face familiarity for rated typicality, using two frequently used operationalisations of typicality (deviation-based: DEV, and distinctiveness (face in the crowd: FITC for faces of celebrities and their corresponding anti-faces. We further assessed attractiveness, likeability and trustworthiness ratings of the stimuli, which are potentially related to typicality. For unfamiliar faces and their corresponding anti-faces, in line with the predictions of the nMDFS, our results demonstrate comparable levels of perceived typicality (DEV. In contrast, familiar faces were perceived much less typical than their anti-faces. Furthermore, familiar faces were rated higher than their anti-faces in distinctiveness, attractiveness, likability and trustworthiness. These findings suggest that familiarity strongly affects the distribution of facial representations in norm-based face space. Overall, our study suggests (1 that familiarity needs to be considered in studies of mental representations of faces, and (2 that familiarity, general distance-to-norm and more specific vector directions in face space make different and interactive contributions to different types of facial evaluations.
International Nuclear Information System (INIS)
Fradkin, E.S.; Metsaev, R.R.
1996-02-01
Using the language of highest weight representations and the light cone formalism we construct a full list of cubic amplitudes of scattering for all bosonic massless representations of the Poincare group in any even space-time dimension. (author). 29 refs
Hydrogen atom in phase space: the Wigner representation
International Nuclear Information System (INIS)
Praxmeyer, Ludmila; Mostowski, Jan; Wodkiewicz, Krzysztof
2006-01-01
The hydrogen atom is a fundamental exactly soluble system for which the Wigner function, being a quantum analogue of the joint probability distribution of position and momentum, is unknown. In this paper, we present an effective method of calculating the Wigner function, for all bound states of the nonrelativistic hydrogen atom. The formal similarity between the eigenfunctions of the nonrelativistic hydrogen atom in the momentum representation and the Klein-Gordon propagator has allowed the calculation of the Wigner function for an arbitrary bound state of the hydrogen atom, using a simple atomic integral as a generator. These Wigner functions for some low-lying states are depicted and discussed
DEFF Research Database (Denmark)
Mailund, Thomas
The thesis describes the sweep-line method, a newly developed reduction method for alleviating the state explosion problem inherent in explicit-state state space exploration. The basic idea underlying the sweep-line method is, when calculating the state space, to recognise and delete states...... that are not reachable from the currently unprocessed states. Intuitively we drag a sweep-line through the state space with the invariant that all states behind the sweep-line have been processed and are unreachable from the states in front of the sweep-line. When calculating the state space of a system we iteratively...
The structure and properties of color spaces and the representation of color images
Dubois, Eric
2009-01-01
This lecture describes the author's approach to the representation of color spaces and their use for color image processing. The lecture starts with a precise formulation of the space of physical stimuli (light). The model includes both continuous spectra and monochromatic spectra in the form of Dirac deltas. The spectral densities are considered to be functions of a continuous wavelength variable. This leads into the formulation of color space as a three-dimensional vector space, with all the associated structure. The approach is to start with the axioms of color matching for normal human vie
Functional representations for quantized fields
International Nuclear Information System (INIS)
Jackiw, R.
1988-01-01
This paper provides information on Representing transformations in quantum theory bosonic quantum field theories: Schrodinger Picture; Represnting Transformations in Bosonic Quantum Field Theory; Two-Dimensional Conformal Transformations, Schrodinger picture representation, Fock space representation, Inequivalent Schrodinger picture representations; Discussion, Self-Dual and Other Models; Field Theory in de Sitter Space. Fermionic Quantum Field Theories: Schroedinger Picture; Schrodinger Picture Representation for Two-Dimensional; Conformal Transformations; Fock Space Dynamics in the Schrodinger Picture; Fock Space Evaluation of Anomalous Current and Conformal Commutators
Learning spaces as representational scaffolds for learning conceptual knowledge of system behaviour
Bredeweg, B.; Liem, J.; Beek, W.; Salles, P.; Linnebank, F.; Wolpers, M.; Kirschner, P.A.; Scheffel, M.; Lindstaedt, S.; Dimitrova, V.
2010-01-01
Scaffolding is a well-known approach to bridge the gap between novice and expert capabilities in a discovery-oriented learning environment. This paper discusses a set of knowledge representations referred to as Learning Spaces (LSs) that can be used to support learners in acquiring conceptual
Directory of Open Access Journals (Sweden)
Eduard Kelemen
2013-07-01
Full Text Available Neurophysiological studies focus on memory retrieval as a reproduction of what was experienced and have established that neural discharge is replayed to express memory. However, cognitive psychology has established that recollection is not a verbatim replay of stored information. Recollection is constructive, the product of memory retrieval cues, the information stored in memory, and the subject's state of mind. We discovered key features of constructive recollection embedded in the rat CA1 ensemble discharge during an active avoidance task. Rats learned two task variants, one with the arena stable, the other with it rotating; each variant defined a distinct behavioral episode. During the rotating episode, the ensemble discharge of CA1 principal neurons was dynamically organized to concurrently represent space in two distinct codes. The code for spatial reference frame switched rapidly between representing the rat's current location in either the stationary spatial frame of the room or the rotating frame of the arena. The code for task variant switched less frequently between a representation of the current rotating episode and the stable episode from the rat's past. The characteristics and interplay of these two hippocampal codes revealed three key properties of constructive recollection. (1 Although the ensemble representations of the stable and rotating episodes were distinct, ensemble discharge during rotation occasionally resembled the stable condition, demonstrating cross-episode retrieval of the representation of the remote, stable episode. (2 This cross-episode retrieval at the level of the code for task variant was more likely when the rotating arena was about to match its orientation in the stable episode. (3 The likelihood of cross-episode retrieval was influenced by preretrieval information that was signaled at the level of the code for spatial reference frame. Thus key features of episodic recollection manifest in rat hippocampal
3D Maps Representation Using GNG
Directory of Open Access Journals (Sweden)
Vicente Morell
2014-01-01
Full Text Available Current RGB-D sensors provide a big amount of valuable information for mobile robotics tasks like 3D map reconstruction, but the storage and processing of the incremental data provided by the different sensors through time quickly become unmanageable. In this work, we focus on 3D maps representation and propose the use of the Growing Neural Gas (GNG network as a model to represent 3D input data. GNG method is able to represent the input data with a desired amount of neurons or resolution while preserving the topology of the input space. Experiments show how GNG method yields a better input space adaptation than other state-of-the-art 3D map representation methods.
(j,0)circle-plus(0,j) representation space: Dirac-like construct
International Nuclear Information System (INIS)
Ahluwalia, D.V.; Johnson, M.B.; Goldman, T.
1993-01-01
This is first of the two invited lectures presented at the ''XVII International School of Theoretical Physics: Standard Model and Beyond 1993.'' The text is essentially based on a recent publication by the present authors. Here we show that the Dirac-like construct in the (j,0)circle-plus(0,j) representation space support a Bargmann-Wightman-Wigner type quantum field theory
(j,0){circle_plus}(0,j) representation space: Dirac-like construct
Energy Technology Data Exchange (ETDEWEB)
Ahluwalia, D.V.; Johnson, M.B.; Goldman, T.
1993-12-31
This is first of the two invited lectures presented at the ``XVII International School of Theoretical Physics: Standard Model and Beyond 1993.`` The text is essentially based on a recent publication by the present authors. Here we show that the Dirac-like construct in the (j,0){circle_plus}(0,j) representation space support a Bargmann-Wightman-Wigner type quantum field theory.
International Nuclear Information System (INIS)
Rinaldi, Massimiliano
2007-01-01
We consider Green's functions associated to a scalar field propagating on a curved, ultrastatic background, in the presence of modified dispersion relations. The usual proper-time DeWitt-Schwinger procedure to obtain a series representation of Green's functions is doomed to failure because of higher order spatial derivatives in the Klein-Gordon operator. We show how to overcome this difficulty by considering a preferred frame, associated to a unit timelike vector. With respect to this frame, we can express Green's functions as an integral over all frequencies of a space-dependent function. The latter can be expanded in momentum space, as a series with geometric coefficients similar to the DeWitt-Schwinger ones. By integrating over all frequencies, we finally find the expansion of Green's function up to four derivatives of the metric tensor. The relation with the proper-time formalism is also discussed
Representation of SO(4,1) group and Hawking effect in the de-Sitter space
International Nuclear Information System (INIS)
Bogush, A.A.; Otchik, V.S.
1983-01-01
Expression relating the solution of the equation for particles with spin 1/2 to matrix elements of group SO(4, 1), is obtained. When using the relation of the Dirac equation solutions in the de Sitter space with matrix elements of representations of group SO(4, 1) the presence of the Hawking effect in the space is established. The de Sitter space is considered as 4-dimensional hyperboloid, inserted into 5-dimensional pseudo-Euclidean space. It is established, that the average number of emitted spinor particles obeys the Fermi-Dirac distribution
International Nuclear Information System (INIS)
Aizawa, N; Chakrabarti, R; Mohammed, S S Naina; Segar, J
2007-01-01
Representations of the quantum superalgebra U q [osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U q [osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and is observed that they may be expressed in terms of the Q-Hahn polynomials. We next investigate representations of the quantum supergroup OSp q (1/2) which are not well defined in the classical limit. Employing the universal T-matrix, the representation matrices are obtained explicitly, and found to be related to the little Q-Jacobi polynomials. Characteristically, the relation Q = -q is satisfied in all cases. Using the Clebsch-Gordan coefficients derived here, we construct new noncommutative spaces that are covariant under the coaction of the even-dimensional representations of the quantum supergroup OSp q (1/2)
Positive-definite functions and unitary representations of locally compact groups in a Hilbert space
International Nuclear Information System (INIS)
Gali, I.M.; Okb el-Bab, A.S.; Hassan, H.M.
1977-08-01
It is proved that the necessary and sufficient condition for the existence of an integral representation of a group of unitary operators in a Hilbert space is that it is positive-definite and continuous in some topology
DEFF Research Database (Denmark)
Photography not only represents space. Space is produced photographically. Since its inception in the 19th century, photography has brought to light a vast array of represented subjects. Always situated in some spatial order, photographic representations have been operatively underpinned by social...... to the enterprises of the medium. This is the subject of Representational Machines: How photography enlists the workings of institutional technologies in search of establishing new iconic and social spaces. Together, the contributions to this edited volume span historical epochs, social environments, technological...... possibilities, and genre distinctions. Presenting several distinct ways of producing space photographically, this book opens a new and important field of inquiry for photography research....
Evaluating abundance and trends in a Hawaiian avian community using state-space analysis
Camp, Richard J.; Brinck, Kevin W.; Gorresen, P.M.; Paxton, Eben H.
2016-01-01
Estimating population abundances and patterns of change over time are important in both ecology and conservation. Trend assessment typically entails fitting a regression to a time series of abundances to estimate population trajectory. However, changes in abundance estimates from year-to-year across time are due to both true variation in population size (process variation) and variation due to imperfect sampling and model fit. State-space models are a relatively new method that can be used to partition the error components and quantify trends based only on process variation. We compare a state-space modelling approach with a more traditional linear regression approach to assess trends in uncorrected raw counts and detection-corrected abundance estimates of forest birds at Hakalau Forest National Wildlife Refuge, Hawai‘i. Most species demonstrated similar trends using either method. In general, evidence for trends using state-space models was less strong than for linear regression, as measured by estimates of precision. However, while the state-space models may sacrifice precision, the expectation is that these estimates provide a better representation of the real world biological processes of interest because they are partitioning process variation (environmental and demographic variation) and observation variation (sampling and model variation). The state-space approach also provides annual estimates of abundance which can be used by managers to set conservation strategies, and can be linked to factors that vary by year, such as climate, to better understand processes that drive population trends.
Directory of Open Access Journals (Sweden)
Lucinei Pereira da Silva
2012-12-01
Full Text Available The representations and memory of living space are essential to developing mental maps and cartographic documents. In this regard this investigation as a primary objective to understand how mind maps can contribute pedagogically classes in Geography and History as well, breaking the dichotomy space / time. From the point of view of theoretical and methodological the research relied on the analysis of the school project “Our Neighborhood, Our Place” developed at the Municipal School “Vereador Hamilton Teodoro” in Governador Valadares (MG, along with a group of 7th grades from elementary school and the articulation of authors who discuss the concepts of representation, memory, space and place.
International Nuclear Information System (INIS)
Quesne, C.
1986-01-01
In the present series of papers, the coherent states of Sp(2d,R), corresponding to the positive discrete series irreducible representations 1 +n/2> encountered in physical applications, are analyzed in detail with special emphasis on those of Sp(4,R) and Sp(6,R). The present paper discusses the unitary-operator coherent states, as defined by Klauder, Perelomov, and Gilmore. These states are parametrized by the points of the coset space Sp(2d,R)/H, where H is the stability group of the Sp(2d,R) irreducible representation lowest weight state, chosen as the reference state, and depends upon the relative values of lambda 1 ,...,lambda/sub d/, subject to the conditions lambda 1 > or =lambda 2 > or = x x x > or =lambda/sub d/> or =0. A parametrization of Sp(2d,R)/H corresponding to a factorization of the latter into a product of coset spaces Sp(2d,R)/U(d) and U(d)/H is chosen. The overlap of two coherent states is calculated, the action of the Sp(2d,R) generators on the coherent states is determined, and the explicit form of the unity resolution relation satisfied by the coherent states in the representation space of the irreducible representation is obtained. The Hilbert space of analytic functions arising from the coherent state representation is studied in detail. Finally, some applications of the formalism developed in the present paper are outlined
International Nuclear Information System (INIS)
Burdík, C; Reshetnyak, A
2012-01-01
We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux Y(s 1 ,..., s k ) with κ ≥ 2 rows on d-dimensional anti-de-Sitter space. Auxiliary representations for specially deformed non-linear HS symmetry algebra in terms of generalized Verma module in order to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints are found explicitly for the case of HS fields for κ = 2 Young tableaux. The oscillator realization over Heisenberg algebra for obtained Verma module is constructed. The results generalize the method of auxiliary representations construction for symplectic sp(2κ) algebra used for mixed-symmetry HS fields on a flat spaces and can be extended on a case of arbitrary HS fields in AdS-space. Gauge-invariant unconstrained reducible Lagrangian formulation for free bosonic HS fields with generalized spin (s 1 , s 2 ) is derived.
Collective pairing states and nonunitary representations of the quasi-spin group
International Nuclear Information System (INIS)
Lorazo, B.
1975-06-01
A mathematical proof is given of the intimate connection of the physical generalized seniority states (i.e. states the excitation energy spectra of which does not depend upon the number of particles) with states transforming according to non-unitary representations of the quasi-spin group [fr
Coello, Yann; Quesque, François; Gigliotti, Maria-Francesca; Ott, Laurent; Bruyelle, Jean-Luc
2018-01-01
Peripersonal space is a multisensory representation of the environment around the body in relation to the motor system, underlying the interactions with the physical and social world. Although changing body properties and social context have been shown to alter the functional processing of space, little is known about how changing the value of objects influences the representation of peripersonal space. In two experiments, we tested the effect of modifying the spatial distribution of reward-yielding targets on manual reaching actions and peripersonal space representation. Before and after performing a target-selection task consisting of manually selecting a set of targets on a touch-screen table, participants performed a two-alternative forced-choice reachability-judgment task. In the target-selection task, half of the targets were associated with a reward (change of colour from grey to green, providing 1 point), the other half being associated with no reward (change of colour from grey to red, providing no point). In Experiment 1, the target-selection task was performed individually with the aim of maximizing the point count, and the distribution of the reward-yielding targets was either 50%, 25% or 75% in the proximal and distal spaces. In Experiment 2, the target-selection task was performed in a social context involving cooperation between two participants to maximize the point count, and the distribution of the reward-yielding targets was 50% in the proximal and distal spaces. Results showed that changing the distribution of the reward-yielding targets or introducing the social context modified concurrently the amplitude of self-generated manual reaching actions and the representation of peripersonal space. Moreover, a decrease of the amplitude of manual reaching actions caused a reduction of peripersonal space when resulting from the distribution of reward-yielding targets, while this effect was not observed in a social interaction context. In that case, the
Du Toit, Shané
2014-01-01
This study investigates the representation of narrative space in the novel and the film of The Return of the King. As the two representations belong to two different mediums, the theories on narrative space in the novel and in the film are examined in order to distinguish between their modes of representation of space. In essence, the theory utilised for the spatial analysis focuses on the content, function and symbolic meaning within spaces, as created by the description of objects, the repe...
Time evolution of the Wigner function in the entangled-state representation
International Nuclear Information System (INIS)
Fan Hongyi
2002-01-01
For quantum-mechanical entangled states we introduce the entangled Wigner operator in the entangled-state representation. We derive the time evolution equation of the entangled Wigner operator . The trace product rule for entangled Wigner functions is also obtained
State Space Modeling Using SAS
Directory of Open Access Journals (Sweden)
Rajesh Selukar
2011-05-01
Full Text Available This article provides a brief introduction to the state space modeling capabilities in SAS, a well-known statistical software system. SAS provides state space modeling in a few different settings. SAS/ETS, the econometric and time series analysis module of the SAS system, contains many procedures that use state space models to analyze univariate and multivariate time series data. In addition, SAS/IML, an interactive matrix language in the SAS system, provides Kalman filtering and smoothing routines for stationary and nonstationary state space models. SAS/IML also provides support for linear algebra and nonlinear function optimization, which makes it a convenient environment for general-purpose state space modeling.
Osada, Hirofumi; Osada, Shota
2018-01-01
We prove tail triviality of determinantal point processes μ on continuous spaces. Tail triviality has been proved for such processes only on discrete spaces, and hence we have generalized the result to continuous spaces. To do this, we construct tree representations, that is, discrete approximations of determinantal point processes enjoying a determinantal structure. There are many interesting examples of determinantal point processes on continuous spaces such as zero points of the hyperbolic Gaussian analytic function with Bergman kernel, and the thermodynamic limit of eigenvalues of Gaussian random matrices for Sine_2 , Airy_2 , Bessel_2 , and Ginibre point processes. Our main theorem proves all these point processes are tail trivial.
Andersen, Lau M
2018-01-01
An important aim of an analysis pipeline for magnetoencephalographic data is that it allows for the researcher spending maximal effort on making the statistical comparisons that will answer the questions of the researcher, while in turn spending minimal effort on the intricacies and machinery of the pipeline. I here present a set of functions and scripts that allow for setting up a clear, reproducible structure for separating raw and processed data into folders and files such that minimal effort can be spend on: (1) double-checking that the right input goes into the right functions; (2) making sure that output and intermediate steps can be accessed meaningfully; (3) applying operations efficiently across groups of subjects; (4) re-processing data if changes to any intermediate step are desirable. Applying the scripts requires only general knowledge about the Python language. The data analyses are neural responses to tactile stimulations of the right index finger in a group of 20 healthy participants acquired from an Elekta Neuromag System. Two analyses are presented: going from individual sensor space representations to, respectively, an across-group sensor space representation and an across-group source space representation. The processing steps covered for the first analysis are filtering the raw data, finding events of interest in the data, epoching data, finding and removing independent components related to eye blinks and heart beats, calculating participants' individual evoked responses by averaging over epoched data and calculating a grand average sensor space representation over participants. The second analysis starts from the participants' individual evoked responses and covers: estimating noise covariance, creating a forward model, creating an inverse operator, estimating distributed source activity on the cortical surface using a minimum norm procedure, morphing those estimates onto a common cortical template and calculating the patterns of activity
Directory of Open Access Journals (Sweden)
Lau M. Andersen
2018-01-01
Full Text Available An important aim of an analysis pipeline for magnetoencephalographic data is that it allows for the researcher spending maximal effort on making the statistical comparisons that will answer the questions of the researcher, while in turn spending minimal effort on the intricacies and machinery of the pipeline. I here present a set of functions and scripts that allow for setting up a clear, reproducible structure for separating raw and processed data into folders and files such that minimal effort can be spend on: (1 double-checking that the right input goes into the right functions; (2 making sure that output and intermediate steps can be accessed meaningfully; (3 applying operations efficiently across groups of subjects; (4 re-processing data if changes to any intermediate step are desirable. Applying the scripts requires only general knowledge about the Python language. The data analyses are neural responses to tactile stimulations of the right index finger in a group of 20 healthy participants acquired from an Elekta Neuromag System. Two analyses are presented: going from individual sensor space representations to, respectively, an across-group sensor space representation and an across-group source space representation. The processing steps covered for the first analysis are filtering the raw data, finding events of interest in the data, epoching data, finding and removing independent components related to eye blinks and heart beats, calculating participants' individual evoked responses by averaging over epoched data and calculating a grand average sensor space representation over participants. The second analysis starts from the participants' individual evoked responses and covers: estimating noise covariance, creating a forward model, creating an inverse operator, estimating distributed source activity on the cortical surface using a minimum norm procedure, morphing those estimates onto a common cortical template and calculating the patterns
Thermal Wigner Operator in Coherent Thermal State Representation and Its Application
Institute of Scientific and Technical Information of China (English)
FAN HongYi
2002-01-01
In the coherent thermal state representation we introduce thermal Wigner operator and find that it is"squeezed" under the thermal transformation. The thermal Wigner operator provides us with a new direct and neatapproach for deriving Wigner functions of thermal states.
van Dijck, Jean-Philippe; Fias, Wim; Andres, Michael
2015-10-01
It has been proposed that the metrics of space, time and other magnitudes relevant for action are coupled through a generalized magnitude system that also contribute to number representation. Several studies capitalized on stimulus-response compatibility effects to show that numbers map onto left-right representations and grasp representations as a function of their magnitude. However, the tasks typically used do not allow disentangling magnitude from serial order processing. Here, we devised a working memory (WM) task where participants had to remember random sequences of numbers and perform a precision/whole-hand grip (Experiment 1) or a uni-manual left/right button press (Experiment 2) in response to numbers presented during the retention interval. This task does allow differentiating the interference of number magnitude and serial order with each set of responses. Experiment 1 showed that precision grips were initiated faster than whole-hand grips in response to small numbers, irrespective of their serial position in WM. In contrast, Experiment 2 revealed an advantage of right over left button presses as serial position increased, without any influence of number magnitude. These findings demonstrate that grasping and left-right movements overlap with distinct dimensions of number processing. These findings are discussed in the light of different theories explaining the interactions between numbers, space and action.
Thermal Wigner Operator in Coherent Thermal State Representation and Its Application
Institute of Scientific and Technical Information of China (English)
FANHong－Yi
2002-01-01
In the coherent thermal state representation we introduce thermal Wigner operator and find that it is “squeezed” under the thermal transformation.The thermal Wigner operator provides us with a new direct and neat approach for deriving Wigner functions of thermal states.
Operator representations of frames
DEFF Research Database (Denmark)
Christensen, Ole; Hasannasab, Marzieh
2017-01-01
of the properties of the operator T requires more work. For example it is a delicate issue to obtain a representation with a bounded operator, and the availability of such a representation not only depends on the frame considered as a set, but also on the chosen indexing. Using results from operator theory we show......The purpose of this paper is to consider representations of frames {fk}k∈I in a Hilbert space ℋ of the form {fk}k∈I = {Tkf0}k∈I for a linear operator T; here the index set I is either ℤ or ℒ0. While a representation of this form is available under weak conditions on the frame, the analysis...... that by embedding the Hilbert space ℋ into a larger Hilbert space, we can always represent a frame via iterations of a bounded operator, composed with the orthogonal projection onto ℋ. The paper closes with a discussion of an open problem concerning representations of Gabor frames via iterations of a bounded...
International Nuclear Information System (INIS)
Khrennikov, A.
2005-01-01
We constructed the representation of contextual probabilistic dynamics in the complex Hilbert space. Thus dynamics of the wave function can be considered as Hilbert space projection of realistic dynamics in a pre space. The basic condition for representing the pre space-dynamics is the law of statistical conservation of energy-conservation of probabilities. The construction of the dynamical representation is an important step in the development of contextual statistical viewpoint of quantum processes. But the contextual statistical model is essentially more general than the quantum one. Therefore in general the Hilbert space projection of the pre space dynamics can be nonlinear and even irreversible (but it is always unitary). There were found conditions of linearity and reversibility of the Hilbert space dynamical projection. We also found conditions for the conventional Schrodinger dynamics (including time-dependent Hamiltonians). We remark that in general even the Schrodinger dynamics is based just on the statistical conservation of energy; for individual systems the law of conservation of energy can be violated (at least in our theoretical model)
The Political Representation of Women in Public Policy Management Councils
Directory of Open Access Journals (Sweden)
Lígia Helena Hahn Lüchmann
2010-06-01
Full Text Available This work raises some hypotheses to explain the significant presence of women on public policy management councils, which are spaces for discussion and deliberation of policies that have been implemented in Brazil in recent decades. The data about the profile of representatives on these spaces indicates a situation inversely proportional to the low degree of political inclusion of women in traditional spaces of political representation – executive positions, city councils, and state legislatures. There is thus a need to develop new analytical tools to understand the phenomenon of political representation. The data also question a reductive perspective of action and politics, which concludes that there is a low degree of political inclusion of women.
Space-by-time manifold representation of dynamic facial expressions for emotion categorization
Delis, Ioannis; Chen, Chaona; Jack, Rachael E.; Garrod, Oliver G. B.; Panzeri, Stefano; Schyns, Philippe G.
2016-01-01
Visual categorization is the brain computation that reduces high-dimensional information in the visual environment into a smaller set of meaningful categories. An important problem in visual neuroscience is to identify the visual information that the brain must represent and then use to categorize visual inputs. Here we introduce a new mathematical formalism—termed space-by-time manifold decomposition—that describes this information as a low-dimensional manifold separable in space and time. We use this decomposition to characterize the representations used by observers to categorize the six classic facial expressions of emotion (happy, surprise, fear, disgust, anger, and sad). By means of a Generative Face Grammar, we presented random dynamic facial movements on each experimental trial and used subjective human perception to identify the facial movements that correlate with each emotion category. When the random movements projected onto the categorization manifold region corresponding to one of the emotion categories, observers categorized the stimulus accordingly; otherwise they selected “other.” Using this information, we determined both the Action Unit and temporal components whose linear combinations lead to reliable categorization of each emotion. In a validation experiment, we confirmed the psychological validity of the resulting space-by-time manifold representation. Finally, we demonstrated the importance of temporal sequencing for accurate emotion categorization and identified the temporal dynamics of Action Unit components that cause typical confusions between specific emotions (e.g., fear and surprise) as well as those resolving these confusions. PMID:27305521
Braswell, Gregory S.
2015-01-01
This exploratory study examined children's experiences with producing and comprehending external representations in a preschool classroom. Data collection and analyses focused on how artifacts, spaces, adult-guided routines, and social conventions shape young children's representational development. Participants included 4- and…
Social Representations of Aids among rural and urban youngsters on the state of Minas Gerais
Directory of Open Access Journals (Sweden)
Margarete Moreira Coutinho e Silva
2014-12-01
Full Text Available This article analyzes the representations of rural and urban youngsters on the subject of aids. It aims to verify if the intensification of the interaction between country and city that provides increasing access to both spaces results in a symbolic homogeneity on some aspects of the disease. The technological progress and the physical mobility advance promote this approach, which provides information to rural youngsters that put them in situations of consonance of attitudes and vulnerabilities in comparison with the urban youngsters. The research used data based on the sample of 131 students from the Curso Técnico em Agropecuária of the federal institute IF Sudeste de Minas Gerais – Campus Barbacena – amongst whom 40 residents in rural areas. The results reveal that the youngsters assume they are aware of aids, but their responses to the questionnaire betray a state of high vulnerability to the disease. The analysis is guided by the social representation theories and shows that stereotypes about diseases remain instilled in the symbolic countryside, collaborating to the convergence of opinions and conducts.
Sum-over-histories representation for the causal Green function of free scalar field theory
International Nuclear Information System (INIS)
Rudolph, O.
1995-01-01
A set of Green functions scrG α (x-y), α element-of[0,2π] for free scalar field theory is introduced, varying between the Hadamard Green function Δ 1 (x-y)==left-angle 0|{cphi(x),cphi(y)}|0 right-angle and the causal Green function scrG π (x-y)=iΔ(x-y)==[cphi(x),cphi(y)]. For every α element-of[0,2π] a path integral representation for scrG α is obtained both in configuration space and in the phase space of the classical relativistic particle. Setting α=π a sum-over-histories representation for the causal Green function is obtained. Furthermore, a reduced phase space integral representation for the scrG α 's is stated and an alternative BRST path integral representation for scrG α is presented. From these path integral representations the composition laws for the scrG α 's are derived using a modified path decomposition expansion
Energy Technology Data Exchange (ETDEWEB)
Jarvis, P.D.; Corney, S.P.; Tsohantjis, I. [School of Mathematics and Physics, University of Tasmania, Hobart Tas (Australia)
1999-12-03
A covariant spinor representation of iosp(d,2/2) is constructed for the quantization of the spinning relativistic particle. It is found that, with appropriately defined wavefunctions, this representation can be identified with the state space arising from the canonical extended BFV-BRST quantization of the spinning particle with admissible gauge fixing conditions after a contraction procedure. For this model, the cohomological determination of physical states can thus be obtained purely from the representation theory of the iosp(d,2/2) algebra. (author)
Amputation and prosthesis implantation shape body and peripersonal space representations.
Canzoneri, Elisa; Marzolla, Marilena; Amoresano, Amedeo; Verni, Gennaro; Serino, Andrea
2013-10-03
Little is known about whether and how multimodal representations of the body (BRs) and of the space around the body (Peripersonal Space, PPS) adapt to amputation and prosthesis implantation. In order to investigate this issue, we tested BR in a group of upper limb amputees by means of a tactile distance perception task and PPS by means of an audio-tactile interaction task. Subjects performed the tasks with stimulation either on the healthy limb or the stump of the amputated limb, while wearing or not wearing their prosthesis. When patients performed the tasks on the amputated limb, without the prosthesis, the perception of arm length shrank, with a concurrent shift of PPS boundaries towards the stump. Conversely, wearing the prosthesis increased the perceived length of the stump and extended the PPS boundaries so as to include the prosthetic hand, such that the prosthesis partially replaced the missing limb.
25 CFR 16.3 - Legal representation in State courts.
2010-04-01
... Indians BUREAU OF INDIAN AFFAIRS, DEPARTMENT OF THE INTERIOR PROBATE ESTATES OF INDIANS OF THE FIVE CIVILIZED TRIBES § 16.3 Legal representation in State courts. The statutory duties of the Secretary to... necessary to discharge said duties, with due regard to the complexity of the legal action contemplated, the...
Poincaré Embeddings for Learning Hierarchical Representations
CERN. Geneva
2018-01-01
Abstracts: Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically do not account for this property. In this talk, I will discuss a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincaré ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincaré embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability. &...
Periodic Discordance Between Vote Equality and Representational Equality in the United States
Directory of Open Access Journals (Sweden)
Sarah K. Cowan
2015-08-01
Full Text Available American democracy has two central values that are often in tension: vote equality, that each vote has equal influence, and representational equality, that each elected official represents equal numbers of people. The electoral standard of “one person, one vote” ensures representational equality, and that often ensures vote equality. This relationship fails, however, under certain demographic conditions, namely, when a large, non-enfranchised population resides unevenly across jurisdictions. Then, representational equality is preserved and vote equality is violated. Prior to women’s suffrage, for example, western states had relatively fewer women than the remainder of the country, contributing to gross vote inequality, though rectified through extension of the franchise. Given recent high rates of immigration to some states, I ask whether the two values are in tension. I find that they are, and quantify the electoral consequences of this disjuncture at 13 House seats in 2010.
Metropolitan natural area protection to maximize public access and species representation
Jane A. Ruliffson; Robert G. Haight; Paul H. Gobster; Frances R. Homans
2003-01-01
In response to widespread urban development, local governments in metropolitan areas in the United States acquire and protect privately-owned open space. We addressed the planner's problem of allocating a fixed budget for open space protection among eligible natural areas with the twin objectives of maximizing public access and species representation. Both...
DEFF Research Database (Denmark)
Brander, David; Rossman, Wayne; Schmitt, Nicholas
2010-01-01
We give an infinite dimensional generalized Weierstrass representation for spacelike constant mean curvature (CMC) surfaces in Minkowski 3-space $\\R^{2,1}$. The formulation is analogous to that given by Dorfmeister, Pedit and Wu for CMC surfaces in Euclidean space, replacing the group $SU_2$ with...
Factorizations and physical representations
International Nuclear Information System (INIS)
Revzen, M; Khanna, F C; Mann, A; Zak, J
2006-01-01
A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the decomposition of M into prime numbers. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (Zak J 1970 Phys. Today 23 51), and related representations termed q 1 q 2 representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M
DEFF Research Database (Denmark)
Willett, Wesley; Jansen, Yvonne; Dragicevic, Pierre
2017-01-01
We introduce embedded data representations, the use of visual and physical representations of data that are deeply integrated with the physical spaces, objects, and entities to which the data refers. Technologies like lightweight wireless displays, mixed reality hardware, and autonomous vehicles...
Space-group approach to two-electron states in unconventional superconductors
International Nuclear Information System (INIS)
Yarzhemsky, V. G.
2008-01-01
The direct application of the space-group representation theory, makes possible to obtain limitations for the symmetry of SOP on lines and planes of symmetry in one-electron Brillouin zone. In the case of highly symmetric UPt 3 only theoretical nodal structure of IR E 2u is in agreement with all the experimental results. On the other hand, in the case of high-T c superconductors the two electron description of Cooper pairs in D 2h symmetry is not sufficient to describe experimental nodal structure. It was shown that in this case, the nodal structure is the result of underlying interactions between two-electron states and hidden symmetry D-4 h . (author)
Categorification and higher representation theory
Beliakova, Anna
2017-01-01
The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorified representation theory, or higher representation theory, aims to understand a new level of structure present in representation theory. Rather than studying actions of algebras on vector spaces where algebra elements act by linear endomorphisms of the vector space, higher representation theory describes the structure present when algebras act on categories, with algebra elements acting by functors. The new level of structure in higher representation theory arises by studying the natural transformations between functors. This enhanced perspective brings into play a powerful new set of tools that deepens our understanding of traditional representation theory. This volume exhibits some of the current trends in higher representation theory and the diverse te...
Investigation of multidimensional control systems in the state space and wavelet medium
Fedosenkov, D. B.; Simikova, A. A.; Fedosenkov, B. A.
2018-05-01
The notions are introduced of “one-dimensional-point” and “multidimensional-point” automatic control systems. To demonstrate the joint use of approaches based on the concepts of state space and wavelet transforms, a method for optimal control in a state space medium represented in the form of time-frequency representations (maps), is considered. The computer-aided control system is formed on the basis of the similarity transformation method, which makes it possible to exclude the use of reduced state variable observers. 1D-material flow signals formed by primary transducers are converted by means of wavelet transformations into multidimensional concentrated-at-a point variables in the form of time-frequency distributions of Cohen’s class. The algorithm for synthesizing a stationary controller for feeding processes is given here. The conclusion is made that the formation of an optimal control law with time-frequency distributions available contributes to the improvement of transient processes quality in feeding subsystems and the mixing unit. Confirming the efficiency of the method presented is illustrated by an example of the current registration of material flows in the multi-feeding unit. The first section in your paper.
Signal Sampling for Efficient Sparse Representation of Resting State FMRI Data
Ge, Bao; Makkie, Milad; Wang, Jin; Zhao, Shijie; Jiang, Xi; Li, Xiang; Lv, Jinglei; Zhang, Shu; Zhang, Wei; Han, Junwei; Guo, Lei; Liu, Tianming
2015-01-01
As the size of brain imaging data such as fMRI grows explosively, it provides us with unprecedented and abundant information about the brain. How to reduce the size of fMRI data but not lose much information becomes a more and more pressing issue. Recent literature studies tried to deal with it by dictionary learning and sparse representation methods, however, their computation complexities are still high, which hampers the wider application of sparse representation method to large scale fMRI datasets. To effectively address this problem, this work proposes to represent resting state fMRI (rs-fMRI) signals of a whole brain via a statistical sampling based sparse representation. First we sampled the whole brain’s signals via different sampling methods, then the sampled signals were aggregate into an input data matrix to learn a dictionary, finally this dictionary was used to sparsely represent the whole brain’s signals and identify the resting state networks. Comparative experiments demonstrate that the proposed signal sampling framework can speed-up by ten times in reconstructing concurrent brain networks without losing much information. The experiments on the 1000 Functional Connectomes Project further demonstrate its effectiveness and superiority. PMID:26646924
Exploring the Structure of Spatial Representations
Madl, Tamas; Franklin, Stan; Chen, Ke; Trappl, Robert; Montaldi, Daniela
2016-01-01
It has been suggested that the map-like representations that support human spatial memory are fragmented into sub-maps with local reference frames, rather than being unitary and global. However, the principles underlying the structure of these ‘cognitive maps’ are not well understood. We propose that the structure of the representations of navigation space arises from clustering within individual psychological spaces, i.e. from a process that groups together objects that are close in these spaces. Building on the ideas of representational geometry and similarity-based representations in cognitive science, we formulate methods for learning dissimilarity functions (metrics) characterizing participants’ psychological spaces. We show that these learned metrics, together with a probabilistic model of clustering based on the Bayesian cognition paradigm, allow prediction of participants’ cognitive map structures in advance. Apart from insights into spatial representation learning in human cognition, these methods could facilitate novel computational tools capable of using human-like spatial concepts. We also compare several features influencing spatial memory structure, including spatial distance, visual similarity and functional similarity, and report strong correlations between these dimensions and the grouping probability in participants’ spatial representations, providing further support for clustering in spatial memory. PMID:27347681
Induced representations of the affine group and intertwining operators: I. Analytical approach
International Nuclear Information System (INIS)
Elmabrok, Abdelhamid S; Hutník, Ondrej
2012-01-01
We analyze the construction and origin of unitary operators describing the structure of the space of continuous wavelet transforms inside the space L 2 (G,dν L ) of all square-integrable functions on the affine group G with respect to the left-invariant Haar measure from the viewpoint of induced representations of G. We show that these operators are, in fact, intertwining operators among pairs of induced representations of the affine group G. A characterization of the space of wavelet transforms using the Cauchy–Riemann-type equations is given. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)
Condensed State Spaces for Symmetrical Coloured Petri Nets
DEFF Research Database (Denmark)
Jensen, Kurt
1996-01-01
equivalence classes of states and equivalence classes of state changes. It is then possible to construct a condensed state space where each node represents an equivalence class of states while each arc represents an equivalence class of state changes. Such a condensed state space is often much smaller than...... the full state space and it is also much faster to construct. Nevertheless, it is possible to use the condensed state space to verify the same kind of behavioural properties as the full state space. Hence, we do not lose analytic power. We define state spaces and condensed state spaces for a language......-nets (or Petri nets in general) - although such knowledge will, of course, be a help. The first four sections of the paper introduce the basic concepts of CP-nets. The next three sections deal with state spaces, condensed state spaces and computer tools for state space analysis. Finally, there is a short...
Volume of the space of qubit-qubit channels and state transformations under random quantum channels
Lovas, Attila; Andai, Attila
2017-01-01
The simplest building blocks for quantum computations are the qubit-qubit quantum channels. In this paper, we analyze the structure of these channels via their Choi representation. The restriction of a quantum channel to the space of classical states (i.e. probability distributions) is called the underlying classical channel. The structure of quantum channels over a fixed classical channel is studied, the volume of general and unital qubit channels with respect to the Lebesgue measure is comp...
Energy Technology Data Exchange (ETDEWEB)
Hoff da Silva, J.M.; Rogerio, R.J.B. [Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil); Villalobos, C.H.C. [Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil); Universidade Federal Fluminense, Instituto de Fisica, Niteroi, RJ (Brazil); Rocha, Roldao da [Universidade Federal do ABC-UFABC, Centro de Matematica, Computacao e Cognicao, Santo Andre (Brazil)
2017-07-15
A systematic study of the spinor representation by means of the fermionic physical space is accomplished and implemented. The spinor representation space is shown to be constrained by the Fierz-Pauli-Kofink identities among the spinor bilinear covariants. A robust geometric and topological structure can be manifested from the spinor space, wherein the first and second homotopy groups play prominent roles on the underlying physical properties, associated to fermionic fields. The mapping that changes spinor fields classes is then exemplified, in an Einstein-Dirac system that provides the spacetime generated by a fermion. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Zuniga Segundo, A. [Instituto Politecnico Nacional, Mexico, D.F. (Mexico)
2001-10-01
In this work we introduce squeezed states with real and complex squeezing parameters directly obtained in the coherent-representation of the harmonic oscillator in quantum phase space. By means of the Fourier transform, we recover the usual coordinate states and compare these states with those obtained by another method in the coordinate representation. In addition we also describe numerically its time evolution in quantum phase space and the variances Q and P. [Spanish] En este trabajo presentamos estados comprimidos con parametros de compresion reales y complejos, obtenidos directamente en la representacion de estado coherente del oscilador armonico en el espacio fase cuantico. Por medio de una transformada de Fourier recuperamos los estados en la representacion de coordenadas y los comparamos con aquellos obtenidos por otro metodo. Ademas describimos numericamente sus evoluciones temporales en el espacio fase cuantico y calculamos las varianzas de Q y P.
Ground state representation of the infinite one-dimensional Heisenberg ferromagnet. Pt. 2
International Nuclear Information System (INIS)
Babbitt, D.; Thomas, L.
1977-01-01
In its ground state representation, the infinite, spin 1/2 Heisenberg chain provides a model for spin wave scattering, which entails many features of the quantum mechanical N-body problem. Here, we give a complete eigenfunction expansion for the Hamiltonian of the chain in this representation, for all numbers of spin waves. Our results resolve the questions of completeness and orthogonality of the eigenfunctions given by Bethe for finite chains, in the infinite volume limit. (orig.) [de
Defining Spaces of Potential Art: The significance of representation in computer-aided creativity
DEFF Research Database (Denmark)
Dahlstedt, Palle
2005-01-01
One way of looking at the creative process is as a search in a space of possible answers. One way of simulating such a process is through evolutionary algorithms, i.e., simulated evolution by random variation and selection. The search space is defined by the chosen genetic representation, a kind...... of formal description, and the ways of navigating the space are defined by the choice of genetic operators (e.g., mutations). In creative systems, such as computer-aided music composition tools, these choices determine the efficiency of the system, in terms of the diversity of the results, the degree...... of novelty and the coherence within the material. Based on various implementations developed during five years of research, and experiences from real-life artistic applications, I will explain and discuss these mechanisms, from a perspective of the creative artist....
My Life with State Space Models
DEFF Research Database (Denmark)
Lundbye-Christensen, Søren
2007-01-01
. The conceptual idea behind the state space model is that the evolution over time in the object we are observing and the measurement process itself are modelled separately. My very first serious analysis of a data set was done using a state space model, and since then I seem to have been "haunted" by state space...
Covariant representations of nuclear *-algebras
International Nuclear Information System (INIS)
Moore, S.M.
1978-01-01
Extensions of the Csup(*)-algebra theory for covariant representations to nuclear *-algebra are considered. Irreducible covariant representations are essentially unique, an invariant state produces a covariant representation with stable vacuum, and the usual relation between ergodic states and covariant representations holds. There exist construction and decomposition theorems and a possible relation between derivations and covariant representations
Representation of Concrete Logics and Concrete Generalized Orthomodular Posets
Pulmannová, S.; Riečanová, Z.; Vinceková, E.
2014-04-01
In the present paper, we deal with the question when an effect algebra, resp. a generalized effect algebra, can be represented in the projection lattice of a Hilbert space. We show that such representability is closely related to the existence of a rich set of two-valued and Jauch-Piron states, resp. generalized two-valued and Jauch-Piron states. AMS Classification: Primary 81Q10, Secondary 03G12.
An alternative to scale-space representation for extracting local features in image recognition
DEFF Research Database (Denmark)
Andersen, Hans Jørgen; Nguyen, Phuong Giang
2012-01-01
In image recognition, the common approach for extracting local features using a scale-space representation has usually three main steps; first interest points are extracted at different scales, next from a patch around each interest point the rotation is calculated with corresponding orientation...... and compensation, and finally a descriptor is computed for the derived patch (i.e. feature of the patch). To avoid the memory and computational intensive process of constructing the scale-space, we use a method where no scale-space is required This is done by dividing the given image into a number of triangles...... with sizes dependent on the content of the image, at the location of each triangle. In this paper, we will demonstrate that by rotation of the interest regions at the triangles it is possible in grey scale images to achieve a recognition precision comparable with that of MOPS. The test of the proposed method...
A robust state-space kinetics-guided framework for dynamic PET image reconstruction
International Nuclear Information System (INIS)
Tong, S; Alessio, A M; Kinahan, P E; Liu, H; Shi, P
2011-01-01
Dynamic PET image reconstruction is a challenging issue due to the low SNR and the large quantity of spatio-temporal data. We propose a robust state-space image reconstruction (SSIR) framework for activity reconstruction in dynamic PET. Unlike statistically-based frame-by-frame methods, tracer kinetic modeling is incorporated to provide physiological guidance for the reconstruction, harnessing the temporal information of the dynamic data. Dynamic reconstruction is formulated in a state-space representation, where a compartmental model describes the kinetic processes in a continuous-time system equation, and the imaging data are expressed in a discrete measurement equation. Tracer activity concentrations are treated as the state variables, and are estimated from the dynamic data. Sampled-data H ∞ filtering is adopted for robust estimation. H ∞ filtering makes no assumptions on the system and measurement statistics, and guarantees bounded estimation error for finite-energy disturbances, leading to robust performance for dynamic data with low SNR and/or errors. This alternative reconstruction approach could help us to deal with unpredictable situations in imaging (e.g. data corruption from failed detector blocks) or inaccurate noise models. Experiments on synthetic phantom and patient PET data are performed to demonstrate feasibility of the SSIR framework, and to explore its potential advantages over frame-by-frame statistical reconstruction approaches.
International Nuclear Information System (INIS)
Bach, A.
1981-01-01
A representation of quantum mechanics in terms of classical probability theory by means of integration in Hilbert space is discussed. This formal hidden-variables representation is analysed in the context of impossibility proofs concerning hidden-variables theories. The structural analogy of this formulation of quantum theory with classical statistical mechanics is used to elucidate the difference between classical mechanics and quantum mechanics. (author)
Conformal symmetry in two-dimensional space: recursion representation of conformal block
International Nuclear Information System (INIS)
Zamolodchikov, A.B.
1988-01-01
The four-point conformal block plays an important part in the analysis of the conformally invariant operator algebra in two-dimensional space. The behavior of the conformal block is calculated in the present paper in the limit in which the dimension Δ of the intermediate operator tends to infinity. This makes it possible to construct a recursion relation for this function that connects the conformal block at arbitrary Δ to the blocks corresponding to the dimensions of the zero vectors in the degenerate representations of the Virasoro algebra. The relation is convenient for calculating the expansion of the conformal block in powers of the uniformizing parameters q = i π tau
Graphical representation of objects' states for the PF linac control system
International Nuclear Information System (INIS)
Mejuev, I.; Abe, I.; Nakahara, K.
1995-01-01
This paper describes our approach for creating of a graphical representation of the states of accelerator objects. For every object which needs to display its state dynamics we create a chart element. Any changes in the object state are immediately represented on the chart of this object. We use the objects dependencies facility supplied by Smalltalk to keep track of the objects' states changes. This allows us to remove any graphics related features from the Object Model of the accelerator. Thus, the Object Model can be developed separately and reused in a number of applications. (author)
Gauge freedom in the representations of BRS algebra
International Nuclear Information System (INIS)
Nishijima, K.
1989-01-01
The study of the representations of BRS algebra plays an important role in the physical interpretation of non-abelian gauge theories. The entire state vector space is decomposed into a direct sum of the singlet, daughter and parent subspaces by exploiting BRS algebra. This decomposition is not unique, however, and an inquiry is made into the nature of this arbitrariness
Directory of Open Access Journals (Sweden)
Mariangela Albano
2016-12-01
Full Text Available Many tourist services are connected to the care of the body. The tourist industry proposes different vacation opportunities where the body is the main focus of the experience. This kind of tourism implies specific services that show a particular universe of representation and particular languages. In this context, cruise tourism is an interesting case to analyze because a part of its services gives a central role to the body which, on-board, organizes and is organized within dedicated spaces and times. Cruise ships provide spaces for the wellness of the passengers such as swimming pools, gyms, spas or beauty centres. The analysis proposed in this work is based, on one hand, on a recent anthropological fieldwork on a Costa Crociere cruise in the Mediterranean Sea. On cruises people use a limited space, the ship, in different ways. This use also reflects a particular conception of the body, built through an interaction of different systems of representation. So, the ship can become a space for social aggregation or separation. On the other hand, this study considers different textual advertisements from the Costa Web site where the company presents specific services for the body to future passengers . This paper analyzes them using a joint approach: both semiotic and linguistic. Through texts and pictures Costa Crociere creates a “synthesis” of the wellness spaces which prefiguresthe behaviour of the passengers on the cruise. More particularly, in order to analyze advertisements, a cognitive linguistics approach is suitable to show the authors’ linguistic choices and the paratextual elements used to promote the cruise. .
Impact of the basic state and MJO representation on MJO Pacific teleconnections in GCMs
Henderson, S. A.; Maloney, E. D.; Son, S. W.
2017-12-01
Teleconnection patterns induced by the Madden-Julian Oscillation (MJO) are known to significantly alter extratropical weather and climate patterns. However, accurate MJO representation has been difficult for many General Circulation Models (GCMs). Furthermore, many GCMs contain large basic state biases. These issues present challenges to the simulation of MJO teleconnections and, in turn, their associated extratropical impacts. This study examines the impacts of basic state quality and MJO representation on the quality of MJO teleconnection patterns in GCMs from phase 5 of the Coupled Model Intercomparison Project (CMIP5). Results suggest that GCMs assessed to have a good MJO but with large basic state biases have similarly low skill in reproducing MJO teleconnections as GCMs with poor MJO representation. In the good MJO models examined, poor teleconnection quality is associated with large errors in the zonal extent of the Pacific subtropical jet. Whereas the horizontal structure of MJO heating in the Indo-Pacific region is found to have modest impacts on the teleconnection patterns, results suggest that MJO heating east of the dateline can alter the teleconnection pattern characteristics over North America. These findings suggest that in order to accurately simulate the MJO teleconnection patterns and associated extratropical impacts, both the MJO and the basic state must be well represented.
State Space Analysis of Hierarchical Coloured Petri Nets
DEFF Research Database (Denmark)
Christensen, Søren; Kristensen, Lars Michael
2003-01-01
In this paper, we consider state space analysis of Coloured Petri Nets. It is well-known that almost all dynamic properties of the considered system can be verified when the state space is finite. However, state space analysis is more than just formulating a set of formal requirements and invokin...... supporting computation and storage of state spaces which exploi the hierarchical structure of the models....... in which formal verification, partial state spaces, and analysis by means of graphical feedback and simulation are integrated entities. The focus of the paper is twofold: the support for graphical feedback and the way it has been integrated with simulation, and the underlying algorithms and data-structures......In this paper, we consider state space analysis of Coloured Petri Nets. It is well-known that almost all dynamic properties of the considered system can be verified when the state space is finite. However, state space analysis is more than just formulating a set of formal requirements and invoking...
Statistical Software for State Space Methods
Directory of Open Access Journals (Sweden)
Jacques J. F. Commandeur
2011-05-01
Full Text Available In this paper we review the state space approach to time series analysis and establish the notation that is adopted in this special volume of the Journal of Statistical Software. We first provide some background on the history of state space methods for the analysis of time series. This is followed by a concise overview of linear Gaussian state space analysis including the modelling framework and appropriate estimation methods. We discuss the important class of unobserved component models which incorporate a trend, a seasonal, a cycle, and fixed explanatory and intervention variables for the univariate and multivariate analysis of time series. We continue the discussion by presenting methods for the computation of different estimates for the unobserved state vector: filtering, prediction, and smoothing. Estimation approaches for the other parameters in the model are also considered. Next, we discuss how the estimation procedures can be used for constructing confidence intervals, detecting outlier observations and structural breaks, and testing model assumptions of residual independence, homoscedasticity, and normality. We then show how ARIMA and ARIMA components models fit in the state space framework to time series analysis. We also provide a basic introduction for non-Gaussian state space models. Finally, we present an overview of the software tools currently available for the analysis of time series with state space methods as they are discussed in the other contributions to this special volume.
State Space Methods for Timed Petri Nets
DEFF Research Database (Denmark)
Christensen, Søren; Jensen, Kurt; Mailund, Thomas
2001-01-01
it possible to condense the usually infinite state space of a timed Petri net into a finite condensed state space without loosing analysis power. The second method supports on-the-fly verification of certain safety properties of timed systems. We discuss the application of the two methods in a number......We present two recently developed state space methods for timed Petri nets. The two methods reconciles state space methods and time concepts based on the introduction of a global clock and associating time stamps to tokens. The first method is based on an equivalence relation on states which makes...
Directory of Open Access Journals (Sweden)
Tomas eVeloz
2015-11-01
Full Text Available Quantum models of concept combinations have been successful in representing various experimental situations that cannot be accommodated by traditional models based on classical probability or fuzzy set theory. In many cases, the focus has been on producing a representation that fits experimental results to validate quantum models. However, these representations are not always consistent with the cognitive modeling principles. Moreover, some important issues related to the representation of concepts such as the dimensionality of the realization space, the uniqueness of solutions, and the compatibility of measurements, have been overlooked.In this paper, we provide a dimensional analysis of the realization space for the two-sector Fock space model for conjunction of concepts focusing on the first and second sectors separately. We then introduce various representation of concepts that arise from the use of unitary operators in the realization space. In these concrete representations, a pair of concepts and their combination are modeled by a single conceptual state, and by a collection of exemplar-dependent operators. Therefore, they are consistent with cognitive modeling principles. %Moreover, we show that each representation is unique up to change of basis. This framework not only provides a uniform approach to model an entire data set, but, because all measurement operators are expressed in the same basis, allows us to address the question of compatibility of measurements. In particular, we present evidence that it may be possible to predict non-commutative effects from partial measurements of conceptual combinations.
2010-04-01
... liability. (b) Criminal proceedings. Only the Federal Government shall have the right to bring a criminal... representation of State interests. (a) Civil proceedings—(1) General rule. Any person shall have the same right... procedures under State law. (2) Exception. The right or power of the courts of any State to pass on matters...
Multiscale wavelet representations for mammographic feature analysis
Laine, Andrew F.; Song, Shuwu
1992-12-01
This paper introduces a novel approach for accomplishing mammographic feature analysis through multiresolution representations. We show that efficient (nonredundant) representations may be identified from digital mammography and used to enhance specific mammographic features within a continuum of scale space. The multiresolution decomposition of wavelet transforms provides a natural hierarchy in which to embed an interactive paradigm for accomplishing scale space feature analysis. Choosing wavelets (or analyzing functions) that are simultaneously localized in both space and frequency, results in a powerful methodology for image analysis. Multiresolution and orientation selectivity, known biological mechanisms in primate vision, are ingrained in wavelet representations and inspire the techniques presented in this paper. Our approach includes local analysis of complete multiscale representations. Mammograms are reconstructed from wavelet coefficients, enhanced by linear, exponential and constant weight functions localized in scale space. By improving the visualization of breast pathology we can improve the changes of early detection of breast cancers (improve quality) while requiring less time to evaluate mammograms for most patients (lower costs).
Learning connective-based word representations for implicit discourse relation identification
DEFF Research Database (Denmark)
Braud, Chloé Elodie; Denis, Pascal
2016-01-01
We introduce a simple semi-supervised ap-proach to improve implicit discourse relation identification. This approach harnesses large amounts of automatically extracted discourse connectives along with their arguments to con-struct new distributional word representations. Specifically, we represen...... their simplicity, these connective-based rep-resentations outperform various off-the-shelf word embeddings, and achieve state-of-the-art performance on this problem.......We introduce a simple semi-supervised ap-proach to improve implicit discourse relation identification. This approach harnesses large amounts of automatically extracted discourse connectives along with their arguments to con-struct new distributional word representations. Specifically, we represent...... words in the space of discourse connectives as a way to directly encode their rhetorical function. Experiments on the Penn Discourse Treebank demonstrate the effectiveness of these task-tailored repre-sentations in predicting implicit discourse re-lations. Our results indeed show that, despite...
Chern--Simons theory in the Schroedinger representation
International Nuclear Information System (INIS)
Dunne, G.V.; Jackiw, R.; Trugenberger, C.A.
1989-01-01
We quantize the (2+1)-dimensional Chern--Simons theory in the functional Schroedinger representation. The realization of gauge transformations on states involves a 1-cocycle. We determine this cocycle; we show how solving the Gauss law constraint in the non-Abelian theory requires quantizing the parameter that normalizes the action; we trivialize the 1-cocycle with a spatially non-local cochain related to a 2-dimensional fermion determinant and we find the physical states that satisfy the Gauss law constraint. The quantum holonomy of physical states involves a contribution that is missed when the constraint is solved before quantization. We compute this quantity for the Abelian theory in Minkowski space, where it exhibits an interesting group theoretic structure. (In a note added in proof the corresponding non-Abelian computation is presented.) Also we consider coupling to external sources and offer yet another derivation of the anomalous statistics and spin of the charge and flux carrying particles---a calculation which is especially simple in the functional Schroedinger representation. copyright 1989 Academic Press, Inc
Unitary Transformations in 3 D Vector Representation of Qutrit States
2018-03-12
ARL-TR-8330 ● MAR 2018 US Army Research Laboratory Unitary Transformations in 3- D Vector Representation of Qutrit States by...return it to the originator. ARL-TR-8330 ● MAR 2018 US Army Research Laboratory Unitary Transformations in 3- D Vector...2018 2. REPORT TYPE Technical Report 3. DATES COVERED June–December 2017 4. TITLE AND SUBTITLE Unitary Transformations in 3- D Vector
Bispo Júnior, José Patrício; Gerschman, Sílvia
2015-01-01
The electoral representation model is insufficient and inadequate for new participatory roles such as those played by members of health councils. This article analyzes representation and representativeness in the Bahia State Health Council, Brazil. The study included interviews with 20 current or former members of the State Health Council, analysis of the council minutes and bylaws, and observation of plenary meetings. Discourse analysis technique was used to analyze interventions by members. The article discusses the results in four analytical lines: the process by which various organizations name representatives to the Council; the relationship between Council members and their constituencies; interest representation in the Council; and criteria used by the plenary to take positions. The study reveals various problems with the representativeness of the Bahia State Health Council and discusses the peculiarities of representation in social participation forums and the characteristics that give legitimacy to representatives.
Veloz, Tomas; Desjardins, Sylvie
2015-01-01
Quantum models of concept combinations have been successful in representing various experimental situations that cannot be accommodated by traditional models based on classical probability or fuzzy set theory. In many cases, the focus has been on producing a representation that fits experimental results to validate quantum models. However, these representations are not always consistent with the cognitive modeling principles. Moreover, some important issues related to the representation of concepts such as the dimensionality of the realization space, the uniqueness of solutions, and the compatibility of measurements, have been overlooked. In this paper, we provide a dimensional analysis of the realization space for the two-sector Fock space model for conjunction of concepts focusing on the first and second sectors separately. We then introduce various representation of concepts that arise from the use of unitary operators in the realization space. In these concrete representations, a pair of concepts and their combination are modeled by a single conceptual state, and by a collection of exemplar-dependent operators. Therefore, they are consistent with cognitive modeling principles. This framework not only provides a uniform approach to model an entire data set, but, because all measurement operators are expressed in the same basis, allows us to address the question of compatibility of measurements. In particular, we present evidence that it may be possible to predict non-commutative effects from partial measurements of conceptual combinations.
Recursion method in the k-space representation
International Nuclear Information System (INIS)
Anlage, S.M.; Smith, D.L.
1986-01-01
We show that by using a unitary transformation to k space and the special-k-point method for evaluating Brillouin-zone sums, the recursion method can be very effectively applied to translationally invariant systems. We use this approach to perform recursion calculations for realistic tight-binding Hamiltonians which describe diamond- and zinc-blende-structure semiconductors. Projected densities of states for these Hamiltonians have band gaps and internal van Hove singularities. We calculate coefficients for 63 recursion levels exactly and for about 200 recursion levels to a good approximation. Comparisons are made for materials with different magnitude band gaps (diamond, Si, α-Sn). Comparison is also made between materials with one (e.g., diamond) and two (e.g., GaAs) band gaps. The asymptotic behavior of the recursion coefficients is studied by Fourier analysis. Band gaps in the projected density of states dominate the asymptotic behavior. Perturbation analysis describes the asymptotic behavior rather well. Projected densities of states are calculated using a very simple termination scheme. These densities of states compare favorably with the results of Gilat-Raubenheimer integration
Discretized representations of harmonic variables by bilateral Jacobi operators
Directory of Open Access Journals (Sweden)
Andreas Ruffing
2000-01-01
Full Text Available Starting from a discrete Heisenberg algebra we solve several representation problems for a discretized quantum oscillator in a weighted sequence space. The Schrödinger operator for a discrete harmonic oscillator is derived. The representation problem for a q-oscillator algebra is studied in detail. The main result of the article is the fact that the energy representation for the discretized momentum operator can be interpreted as follows: It allows to calculate quantum properties of a large number of non-interacting harmonic oscillators at the same time. The results can be directly related to current research on squeezed laser states in quantum optics. They reveal and confirm the observation that discrete versions of continuum Schrodinger operators allow more structural freedom than their continuum analogs do.
Physics student ideas on quantum state and its formal representations
International Nuclear Information System (INIS)
Zuccarini, G.
2014-01-01
Developing a quantum way of thinking is a core and challenging task for physics students. The concept of quantum state, whose physical meaning is connected to the formal structure of the theory, plays an important role in the construction of a quantum perspective and in student difficulties elicited by research. A questionnaire and interview protocol were devised to explore student understanding of the state concept in connection to the properties of its formal representations and to quantum behavior. Results of a calibration of research instruments performed on 6 physics students from different universities are here presented.
Graph Regularized Auto-Encoders for Image Representation.
Yiyi Liao; Yue Wang; Yong Liu
2017-06-01
Image representation has been intensively explored in the domain of computer vision for its significant influence on the relative tasks such as image clustering and classification. It is valuable to learn a low-dimensional representation of an image which preserves its inherent information from the original image space. At the perspective of manifold learning, this is implemented with the local invariant idea to capture the intrinsic low-dimensional manifold embedded in the high-dimensional input space. Inspired by the recent successes of deep architectures, we propose a local invariant deep nonlinear mapping algorithm, called graph regularized auto-encoder (GAE). With the graph regularization, the proposed method preserves the local connectivity from the original image space to the representation space, while the stacked auto-encoders provide explicit encoding model for fast inference and powerful expressive capacity for complex modeling. Theoretical analysis shows that the graph regularizer penalizes the weighted Frobenius norm of the Jacobian matrix of the encoder mapping, where the weight matrix captures the local property in the input space. Furthermore, the underlying effects on the hidden representation space are revealed, providing insightful explanation to the advantage of the proposed method. Finally, the experimental results on both clustering and classification tasks demonstrate the effectiveness of our GAE as well as the correctness of the proposed theoretical analysis, and it also suggests that GAE is a superior solution to the current deep representation learning techniques comparing with variant auto-encoders and existing local invariant methods.
Projective loop quantum gravity. I. State space
Lanéry, Suzanne; Thiemann, Thomas
2016-12-01
Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In a latter work by Okolów, the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels. If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that the projective approach allows for a more balanced treatment of the holonomy and flux variables, so it might pave the way for the development of more satisfactory coherent states.
Representations of locally symmetric spaces
International Nuclear Information System (INIS)
Rahman, M.S.
1995-09-01
Locally symmetric spaces in reference to globally and Hermitian symmetric Riemannian spaces are studied. Some relations between locally and globally symmetric spaces are exhibited. A lucid account of results on relevant spaces, motivated by fundamental problems, are formulated as theorems and propositions. (author). 10 refs
Gender and Space: Analysis of Factors Conditioning Equity in the Public Space
Directory of Open Access Journals (Sweden)
Pablo Paramo Bernal
2011-01-01
Full Text Available This article discusses gender research in urban public space through three different perspectives: the social representations and differentiated uses of space, the division of roles in public and private spaces, and urban planning of public space. The paper gathers and analyses some studies that complement the state of art and literature on women and space giving evidence on how women have been segregated from public space and are victim of gender inequalities. Public space does not exist absolutely nor gender; instead both are socially constructed by social order and reproduced by social practices. Finally, some suggestions for urban planning and research are given in order to respond women’s needs in public space.
International Nuclear Information System (INIS)
Cohen, Scott M.
2014-01-01
We give a sufficient condition that an operator sum representation of a separable quantum channel in terms of product operators is the unique product representation for that channel, and then provide examples of such channels for any number of parties. This result has implications for efforts to determine whether or not a given separable channel can be exactly implemented by local operations and classical communication. By the Choi-Jamiolkowski isomorphism, it also translates to a condition for the uniqueness of product state ensembles representing a given quantum state. These ideas follow from considerations concerning whether or not a subspace spanned by a given set of product operators contains at least one additional product operator
Neural representations of emotion are organized around abstract event features.
Skerry, Amy E; Saxe, Rebecca
2015-08-03
Research on emotion attribution has tended to focus on the perception of overt expressions of at most five or six basic emotions. However, our ability to identify others' emotional states is not limited to perception of these canonical expressions. Instead, we make fine-grained inferences about what others feel based on the situations they encounter, relying on knowledge of the eliciting conditions for different emotions. In the present research, we provide convergent behavioral and neural evidence concerning the representations underlying these concepts. First, we find that patterns of activity in mentalizing regions contain information about subtle emotional distinctions conveyed through verbal descriptions of eliciting situations. Second, we identify a space of abstract situation features that well captures the emotion discriminations subjects make behaviorally and show that this feature space outperforms competing models in capturing the similarity space of neural patterns in these regions. Together, the data suggest that our knowledge of others' emotions is abstract and high dimensional, that brain regions selective for mental state reasoning support relatively subtle distinctions between emotion concepts, and that the neural representations in these regions are not reducible to more primitive affective dimensions such as valence and arousal. Copyright © 2015 Elsevier Ltd. All rights reserved.
Relativistic algebraic spinors and quantum motions in phase space
International Nuclear Information System (INIS)
Holland, P.R.
1986-01-01
Following suggestions of Schonberg and Bohm, we study the tensorial phase space representation of the Dirac and Feynman-Gell-Mann equations in terms of the complex Dirac algebra C 4 , a Jordan-Wigner algebra G 4 , and Wigner transformations. To do this we solve the problem of the conditions under which elements in C 4 generate minimal ideals, and extend this to G 4 . This yields the linear theory of Dirac spin spaces and tensor representations of Dirac spinors, and the spin-1/2 wave equations are represented through fermionic state vectors in a higher space as a set of interconnected tensor relations
Physical Fock space of tensionless strings
Antoniadis, Ignatios; Antoniadis, Ignatios; Savvidy, George
2004-01-01
We study the physical Fock space of the tensionless string theory with perimeter action which has pure massless spectrum. The states are classified by the Wigner's little group for massless particles. The ground state contains infinite many massless fields of fixed helicity, the excitation levels realize CSR representations. We demonstrate that the first and the second excitation levels are physical null states.
State-Space Formulation for Circuit Analysis
Martinez-Marin, T.
2010-01-01
This paper presents a new state-space approach for temporal analysis of electrical circuits. The method systematically obtains the state-space formulation of nondegenerate linear networks without using concepts of topology. It employs nodal/mesh systematic analysis to reduce the number of undesired variables. This approach helps students to…
van der Laarse, R.; Reijnen, C.; Mazzucchelli, F.
2014-01-01
Traces of Terror, Signs of Trauma. Practices of (Re)Presentation of Collective Memory in Space in Contemporary Europe Edited by Rob van der Laarse, Francesco Mazzucchelli, Carlos Reijnen This special issue of Vs. – Quaderni di studi semiotici edited by Rob van der Laarse, Francesco Mazzucchelli and
MODELING OF DYNAMIC SYSTEMS WITH MODULATION BY MEANS OF KRONECKER VECTOR-MATRIX REPRESENTATION
Directory of Open Access Journals (Sweden)
A. S. Vasilyev
2015-09-01
Full Text Available The paper deals with modeling of dynamic systems with modulation by the possibilities of state-space method. This method, being the basis of modern control theory, is based on the possibilities of vector-matrix formalism of linear algebra and helps to solve various problems of technical control of continuous and discrete nature invariant with respect to the dimension of their “input-output” objects. Unfortunately, it turned its back on the wide group of control systems, which hardware environment modulates signals. The marked system deficiency is partially offset by this paper, which proposes Kronecker vector-matrix representations for purposes of system representation of processes with signal modulation. The main result is vector-matrix representation of processes with modulation with no formal difference from continuous systems. It has been found that abilities of these representations could be effectively used in research of systems with modulation. Obtained model representations of processes with modulation are best adapted to the state-space method. These approaches for counting eigenvalues of Kronecker matrix summaries, that are matrix basis of model representations of processes described by Kronecker vector products, give the possibility to use modal direction in research of dynamics for systems with modulation. It is shown that the use of controllability for eigenvalues of general matrixes applied to Kronecker structures enabled to divide successfully eigenvalue spectrum into directed and not directed components. Obtained findings including design problems for models of dynamic processes with modulation based on the features of Kronecker vector and matrix structures, invariant with respect to the dimension of input-output relations, are applicable in the development of alternate current servo drives.
Unitary Representations of Gauge Groups
Huerfano, Ruth Stella
I generalize to the case of gauge groups over non-trivial principal bundles representations that I. M. Gelfand, M. I. Graev and A. M. Versik constructed for current groups. The gauge group of the principal G-bundle P over M, (G a Lie group with an euclidean structure, M a compact, connected and oriented manifold), as the smooth sections of the associated group bundle is presented and studied in chapter I. Chapter II describes the symmetric algebra associated to a Hilbert space, its Hilbert structure, a convenient exponential and a total set that later play a key role in the construction of the representation. Chapter III is concerned with the calculus needed to make the space of Lie algebra valued 1-forms a Gaussian L^2-space. This is accomplished by studying general projective systems of finitely measurable spaces and the corresponding systems of sigma -additive measures, all of these leading to the description of a promeasure, a concept modeled after Bourbaki and classical measure theory. In the case of a locally convex vector space E, the corresponding Fourier transform, family of characters and the existence of a promeasure for every quadratic form on E^' are established, so the Gaussian L^2-space associated to a real Hilbert space is constructed. Chapter III finishes by exhibiting the explicit Hilbert space isomorphism between the Gaussian L ^2-space associated to a real Hilbert space and the complexification of its symmetric algebra. In chapter IV taking as a Hilbert space H the L^2-space of the Lie algebra valued 1-forms on P, the gauge group acts on the motion group of H defining in an straight forward fashion the representation desired.
Quantum computers in phase space
International Nuclear Information System (INIS)
Miquel, Cesar; Paz, Juan Pablo; Saraceno, Marcos
2002-01-01
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples, such as the Fourier transform and Grover's search, we examine the conditions for the existence of a direct correspondence between quantum and classical evolutions in phase space. Finally, we describe how to measure directly the Wigner function in a given phase-space point by means of a tomographic method that, itself, can be interpreted as a simple quantum algorithm
Phase space approach to quantum dynamics
International Nuclear Information System (INIS)
Leboeuf, P.
1991-03-01
The Schroedinger equation for the time propagation of states of a quantised two-dimensional spherical phase space is replaced by the dynamics of a system of N particles lying in phase space. This is done through factorization formulae of analytic function theory arising in coherent-state representation, the 'particles' being the zeros of the quantum state. For linear Hamiltonians, like a spin in a uniform magnetic field, the motion of the particles is classical. However, non-linear terms induce interactions between the particles. Their time propagation is studied and it is shown that, contrary to integrable systems, for chaotic maps they tend to fill, as their classical counterpart, the whole phase space. (author) 13 refs., 3 figs
Gupta-Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times
Finster, Felix; Strohmaier, Alexander
2015-08-01
We give a complete framework for the Gupta-Bleuler quantization of the free electromagnetic field on globally hyperbolic space-times. We describe one-particle structures that give rise to states satisfying the microlocal spectrum condition. The field algebras in the so-called Gupta-Bleuler representations satisfy the time-slice axiom, and the corresponding vacuum states satisfy the microlocal spectrum condition. We also give an explicit construction of ground states on ultrastatic space-times. Unlike previous constructions, our method does not require a spectral gap or the absence of zero modes. The only requirement, the absence of zero-resonance states, is shown to be stable under compact perturbations of topology and metric. Usual deformation arguments based on the time-slice axiom then lead to a construction of Gupta-Bleuler representations on a large class of globally hyperbolic space-times. As usual, the field algebra is represented on an indefinite inner product space, in which the physical states form a positive semi-definite subspace. Gauge transformations are incorporated in such a way that the field can be coupled perturbatively to a Dirac field. Our approach does not require any topological restrictions on the underlying space-time.
Fermionic bound states in Minkowski space. Light-cone singularities and structure
Energy Technology Data Exchange (ETDEWEB)
Paula, Wayne de; Frederico, Tobias; Pimentel, Rafael [Instituto Tecnologico de Aeronautica, DCTA, Dept. de Fisica, Sao Jose dos Campos, Sao Paulo (Brazil); Salme, Giovanni [Istituto Nazionale di Fisica Nucleare, Rome (Italy); Viviani, Michele [Istituto Nazionale di Fisica Nucleare, Pisa (Italy)
2017-11-15
The Bethe-Salpeter equation for two-body bound system with spin 1/2 constituent is addressed directly in the Minkowski space. In order to accomplish this aim we use the Nakanishi integral representation of the Bethe-Salpeter amplitude and exploit the formal tool represented by the exact projection onto the null-plane. This formal step allows one (i) to deal with end-point singularities one meets and (ii) to find stable results, up to strongly relativistic regimes, which settle in strongly bound systems. We apply this technique to obtain the numerical dependence of the binding energies upon the coupling constants and the light-front amplitudes for a fermion-fermion 0{sup +} state with interaction kernels, in ladder approximation, corresponding to scalar-, pseudoscalar- and vector-boson exchanges, respectively. After completing the numerical survey of the previous cases, we extend our approach to a quark-antiquark system in 0{sup -} state, taking both constituent-fermion and exchanged-boson masses, from lattice calculations. Interestingly, the calculated light-front amplitudes for such a mock pion show peculiar signatures of the spin degrees of freedom. (orig.)
Graph-representation of oxidative folding pathways
Directory of Open Access Journals (Sweden)
Kaján László
2005-01-01
Full Text Available Abstract Background The process of oxidative folding combines the formation of native disulfide bond with conformational folding resulting in the native three-dimensional fold. Oxidative folding pathways can be described in terms of disulfide intermediate species (DIS which can also be isolated and characterized. Each DIS corresponds to a family of folding states (conformations that the given DIS can adopt in three dimensions. Results The oxidative folding space can be represented as a network of DIS states interconnected by disulfide interchange reactions that can either create/abolish or rearrange disulfide bridges. We propose a simple 3D representation wherein the states having the same number of disulfide bridges are placed on separate planes. In this representation, the shuffling transitions are within the planes, and the redox edges connect adjacent planes. In a number of experimentally studied cases (bovine pancreatic trypsin inhibitor, insulin-like growth factor and epidermal growth factor, the observed intermediates appear as part of contiguous oxidative folding pathways. Conclusions Such networks can be used to visualize folding pathways in terms of the experimentally observed intermediates. A simple visualization template written for the Tulip package http://www.tulip-software.org/ can be obtained from V.A.
On Space-Time Resolution of Inflow Representations for Wind Turbine Loads Analysis
Directory of Open Access Journals (Sweden)
Lance Manuel
2012-06-01
Full Text Available Efficient spatial and temporal resolution of simulated inflow wind fields is important in order to represent wind turbine dynamics and derive load statistics for design. Using Fourier-based stochastic simulation of inflow turbulence, we first investigate loads for a utility-scale turbine in the neutral atmospheric boundary layer. Load statistics, spectra, and wavelet analysis representations for different space and time resolutions are compared. Next, large-eddy simulation (LES is employed with space-time resolutions, justified on the basis of the earlier stochastic simulations, to again derive turbine loads. Extreme and fatigue loads from the two approaches used in inflow field generation are compared. On the basis of simulation studies carried out for three different wind speeds in the turbine’s operating range, it is shown that inflow turbulence described using 10-meter spatial resolution and 1 Hz temporal resolution is adequate for assessing turbine loads. Such studies on the investigation of adequate filtering or resolution of inflow wind fields help to establish efficient strategies for LES and other physical or stochastic simulation needed in turbine loads studies.
International Nuclear Information System (INIS)
Kessel, Alexander R.; Yakovleva, Natalia M.
2002-01-01
Schemes of experimental realization of the main two-qubit processors for quantum computers and the Deutsch-Jozsa algorithm are derived in virtual spin representation. The results are applicable for every four quantum states allowing the required properties for quantum processor implementation if for qubit encoding, virtual spin representation is used. A four-dimensional Hilbert space of nuclear spin 3/2 is considered in detail for this aim
Representation of coherent states in many-boson theory
International Nuclear Information System (INIS)
Vakarchuk, I.A.
1978-01-01
Solution of the Bloch equation for the density matrix of the system of interacting Bose particles in the coherent states representation is obtained. The matrix of the thermodynamical potential functional is represented in the form of the functional series over the eigen-values of the annihilation operator and the coefficient functions are the matrix elements of cluster operators. A simple functional integration in the partition sum leads to the well-known quantum virial expansions and the standard perturbation theory series. Possibilities of application of the expressions obtained to the investigation of the lambda-transition in the liquid He 4 and the generalization to the case of the many-fermion system is discussed
Hohenberg-Kohn theorem and non-V-representable densities
International Nuclear Information System (INIS)
Englisch, H.; Englisch, R.
1983-01-01
In the density-functional formalism of Hohenberg and Kohn, the variation is only allowed over the one-particle densities which are pure-state-V-representable (PS-V-representable). Levy and Lieb proved that not every ensemble-V-representable (E-V-representable) density is PS-V-representable. Since we show that the Hohenberg-Kohn formalism can be extended to a variation over E-V-representable densities for degenerated ground states, Levy's and Lieb's result is not a counterexample to the universality of the Hohenberg-Kohn theorem. The question whether every N-representable density is E-V-representable has remained open so far. Presenting examples of non-E-V-representable densities we answer this question in the negative. Thus the value of Levy's functional for the calculation of ground-state energies is obvious, since this functional only requires the N-representability of the densities. Therefore we transfer two approaches for the calculation of excited-state energies into the framework of Levy's formalism. (orig.)
Islamic representation and urban space in Banda Aceh: Linking the social and spatial
Istiqamah; Herlily
2018-03-01
Post conflict and tsunami; the city of Banda Aceh is experiencing a massive development as an effort to represent an Islamic city. Some strategic points have been chosen by the municipality to build architectural objects that are considered to represent Islam in the urban space. The issue of such representational practice is the development of neglecting the activities of local communities as users of urban public spaces. The purpose of this design study is to provide an alternative to the urban design of Banda Aceh to represent Islam that is not moving from physical development but by involving community activities. Establish and rediscover the relationship between Islam and urban life in Banda Aceh. This design study uses mental maps of 50 inhabitants of Banda Aceh city of various ages who live in 10 villages around the city center. We use mental maps as a tool to read the daily activities of the community and determine the familiar urban territory with the community. The results of this study will be used to form a Muslim community and present community activities to represent Islam in the urban space.
Coherent states and covariant semi-spectral measures
International Nuclear Information System (INIS)
Scutaru, H.
1976-01-01
The close connection between Mackey's theory of imprimitivity systems and the so called generalized coherent states introduced by Perelomov is established. Coherent states give a covariant description of the ''localization'' of a quantum system in the phase space in a similar way as the imprimitivity systems give a covariant description of the localization of a quantum system in the configuration space. The observation that for any system of coherent states one can define a covariant semi-spectral measure made possible a rigurous formulation of this idea. A generalization of the notion of coherent states is given. Covariant semi-spectral measures associated with systems of coherent states are defined and characterized. Necessary and sufficient conditions for a unitary representation of a Lie group to be i) a subrepresentation of an induced one and ii) a representation with coherent states are given (author)
Linear entropy in quantum phase space
International Nuclear Information System (INIS)
Rosales-Zarate, Laura E. C.; Drummond, P. D.
2011-01-01
We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.
Linear entropy in quantum phase space
Energy Technology Data Exchange (ETDEWEB)
Rosales-Zarate, Laura E. C.; Drummond, P. D. [Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122 (Australia)
2011-10-15
We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.
DEFF Research Database (Denmark)
Chen, Xiaoshuang; Lin, Jin; Wan, Can
2016-01-01
State estimation (SE) in distribution networks is not as accurate as that in transmission networks. Traditionally, distribution networks (DNs) are lack of direct measurements due to the limitations of investments and the difficulties of maintenance. Therefore, it is critical to improve the accuracy...... of SE in distribution networks by placing additional physical meters. For state-of-the-art SE models, it is difficult to clearly quantify measurements' influences on SE errors, so the problems of optimal meter placement for reducing SE errors are mostly solved by heuristic or suboptimal algorithms....... Under this background, this paper proposes a circuit representation model to represent SE errors. Based on the matrix formulation of the circuit representation model, the problem of optimal meter placement can be transformed to a mixed integer linear programming problem (MILP) via the disjunctive model...
Twisted boundary states and representation of generalized fusion algebra
International Nuclear Information System (INIS)
Ishikawa, Hiroshi; Tani, Taro
2006-01-01
The mutual consistency of boundary conditions twisted by an automorphism group G of the chiral algebra is studied for general modular invariants of rational conformal field theories. We show that a consistent set of twisted boundary states associated with any modular invariant realizes a non-negative integer matrix representation (NIM-rep) of the generalized fusion algebra, an extension of the fusion algebra by representations of the twisted chiral algebra associated with the automorphism group G. We check this result for several concrete cases. In particular, we find that two NIM-reps of the fusion algebra for su(3) k (k=3,5) are organized into a NIM-rep of the generalized fusion algebra for the charge-conjugation automorphism of su(3) k . We point out that the generalized fusion algebra is non-commutative if G is non-Abelian and provide some examples for G-bar S 3 . Finally, we give an argument that the graph fusion algebra associated with simple current extensions coincides with the generalized fusion algebra for the extended chiral algebra, and thereby explain that the graph fusion algebra contains the fusion algebra of the extended theory as a subalgebra
Social exclusion modulates pre-reflective interpersonal body representation
DEFF Research Database (Denmark)
Ambrosini, Ettore; Blomberg, Olle; Mandrigin, Alisa
2014-01-01
social exclusion condition. The results were that the SAE that normally occurs when the mug is in the avatar’s reaching space is extinguished by the induced social exclusion. This indicates that judgments about one’s own social status modulate the effect of IBR.......Perception of an affordance is enhanced not only when the relevant object is located in one’s own peripersonal space, as compared to when it is located within extrapersonal space, but also when the object is located in another person’s peripersonal space (as measured by a Spatial Alignment Effect...... (SAE)). It has been suggested that this reflects the existence of an interpersonal body representation (IBR) that allows us to represent the perceptual states and action possibilities of others. Here, we address the question of whether IBR can be modulated by higher level/reflective social cognition...
Personal neglect-a disorder of body representation?
Baas, Ulrike; de Haan, Bianca; Grässli, Tanja; Karnath, Hans-Otto; Mueri, René; Perrig, Walter J; Wurtz, Pascal; Gutbrod, Klemens
2011-04-01
The cognitive mechanisms underlying personal neglect are not well known. One theory postulates that personal neglect is due to a disorder of contralesional body representation. In the present study, we have investigated whether personal neglect is best explained by impairments in the representation of the contralesional side of the body, in particular, or a dysfunction of the mental representation of the contralesional space in general. For this, 22 patients with right hemisphere cerebral lesions (7 with personal neglect, 15 without personal neglect) and 13 healthy controls have been studied using two experimental tasks measuring representation of the body and extrapersonal space. In the tasks, photographs of left and right hands as well as left and right rear-view mirrors presented from the front and the back had to be judged as left or right. Our results show that patients with personal neglect made more errors when asked to judge stimuli of left hands and left rear-view mirrors than either patients without personal neglect or healthy controls. Furthermore, regression analyses indicated that errors in interpreting left hands were the best predictor of personal neglect, while other variables such as extrapersonal neglect, somatosensory or motor impairments, or deficits in left extrapersonal space representation had no predictive value of personal neglect. These findings suggest that deficient body representation is the major mechanism underlying personal neglect. Copyright © 2011 Elsevier Ltd. All rights reserved.
Gender representation trends and relations at the United States Naval Academy
Lewis, Shannon FitzPatrick.
2005-01-01
This study employed quantitative and qualitative methods to examine gender trends and the quality of gender interactions at the United States Naval Academy (USNA). In addition to gender, midshipmen demographics, experiences, personality types, interests, and graduation outcomes were compared within and across gender for graduation years, 1980, 1985, 1990, 1995, 2000, and 2004. Representation of women has increased to the current high of around 16%. Further, the data revealed similarities and ...
Space strategy and governance of ESA small member states
Sagath, Daniel; Papadimitriou, Angeliki; Adriaensen, Maarten; Giannopapa, Christina
2018-01-01
The European Space Agency (ESA) has twenty-two Member States with a variety of governance structures and strategic priorities regarding their space activities. The objective of this paper is to provide an up-to date overview and a holistic assessment of the national space governance structures and strategic priorities of the eleven smaller Member States (based on annual ESA contributions). A link is made between the governance structure and the main strategic objectives. The specific needs and interests of small and new Member States in the frame of European Space Integration are addressed. The first part of the paper focuses on the national space governance structures in the eleven smaller ESA Member States. The governance models of these Member States are identified including the responsible ministries and the entities entrusted with the implementation of space strategy/policy and programmes of the country. The second part of this paper focuses on the content and analysis of the national space strategies and indicates the main priorities and trends in the eleven smaller ESA Member States. The priorities are categorised with regards to technology domains, the role of space in the areas of sustainability and the motivators for space investments. In a third and final part, attention is given to the specific needs and interests of the smaller Member States in the frame of European space integration. ESA instruments are tailored to facilitate the needs and interests of the eleven smaller and/or new Member States.
A Sweep-Line Method for State Space Exploration
DEFF Research Database (Denmark)
Christensen, Søren; Kristensen, Lars Michael; Mailund, Thomas
2001-01-01
generation, since these states can never be reached again. This in turn reduces the memory used for state space storage during the task of verification. Examples of progress measures are sequence numbers in communication protocols and time in certain models with time. We illustrate the application...... of the method on a number of Coloured Petri Net models, and give a first evaluation of its practicality by means of an implementation based on the Design/CPN state space tool. Our experiments show significant reductions in both space and time used during state space exploration. The method is not specific...... to Coloured Petri Nets but applicable to a wide range of modelling languages....
Meyer, Harvey B.
2017-09-01
We present a Lorentz-covariant, Euclidean coordinate-space expression for the hadronic vacuum polarisation, the Adler function and the leading hadronic contribution to the anomalous magnetic moment of the muon. The representation offers a high degree of flexibility for an implementation in lattice QCD. We expect it to be particularly helpful for the quark-line disconnected contributions.
Energy Technology Data Exchange (ETDEWEB)
Meyer, Harvey B. [Mainz Univ., PRISMA Cluster of Excellence, Inst. fuer Kernphysik und Helmholtz Institut Mainz (Germany)
2017-09-15
We present a Lorentz-covariant, Euclidean coordinate-space expression for the hadronic vacuum polarisation, the Adler function and the leading hadronic contribution to the anomalous magnetic moment of the muon. The representation offers a high degree of flexibility for an implementation in lattice QCD. We expect it to be particularly helpful for the quark-line disconnected contributions. (orig.)
Directory of Open Access Journals (Sweden)
Joana Tereza Vaz de Moura
2010-05-01
Full Text Available Councils are a key institutional innovation within the Brazilian post-1988 constitutional framework. They are structured so as to include representatives of civil society and the State within the same arena. The aim of this article is to engage in critical discussion on the representation of social organizations within these arenas. Our hypothesis suggests that representatives often distance themselves so much from their social base that they actually become a sort of elite. Thus, we raise the issue of whether the formal democratic structure and mechanisms that these councils incorporate are enough to guarantee a diversity of representatives and representational practices, or if, through the social and political resources that representatives hold, gaps between constituents’ demands and representatives’ actions re-emerge, notwithstanding the normative precepts of equality that the councils themselves advocate. Keywords: councils, elites, representation.
Description of quantum states using in free space optic communication
Kučera, Petr
2017-11-01
In the article we concentrate our attention on the quantum description of states which are prepared by light sources. The main goal of the article is the determination of density matrix of background radiation source. It is shown that these matrix elements satisfy Geometric distribution in the number state representation.
Rigid Body Attitude Control Based on a Manifold Representation of Direction Cosine Matrices
International Nuclear Information System (INIS)
Nakath, David; Clemens, Joachim; Rachuy, Carsten
2017-01-01
Autonomous systems typically actively observe certain aspects of their surroundings, which makes them dependent on a suitable controller. However, building an attitude controller for three degrees of freedom is a challenging task, mainly due to singularities in the different parametrizations of the three dimensional rotation group SO (3). Thus, we propose an attitude controller based on a manifold representation of direction cosine matrices: In state space, the attitude is globally and uniquely represented as a direction cosine matrix R ∈ SO (3). However, differences in the state space, i.e., the attitude errors, are exposed to the controller in the vector space ℝ 3 . This is achieved by an operator, which integrates the matrix logarithm mapping from SO (3) to so(3) and the map from so(3) to ℝ 3 . Based on this representation, we derive a proportional and derivative feedback controller, whose output has an upper bound to prevent actuator saturation. Additionally, the feedback is preprocessed by a particle filter to account for measurement and state transition noise. We evaluate our approach in a simulator in three different spacecraft maneuver scenarios: (i) stabilizing, (ii) rest-to-rest, and (iii) nadir-pointing. The controller exhibits stable behavior from initial attitudes near and far from the setpoint. Furthermore, it is able to stabilize a spacecraft and can be used for nadir-pointing maneuvers. (paper)
Autoscopic phenomena and one's own body representation in dreams.
Occhionero, Miranda; Cicogna, Piera Carla
2011-12-01
Autoscopic phenomena (AP) are complex experiences that include the visual illusory reduplication of one's own body. From a phenomenological point of view, we can distinguish three conditions: autoscopic hallucinations, heautoscopy, and out-of-body experiences. The dysfunctional pattern involves multisensory disintegration of personal and extrapersonal space perception. The etiology, generally either neurological or psychiatric, is different. Also, the hallucination of Self and own body image is present during dreams and differs according to sleep stage. Specifically, the representation of the Self in REM dreams is frequently similar to the perception of Self in wakefulness, whereas in NREM dreams, a greater polymorphism of Self and own body representation is observed. The parallels between autoscopic phenomena in pathological cases and the Self-hallucination in dreams will be discussed to further the understanding of the particular states of self awareness, especially the complex integration of different memory sources in Self and body representation. Copyright © 2011 Elsevier Inc. All rights reserved.
The graph representation approach to topological field theory in 2 + 1 dimensions
International Nuclear Information System (INIS)
Martin, S.P.
1991-02-01
An alternative definition of topological quantum field theory in 2+1 dimensions is discussed. The fundamental objects in this approach are not gauge fields as in the usual approach, but non-local observables associated with graphs. The classical theory of graphs is defined by postulating a simple diagrammatic rule for computing the Poisson bracket of any two graphs. The theory is quantized by exhibiting a quantum deformation of the classical Poisson bracket algebra, which is realized as a commutator algebra on a Hilbert space of states. The wavefunctions in this ''graph representation'' approach are functionals on an appropriate set of graphs. This is in contrast to the usual ''connection representation'' approach in which the theory is defined in terms of a gauge field and the wavefunctions are functionals on the space of flat spatial connections modulo gauge transformations
Paxton, Pamela; Painter, Matthew A; Hughes, Melanie M
2009-03-01
The expansion of women's political representation ranks among the most significant trends in American politics of the last 100 years. In this paper, we develop two longitudinal theories to explain patterns of growth and change in women's state legislative representation over time. Gender salience suggests that years in which women's absence from politics is problematized (e.g., 1992-the Year of the Woman) will demonstrate higher levels of growth. Political climate suggests that periods in which domestic issues are stressed (e.g., the 1990s) will produce higher levels of growth than periods in which international issues are stressed (e.g., post 9/11). Combinations of these two theories create four possible trajectories of growth in women's representation that may be observed over time. We use latent growth curve models to assess the four theoretical trajectories, using data on women's state legislative representation from 1982 to 2006. We find that while women achieved fleeting success in the Year of the Woman, further gains were limited in the remainder of the 1990s and average growth stalled completely after 2001. Our results show futher that gender salience and, to a lesser extent political, climate matter to growth and change in women's political power over time.
Flexibility of representational states in working memory
Directory of Open Access Journals (Sweden)
Nahid eZokaei
2014-11-01
Full Text Available The relationship between working memory (WM and attention is a highly interdependent one, with evidence that attention determines the state in which items in WM are retained. Through focusing of attention, an item might be held in a more prioritized state, commonly termed as the focus of attention (FOA. The remaining items, although still retrievable, are considered to be in a different representational state. One means to bring an item into the FOA is to use retrospective cues (‘retro-cues’ which direct attention to one of the objects retained in WM. Alternatively, an item can enter a privileged state once attention is directed towards it through bottom-up influences (e.g. recency effect or by performing an action on one of the retained items (‘incidental’ cueing. In all these cases, the item in the FOA is recalled with better accuracy compared to the other items in WM. Far less is known about the nature of the other items in WM and whether they can be flexibly manipulated in and out of the FOA. We present data from three types of experiments as well as transcranial magnetic stimulation to early visual cortex to manipulate the item inside FOA. Taken together, our results suggest that the context in which items are retained in WM matters. When an item remains behaviourally relevant, despite not being inside the FOA, re-focusing attention upon it can increase its recall precision. This suggests that a non-FOA item can be held in a state in which it can be later retrieved. However, if an item is rendered behaviourally unimportant because it is very unlikely to be probed, it cannot be brought back into the FOA, nor recalled with high precision. Under such conditions, some information appears to be irretrievably lost from WM. These findings, obtained from several different methods, demonstrate quite considerable flexibility with which items in WM can be represented depending upon context. They have important consequences for emerging state
Finite Word-Length Effects in Digital State-Space Filters
Directory of Open Access Journals (Sweden)
B. Psenicka
1999-12-01
Full Text Available The state-space description of digital filters involves except the relationship between input and output signals an additional set of state variables. The state-space structures of digital filters have many positive properties compared with direct canonical structures. The main advantage of digital filter structures developed using state-space technique is a smaller sensitivity to quantization effects by fixed-point implementation. In our presentation, the emphasis is on the analysis of coefficient quantization and on existence of zero-input limit cycles in state-space digital filters. The comparison with direct form II structure is presented.
Assadi, Amir H.
2001-11-01
Perceptual geometry is an emerging field of interdisciplinary research whose objectives focus on study of geometry from the perspective of visual perception, and in turn, apply such geometric findings to the ecological study of vision. Perceptual geometry attempts to answer fundamental questions in perception of form and representation of space through synthesis of cognitive and biological theories of visual perception with geometric theories of the physical world. Perception of form and space are among fundamental problems in vision science. In recent cognitive and computational models of human perception, natural scenes are used systematically as preferred visual stimuli. Among key problems in perception of form and space, we have examined perception of geometry of natural surfaces and curves, e.g. as in the observer's environment. Besides a systematic mathematical foundation for a remarkably general framework, the advantages of the Gestalt theory of natural surfaces include a concrete computational approach to simulate or recreate images whose geometric invariants and quantities might be perceived and estimated by an observer. The latter is at the very foundation of understanding the nature of perception of space and form, and the (computer graphics) problem of rendering scenes to visually invoke virtual presence.
Represenation of process state, structure and control
International Nuclear Information System (INIS)
Goodstein, L.P.; Rasmussen, J.
1987-04-01
Supervisory control is essentially a decision-making activity where, among other things, the dm has to maneuver within a complex problem space which reflects key dimensions and attributes of the object system (power plant ...). Of considerable importance therefore is the representation for the dm of this problem space comprising at the one end the target demands, goals, constraints and, at the other, the resources available for meeting the assigned goals - and all of this in pace with the dynamic event-driven environment which characterizes the types of systems of interest. Previous work has identified the advantages of utilizing the two-dimensional means-ends/part-whole space as a basic ingredient in a system representation. This paper associates more detailed representational requirements at the various levels of the means-ends axis with the activities of state identification and diagnosis. In addition, some examples of display formats which attempt to incorporate the outlined representational principles within the context of a PWR plant are discussed. (authors)
Cohen, Adam S; Sasaki, Joni Y; German, Tamsin C
2015-03-01
Does theory of mind depend on a capacity to reason about representations generally or on mechanisms selective for the processing of mental state representations? In four experiments, participants reasoned about beliefs (mental representations) and notes (non-mental, linguistic representations), which according to two prominent theories are closely matched representations because both are represented propositionally. Reaction times were faster and accuracies higher when participants endorsed or rejected statements about false beliefs than about false notes (Experiment 1), even when statements emphasized representational format (Experiment 2), which should have favored the activation of representation concepts. Experiments 3 and 4 ruled out a counterhypothesis that differences in task demands were responsible for the advantage in belief processing. These results demonstrate for the first time that understanding of mental and linguistic representations can be dissociated even though both may carry propositional content, supporting the theory that mechanisms governing theory of mind reasoning are narrowly specialized to process mental states, not representations more broadly. Extending this theory, we discuss whether less efficient processing of non-mental representations may be a by-product of mechanisms specialized for processing mental states. Crown Copyright © 2014. Published by Elsevier B.V. All rights reserved.
A Database Approach to Distributed State Space Generation
Blom, Stefan; Lisser, Bert; van de Pol, Jan Cornelis; Weber, M.
2007-01-01
We study distributed state space generation on a cluster of workstations. It is explained why state space partitioning by a global hash function is problematic when states contain variables from unbounded domains, such as lists or other recursive datatypes. Our solution is to introduce a database
A Database Approach to Distributed State Space Generation
Blom, Stefan; Lisser, Bert; van de Pol, Jan Cornelis; Weber, M.; Cerna, I.; Haverkort, Boudewijn R.H.M.
2008-01-01
We study distributed state space generation on a cluster of workstations. It is explained why state space partitioning by a global hash function is problematic when states contain variables from unbounded domains, such as lists or other recursive datatypes. Our solution is to introduce a database
Directory of Open Access Journals (Sweden)
Farhad Hazhir
2012-01-01
Full Text Available Background: Illness representations (based on Leventhal's model are associated with chronic illness outcomes. It has been suggested that targeting these cognitive components improves illness outcomes. Multiple sclerosis is a common disorder between neural and immune systems that creates physical and psychological consequences. There are few pre psychological trails on these patients. The aim of this study was to determine effectiveness of cognitive-behavior therapy on altering illness representations and improving emotional states of the patients.Methods: By using a randomized controlled trial design, among 52 selected patients, 35 volunteers randomly were allocated into intervention and control groups. An extensive interventional cognitive behavior therapy based package was conducted to intervention group in 10 weekly sessions. The control group stayed in waiting list and participated in 5 group meeting sessions. (IPQR and (DASS-42 psychological scales were administered, Leven and T statistical tests were applied for dat analysis.Results: The results showed positive changes in four illness representation components of patients including illness (identity, consequences, coherence and personal control. Associated improvement occurred in depression, anxiety, stress and emotional representations.Conclusion: Mooney and Padeskey's theoretically based cognitive-behavior therapy, is effective on illness representations modification and improving emotional states of the patients. The findings are less similar to Goodman's trial on Systemic Lupus Erythematosus patients and more similar to Petrie's trail on cardiac patients.
The Coulomb Branch Formula for Quiver Moduli Spaces
Manschot, Jan; Sen, Ashoke
2014-01-01
In recent series of works, by translating properties of multi-centered supersymmetric black holes into the language of quiver representations, we proposed a formula that expresses the Hodge numbers of the moduli space of semi-stable representations of quivers with generic superpotential in terms of a set of invariants associated to `single-centered' or `pure-Higgs' states. The distinguishing feature of these invariants is that they are independent of the choice of stability condition. Furthermore they are uniquely determined by the $\\chi_y$-genus of the moduli space. Here, we provide a self-contained summary of the Coulomb branch formula, spelling out mathematical details but leaving out proofs and physical motivations.
Braid group representation on quantum computation
Energy Technology Data Exchange (ETDEWEB)
Aziz, Ryan Kasyfil, E-mail: kasyfilryan@gmail.com [Department of Computational Sciences, Bandung Institute of Technology (Indonesia); Muchtadi-Alamsyah, Intan, E-mail: ntan@math.itb.ac.id [Algebra Research Group, Bandung Institute of Technology (Indonesia)
2015-09-30
There are many studies about topological representation of quantum computation recently. One of diagram representation of quantum computation is by using ZX-Calculus. In this paper we will make a diagrammatical scheme of Dense Coding. We also proved that ZX-Calculus diagram of maximally entangle state satisfies Yang-Baxter Equation and therefore, we can construct a Braid Group representation of set of maximally entangle state.
State-Space Inference and Learning with Gaussian Processes
Turner, R; Deisenroth, MP; Rasmussen, CE
2010-01-01
18.10.13 KB. Ok to add author version to spiral, authors hold copyright. State-space inference and learning with Gaussian processes (GPs) is an unsolved problem. We propose a new, general methodology for inference and learning in nonlinear state-space models that are described probabilistically by non-parametric GP models. We apply the expectation maximization algorithm to iterate between inference in the latent state-space and learning the parameters of the underlying GP dynamics model. C...
ASAP: An Extensible Platform for State Space Analysis
DEFF Research Database (Denmark)
Westergaard, Michael; Evangelista, Sami; Kristensen, Lars Michael
2009-01-01
The ASCoVeCo State space Analysis Platform (ASAP) is a tool for performing explicit state space analysis of coloured Petri nets (CPNs) and other formalisms. ASAP supports a wide range of state space reduction techniques and is intended to be easy to extend and to use, making it a suitable tool fo...... for students, researchers, and industrial users that would like to analyze protocols and/or experiment with different algorithms. This paper presents ASAP from these two perspectives....
Optimal Couple Projections for Domain Adaptive Sparse Representation-based Classification.
Zhang, Guoqing; Sun, Huaijiang; Porikli, Fatih; Liu, Yazhou; Sun, Quansen
2017-08-29
In recent years, sparse representation based classification (SRC) is one of the most successful methods and has been shown impressive performance in various classification tasks. However, when the training data has a different distribution than the testing data, the learned sparse representation may not be optimal, and the performance of SRC will be degraded significantly. To address this problem, in this paper, we propose an optimal couple projections for domain-adaptive sparse representation-based classification (OCPD-SRC) method, in which the discriminative features of data in the two domains are simultaneously learned with the dictionary that can succinctly represent the training and testing data in the projected space. OCPD-SRC is designed based on the decision rule of SRC, with the objective to learn coupled projection matrices and a common discriminative dictionary such that the between-class sparse reconstruction residuals of data from both domains are maximized, and the within-class sparse reconstruction residuals of data are minimized in the projected low-dimensional space. Thus, the resulting representations can well fit SRC and simultaneously have a better discriminant ability. In addition, our method can be easily extended to multiple domains and can be kernelized to deal with the nonlinear structure of data. The optimal solution for the proposed method can be efficiently obtained following the alternative optimization method. Extensive experimental results on a series of benchmark databases show that our method is better or comparable to many state-of-the-art methods.
Bosmans, Guy; Bowles, David, P.; Dewitte, Marieke; De Winter, Simon; Braet, Caroline
2014-01-01
Attachment theory predicts cross-contextual stability of attachment representations, but research findings are rather mixed. Recently, it has been suggested that these mixed findings reflect the existence of both state and trait attachment components. The development of the State Adult Attachment Measure (SAAM) has enabled an investigation of this hypothesis. The current study aimed to evaluate the extent to which the SAAM is a useful instrument for studying such state attachment hypotheses. ...
Introduction to representation theory
Etingof, Pavel; Hensel, Sebastian; Liu, Tiankai; Schwendner, Alex
2011-01-01
Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a "holistic" introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic k...
A Compositional Sweep-Line State Space Exploration Method
DEFF Research Database (Denmark)
Kristensen, Lars Michael; Mailund, Thomas
2002-01-01
State space exploration is a main approach to verification of finite-state systems. The sweep-line method exploits a certain kind of progress present in many systems to reduce peak memory usage during state space exploration. We present a new sweep-line algorithm for a compositional setting where...
Transformations and representations supporting spatial perspective taking
Yu, Alfred B.; Zacks, Jeffrey M.
2018-01-01
Spatial perspective taking is the ability to reason about spatial relations relative to another’s viewpoint. Here, we propose a mechanistic hypothesis that relates mental representations of one’s viewpoint to the transformations used for spatial perspective taking. We test this hypothesis using a novel behavioral paradigm that assays patterns of response time and variation in those patterns across people. The results support the hypothesis that people maintain a schematic representation of the space around their body, update that representation to take another’s perspective, and thereby to reason about the space around their body. This is a powerful computational mechanism that can support imitation, coordination of behavior, and observational learning. PMID:29545731
Parameter and State Estimator for State Space Models
Directory of Open Access Journals (Sweden)
Ruifeng Ding
2014-01-01
Full Text Available This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective.
Octonionic matrix representation and electromagnetism
Energy Technology Data Exchange (ETDEWEB)
Chanyal, B. C. [Kumaun University, S. S. J. Campus, Almora (India)
2014-12-15
Keeping in mind the important role of octonion algebra, we have obtained the electromagnetic field equations of dyons with an octonionic 8 x 8 matrix representation. In this paper, we consider the eight - dimensional octonionic space as a combination of two (external and internal) four-dimensional spaces for the existence of magnetic monopoles (dyons) in a higher-dimensional formalism. As such, we describe the octonion wave equations in terms of eight components from the 8 x 8 matrix representation. The octonion forms of the generalized potential, fields and current source of dyons in terms of 8 x 8 matrix are discussed in a consistent manner. Thus, we have obtained the generalized Dirac-Maxwell equations of dyons from an 8x8 matrix representation of the octonion wave equations in a compact and consistent manner. The generalized Dirac-Maxwell equations are fully symmetric Maxwell equations and allow for the possibility of magnetic charges and currents, analogous to electric charges and currents. Accordingly, we have obtained the octonionic Dirac wave equations in an external field from the matrix representation of the octonion-valued potentials of dyons.
Holstein-Primakoff representation and supercoherent states for strongly correlated electron systems
International Nuclear Information System (INIS)
Azakov, S.
1999-09-01
First we show that the algebra of operators entering the Hamiltonian of the t-J model describing the strongly correlated electron system is graded spl(2.1) algebra. Then after a brief discussion of its atypical representations we construct the Holstein-Primakoff nonlinear realization of these operators which allows to carry out the systematic semiclassical approximation, similarly to the spin-wave theory of localized magnetism. The fact that the t-J model describes the itinerant magnetism is reflected in the presence of the spinless fermions. For the supersymmetric spl(2.1) algebra the supercoherent states are proposed and the partition function of the t-J model is represented as a path integral with the help of these states. (author)
Adriaensen, Maarten; Giannopapa, Christina; Sagath, Daniel; Papastefanou, Anastasia
2015-12-01
The European Space Agency (ESA) has twenty Member States with a variety of strategic priorities and governance structures regarding their space activities. A number of countries engage in space activities exclusively though ESA, while others have also their own national space programme. Some consider ESA as their prime space agency and others have additionally their own national agency with respective programmes. The main objective of this paper is to provide an up-to date overview and a holistic assessment of strategic priorities and the national space governance structures in 20 ESA Member States. This analysis and assessment has been conducted by analysing the Member States public documents, information provided at ESA workshop on this topic and though unstructured interviews. The paper is structured to include two main elements: priorities and trends in national space strategies and space governance in ESA Member States. The first part of this paper focuses on the content and analysis of the national space strategies and indicates the main priorities and trends in Member States. The priorities are categorised with regards to technology domains, the role of space in the areas of sustainability and the motivators that boost engagement in space. These vary from one Member State to another and include with different levels of engagement in technology domains amongst others: science and exploration, navigation, Earth observation, human space flight, launchers, telecommunications, and integrated applications. Member States allocate a different role of space as enabling tool adding to the advancement of sustainability areas including: security, resources, environment and climate change, transport and communication, energy, and knowledge and education. The motivators motivating reasoning which enhances or hinders space engagement also differs. The motivators identified are industrial competitiveness, job creation, technology development and transfer, social benefits
International Nuclear Information System (INIS)
Ferrie, Christopher; Emerson, Joseph
2008-01-01
Several finite-dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted dimensions and their physical significance in contexts such as drawing quantum-classical comparisons is limited by the non-uniqueness of the particular representation. Here we show how the mathematical theory of frames provides a unified formalism which accommodates all known quasi-probability representations of finite-dimensional quantum systems. Moreover, we show that any quasi-probability representation is equivalent to a frame representation and then prove that any such representation of quantum mechanics must exhibit either negativity or a deformed probability calculus. (fast track communication)
Dynamic representation of 3D auditory space in the midbrain of the free-flying echolocating bat
2018-01-01
Essential to spatial orientation in the natural environment is a dynamic representation of direction and distance to objects. Despite the importance of 3D spatial localization to parse objects in the environment and to guide movement, most neurophysiological investigations of sensory mapping have been limited to studies of restrained subjects, tested with 2D, artificial stimuli. Here, we show for the first time that sensory neurons in the midbrain superior colliculus (SC) of the free-flying echolocating bat encode 3D egocentric space, and that the bat’s inspection of objects in the physical environment sharpens tuning of single neurons, and shifts peak responses to represent closer distances. These findings emerged from wireless neural recordings in free-flying bats, in combination with an echo model that computes the animal’s instantaneous stimulus space. Our research reveals dynamic 3D space coding in a freely moving mammal engaged in a real-world navigation task. PMID:29633711
Energy Technology Data Exchange (ETDEWEB)
Kowalski, K., E-mail: karol.kowalski@pnnl.gov; Bhaskaran-Nair, K.; Shelton, W. A. [William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352 (United States)
2014-09-07
In this paper we discuss a new formalism for producing an analytic coupled-cluster (CC) Green's function for an N-electron system by shifting the poles of similarity transformed Hamiltonians represented in N − 1 and N + 1 electron Hilbert spaces. Simple criteria are derived for the states in N − 1 and N + 1 electron spaces that are then corrected in the spectral resolution of the corresponding matrix representations of the similarity transformed Hamiltonian. The accurate description of excited state processes within a Green's function formalism would be of significant importance to a number of scientific communities ranging from physics and chemistry to engineering and the biological sciences. This is because the Green's function methodology provides a direct path for not only calculating properties whose underlying origins come from coupled many-body interactions but also provides a straightforward path for calculating electron transport, response, and correlation functions that allows for a direct link with experiment. As a special case of this general formulation, we discuss the application of this technique for Green's function defined by the CC with singles and doubles representation of the ground-state wave function.
Energy Technology Data Exchange (ETDEWEB)
Kowalski, K. [William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA; Bhaskaran-Nair, K. [William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA; Shelton, W. A. [William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
2014-09-07
In this paper we discuss a new formalism for producing an analytic coupled-cluster (CC) Green's function for an N-electron system by shifting the poles of similarity transformed Hamiltonians represented in N - 1 and N + 1 electron Hilbert spaces. Simple criteria are derived for the states in N - 1 and N + 1 electron spaces that are then corrected in the spectral resolution of the corresponding matrix representations of the similarity transformed Hamiltonian. The accurate description of excited state processes within a Green's function formalism would be of significant importance to a number of scientific communities ranging from physics and chemistry to engineering and the biological sciences. This is because the Green's function methodology provides a direct path for not only calculating properties whose underlying origins come from coupled many-body interactions but also provides a straightforward path for calculating electron transport, response, and correlation functions that allows for a direct link with experiment. Finally, as a special case of this general formulation, we discuss the application of this technique for Green's function defined by the CC with singles and doubles representation of the ground-state wave function.
International Nuclear Information System (INIS)
Kowalski, K.; Bhaskaran-Nair, K.; Shelton, W. A.
2014-01-01
In this paper we discuss a new formalism for producing an analytic coupled-cluster (CC) Green's function for an N-electron system by shifting the poles of similarity transformed Hamiltonians represented in N − 1 and N + 1 electron Hilbert spaces. Simple criteria are derived for the states in N − 1 and N + 1 electron spaces that are then corrected in the spectral resolution of the corresponding matrix representations of the similarity transformed Hamiltonian. The accurate description of excited state processes within a Green's function formalism would be of significant importance to a number of scientific communities ranging from physics and chemistry to engineering and the biological sciences. This is because the Green's function methodology provides a direct path for not only calculating properties whose underlying origins come from coupled many-body interactions but also provides a straightforward path for calculating electron transport, response, and correlation functions that allows for a direct link with experiment. As a special case of this general formulation, we discuss the application of this technique for Green's function defined by the CC with singles and doubles representation of the ground-state wave function
Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.
2018-04-01
This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.
Nanna, Robert J.
2016-01-01
Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…
Representational State Transfer a its support in programming language Java
Tran, Dac Ngoc Lam
2010-01-01
This bachelor thesis focuses on explaining the term Representational State Transfer (REST) and its usage in the programming language Java. The first chapter introduces readers with the theoretical basis of REST, its presence in HTTP protocol and its pros and cons in general. The second chapter is dedicated to the application of principles mentioned in the first chapter. On two different programs, a client and a server, I go through the analysis and programming the REST layer. After this chapt...
State space modeling of reactor core in a pressurized water reactor
Energy Technology Data Exchange (ETDEWEB)
Ashaari, A.; Ahmad, T.; M, Wan Munirah W. [Department of Mathematical Science, Faculty of Science, Universiti Teknologi Malaysia, 81310 Skudai, Johor (Malaysia); Shamsuddin, Mustaffa [Institute of Ibnu Sina, Universiti Teknologi Malaysia, 81310 Skudai, Johor (Malaysia); Abdullah, M. Adib [Swinburne University of Technology, Faculty of Engineering, Computing and Science, Jalan Simpang Tiga, 93350 Kuching, Sarawak (Malaysia)
2014-07-10
The power control system of a nuclear reactor is the key system that ensures a safe operation for a nuclear power plant. However, a mathematical model of a nuclear power plant is in the form of nonlinear process and time dependent that give very hard to be described. One of the important components of a Pressurized Water Reactor is the Reactor core. The aim of this study is to analyze the performance of power produced from a reactor core using temperature of the moderator as an input. Mathematical representation of the state space model of the reactor core control system is presented and analyzed in this paper. The data and parameters are taken from a real time VVER-type Pressurized Water Reactor and will be verified using Matlab and Simulink. Based on the simulation conducted, the results show that the temperature of the moderator plays an important role in determining the power of reactor core.
The use of virtual reality to reimagine two-dimensional representations of three-dimensional spaces
Fath, Elaine
2015-03-01
A familiar realm in the world of two-dimensional art is the craft of taking a flat canvas and creating, through color, size, and perspective, the illusion of a three-dimensional space. Using well-explored tricks of logic and sight, impossible landscapes such as those by surrealists de Chirico or Salvador Dalí seem to be windows into new and incredible spaces which appear to be simultaneously feasible and utterly nonsensical. As real-time 3D imaging becomes increasingly prevalent as an artistic medium, this process takes on an additional layer of depth: no longer is two-dimensional space restricted to strategies of light, color, line and geometry to create the impression of a three-dimensional space. A digital interactive environment is a space laid out in three dimensions, allowing the user to explore impossible environments in a way that feels very real. In this project, surrealist two-dimensional art was researched and reimagined: what would stepping into a de Chirico or a Magritte look and feel like, if the depth and distance created by light and geometry were not simply single-perspective illusions, but fully formed and explorable spaces? 3D environment-building software is allowing us to step into these impossible spaces in ways that 2D representations leave us yearning for. This art project explores what we gain--and what gets left behind--when these impossible spaces become doors, rather than windows. Using sketching, Maya 3D rendering software, and the Unity Engine, surrealist art was reimagined as a fully navigable real-time digital environment. The surrealist movement and its key artists were researched for their use of color, geometry, texture, and space and how these elements contributed to their work as a whole, which often conveys feelings of unexpectedness or uneasiness. The end goal was to preserve these feelings while allowing the viewer to actively engage with the space.
On the representations of Poincare group associated with unstable particles
International Nuclear Information System (INIS)
Exner, RP.
1983-01-01
The problem of relativistically-covariant description of unstable particles is reexamined. We follow the approach which associates a unitary reducible representation of Poincare group with a larger isolated system, and compare it with the one ascribing a non-unitary irreducible representation to the unstable particle alone. It is shown that the problem roots in choice of the subspace Hsub(u) of the state Hilbert space which could be related to the unstable particle. Translational invariance of Hsub(u) is proved to be incompatible with unitarity of the boosts. Further we propose a concrete choice of Hsub(u) and argue that in most cases of the actual experimental arrangements, this subspace is effectively one-dimensional. A correct slow-down for decay of a moving particle is obtained
Coherent states in the fermionic Fock space
International Nuclear Information System (INIS)
Oeckl, Robert
2015-01-01
We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing kernel Hilbert space of continuous holomorphic functions. (paper)
Modeling urban landscape: New paradigms and challenges in territorial representation
Directory of Open Access Journals (Sweden)
Sheyla Aguilar de Santana
2013-05-01
Full Text Available This paper aims to give a brief background on the production of urban space considering the social functions of the city, the needs of contemporary urban reforms and the need for tools that assist in decision making. This state of the art about the production space justifies the current studies on the development of geoprocessing tools, techniques and methodologies that attempt the needs of creating interpretive portraits of urban landscapes to facilitate dialogue between urban technical, administrators and community. In this sense, it is presented how GIS has been working within the context of urban planning and appointed the new challenges and paradigms of territorial representation.
Revisiting the conformal invariance of the scalar field: From Minkowski space to de Sitter space
International Nuclear Information System (INIS)
Huguet, E.; Queva, J.; Renaud, J.
2008-01-01
In this article, we clarify the link between the conformal (i.e. Weyl) correspondence from the Minkowski space to the de Sitter space and the conformal [i.e. SO(2,d)] invariance of the conformal scalar field on both spaces. We exhibit the realization on de Sitter space of the massless scalar representation of SO(2,d). It is obtained from the corresponding representation in Minkowski space through an intertwining operator inherited from the Weyl relation between the two spaces. The de Sitter representation is written in a form which allows one to take the point of view of a Minkowskian observer who sees the effect of curvature through additional terms
On integral formulation of the Mach principle in a conformally flat space
International Nuclear Information System (INIS)
Mal'tsev, V.K.
1976-01-01
The integral formulation of the Mach principle represents a rather complicated mathematical formalism in which many aspects of the physical content of theory are not clear. Below an attempt is made to consider the integral representation for the most simple case of conformally flat spaces. The fact that this formalism there is only one scalar function makes it possible to analyse in more detail many physical peculiarities of this representation of the Mach principle: the absence of asymptotically flat spaces, problems of inertia and gravity, constraints on state equations, etc
Directory of Open Access Journals (Sweden)
Devin H. Kehoe
2018-01-01
Full Text Available The oculomotor system utilizes color extensively for planning saccades. Therefore, we examined how the oculomotor system actually encodes color and several factors that modulate these representations: attention-based surround suppression and inherent biases in selecting and encoding color categories. We measured saccade trajectories while human participants performed a memory-guided saccade task with color targets and distractors and examined whether oculomotor target selection processing was functionally related to the CIE (x,y color space distances between color stimuli and whether there were hierarchical differences between color categories in the strength and speed of encoding potential saccade goals. We observed that saccade planning was modulated by the CIE (x,y distances between stimuli thus demonstrating that color is encoded in perceptual color space by the oculomotor system. Furthermore, these representations were modulated by (1 cueing attention to a particular color thereby eliciting surround suppression in oculomotor color space and (2 inherent selection and encoding biases based on color category independent of cueing and perceptual discriminability. Since surround suppression emerges from recurrent feedback attenuation of sensory projections, observing oculomotor surround suppression suggested that oculomotor encoding of behavioral relevance results from integrating sensory and cognitive signals that are pre-attenuated based on task demands and that the oculomotor system therefore does not functionally contribute to this process. Second, although perceptual discriminability did partially account for oculomotor processing differences between color categories, we also observed preferential processing of the red color category across various behavioral metrics. This is consistent with numerous previous studies and could not be simply explained by perceptual discriminability. Since we utilized a memory-guided saccade task, this
Kehoe, Devin H; Rahimi, Maryam; Fallah, Mazyar
2018-01-01
The oculomotor system utilizes color extensively for planning saccades. Therefore, we examined how the oculomotor system actually encodes color and several factors that modulate these representations: attention-based surround suppression and inherent biases in selecting and encoding color categories. We measured saccade trajectories while human participants performed a memory-guided saccade task with color targets and distractors and examined whether oculomotor target selection processing was functionally related to the CIE ( x , y ) color space distances between color stimuli and whether there were hierarchical differences between color categories in the strength and speed of encoding potential saccade goals. We observed that saccade planning was modulated by the CIE ( x , y ) distances between stimuli thus demonstrating that color is encoded in perceptual color space by the oculomotor system. Furthermore, these representations were modulated by (1) cueing attention to a particular color thereby eliciting surround suppression in oculomotor color space and (2) inherent selection and encoding biases based on color category independent of cueing and perceptual discriminability. Since surround suppression emerges from recurrent feedback attenuation of sensory projections, observing oculomotor surround suppression suggested that oculomotor encoding of behavioral relevance results from integrating sensory and cognitive signals that are pre-attenuated based on task demands and that the oculomotor system therefore does not functionally contribute to this process. Second, although perceptual discriminability did partially account for oculomotor processing differences between color categories, we also observed preferential processing of the red color category across various behavioral metrics. This is consistent with numerous previous studies and could not be simply explained by perceptual discriminability. Since we utilized a memory-guided saccade task, this indicates that
Space-time interdependence: evidence against asymmetric mapping between time and space.
Cai, Zhenguang G; Connell, Louise
2015-03-01
Time and space are intimately related, but what is the real nature of this relationship? Is time mapped metaphorically onto space such that effects are always asymmetric (i.e., space affects time more than time affects space)? Or do the two domains share a common representational format and have the ability to influence each other in a flexible manner (i.e., time can sometimes affect space more than vice versa)? In three experiments, we examined whether spatial representations from haptic perception, a modality of relatively low spatial acuity, would lead the effect of time on space to be substantially stronger than the effect of space on time. Participants touched (but could not see) physical sticks while listening to an auditory note, and then reproduced either the length of the stick or the duration of the note. Judgements of length were affected by concurrent stimulus duration, but not vice versa. When participants were allowed to see as well as touch the sticks, however, the higher acuity of visuohaptic perception caused the effects to converge so length and duration influenced each other to a similar extent. These findings run counter to the spatial metaphor account of time, and rather support the spatial representation account in which time and space share a common representational format and the directionality of space-time interaction depends on the perceptual acuity of the modality used to perceive space. Copyright © 2014 Elsevier B.V. All rights reserved.
Wigner representation in scattering problems
International Nuclear Information System (INIS)
Remler, E.A.
1975-01-01
The basic equations of quantum scattering are translated into the Wigner representation. This puts quantum mechanics in the form of a stochastic process in phase space. Instead of complex valued wavefunctions and transition matrices, one now works with real-valued probability distributions and source functions, objects more responsive to physical intuition. Aside from writing out certain necessary basic expressions, the main purpose is to develop and stress the interpretive picture associated with this representation and to derive results used in applications published elsewhere. The quasiclassical guise assumed by the formalism lends itself particularly to approximations of complex multiparticle scattering problems is laid. The foundation for a systematic application of statistical approximations to such problems. The form of the integral equation for scattering as well as its mulitple scattering expansion in this representation are derived. Since this formalism remains unchanged upon taking the classical limit, these results also constitute a general treatment of classical multiparticle collision theory. Quantum corrections to classical propogators are discussed briefly. The basic approximation used in the Monte Carlo method is derived in a fashion that allows for future refinement and includes bound state production. The close connection that must exist between inclusive production of a bound state and of its constituents is brought out in an especially graphic way by this formalism. In particular one can see how comparisons between such cross sections yield direct physical insight into relevant production mechanisms. A simple illustration of scattering by a bound two-body system is treated. Simple expressions for single- and double-scattering contributions to total and differential cross sections, as well as for all necessary shadow corrections thereto, are obtained and compared to previous results of Glauber and Goldberger
Character and determinant formulae of quasifinite representation of the W1+∞ algebra
International Nuclear Information System (INIS)
Awata, H.; Fukuma, M.; Matsuo, Y.; Odake, S.
1994-05-01
We diagonalize the Hilbert space of the quasifinite module of the W 1+∞ algebra. States are classified according to their eigenvalues for infinitely many commuting charges and the Young diagrams. The parameter dependence of their norms is explicitly derived. The full character formulae of the degenerate representations are given as summation of the bilinear combinations of the Schur polynomials. (author)
Directory of Open Access Journals (Sweden)
Stéphane eJacobs
2011-05-01
Full Text Available The study of crossmodal extinction has brought a considerable contribution to our understanding of how the integration of stimuli perceived in multiple sensory modalities is used by the nervous system to build coherent representations of the space that directly surrounds us. Indeed, by revealing interferences between stimuli in a disturbed system, extinction provides an invaluable opportunity to investigate the interactions that normally exist between those stimuli in an intact system. Here, we first review studies on pathological crossmodal extinction, from the original demonstration of its existence, to its role in the exploration of the multisensory neural representation of space and the current theoretical accounts proposed to explain the mechanisms involved in extinction and multisensory competition. Then, in the second part of this paper, we report recent findings showing that physiological multisensory competition phenomena resembling clinical crossmodal extinction exist in the healthy brain. We propose that the development of a physiological model of sensory competition is fundamental to deepen our understanding of the cerebral mechanisms of multisensory perception and integration. In addition, a similar approach to develop a model of physiological sensory competition in nonhuman primates should allow combining functional neuroimaging with more invasive techniques, such as transient focal lesions, in order to bridge the gap between works done in the two species and at different levels of analysis.
Directory of Open Access Journals (Sweden)
Giovanni ePezzulo
2013-11-01
Full Text Available The article explores the possibilities of formalizing and explaining the mechanisms that support spatial and social perspective alignment sustained over the duration of a social interaction. The basic proposed principle is that in social contexts the mechanisms for sensorimotor transformations and multisensory integration (learn to incorporate information relative to the other actor(s, similar to the "re-calibration" of visual receptive fields in response to repeated tool use. This process aligns or merges the co-actors' spatial representations and creates a "Shared Action Space" supporting key computations of social interactions and joint actions; for example, the remapping between the coordinate systems and frames of reference of the co-actors, including perspective taking, the sensorimotor transformations required for lifting jointly an object, and the predictions of the sensory effects of such joint action. The social re-calibration is proposed to be based on common basis function maps and could constitute an optimal solution to sensorimotor transformation and multisensory integration in joint action or more in general social interaction contexts. However, certain situations such as discrepant postural and viewpoint alignment and associated differences in perspectives between the co-actors could constrain the process quite differently. We discuss how alignment is achieved in the first place, and how it is maintained over time, providing a taxonomy of various forms and mechanisms of space alignment and overlap based, for instance, on automaticity vs. control of the transformations between the two agents. Finally, we discuss the link between low-level mechanisms for the sharing of space and high-level mechanisms for the sharing of cognitive representations.
Jurco, B; Jurco, B; Schlieker, M
1995-01-01
In this paper we construct explicitly natural (from the geometrical point of view) Fock space representations (contragradient Verma modules) of the quantized enveloping algebras. In order to do so, we start from the Gauss decomposition of the quantum group and introduce the differential operators on the corresponding q-deformed flag manifold (asuumed as a left comodule for the quantum group) by a projection to it of the right action of the quantized enveloping algebra on the quantum group. Finally, we express the representatives of the elements of the quantized enveloping algebra corresponding to the left-invariant vector fields on the quantum group as first-order differential operators on the q-deformed flag manifold.
Theory of the unitary representations of compact groups
International Nuclear Information System (INIS)
Burzynski, A.; Burzynska, M.
1979-01-01
An introduction contains some basic notions used in group theory, Lie group, Lie algebras and unitary representations. Then we are dealing with compact groups. For these groups we show the problem of reduction of unitary representation of Wigner's projection operators, Clebsch-Gordan coefficients and Wigner-Eckart theorem. We show (this is a new approach) the representations reduction formalism by using superoperators in Hilbert-Schmidt space. (author)
Coherent states for quantum compact groups
Jurco, B
1996-01-01
Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit and interpret the coherent state as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R--matrix formulation (generalizing this way the q--deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel--Weil construction) are described using the concept of coherent state. The relation between representation theory and non--commutative differential geometry is suggested.}
Signal and image representation in combined spaces
Zeevi, Yehoshua; Chui, Charles K
1997-01-01
This volume explains how the recent advances in wavelet analysis provide new means for multiresolution analysis and describes its wide array of powerful tools. The book covers variations of the windowed Fourier transform, constructions of special waveforms suitable for specific tasks, the use of redundant representations in reconstruction and enhancement, applications of efficient numerical compression as a tool for fast numerical analysis, and approximation properties of various waveforms in different contexts.
Representation and redistribution in federations.
Dragu, Tiberiu; Rodden, Jonathan
2011-05-24
Many of the world's most populous democracies are political unions composed of states or provinces that are unequally represented in the national legislature. Scattered empirical studies, most of them focusing on the United States, have discovered that overrepresented states appear to receive larger shares of the national budget. Although this relationship is typically attributed to bargaining advantages associated with greater legislative representation, an important threat to empirical identification stems from the fact that the representation scheme was chosen by the provinces. Thus, it is possible that representation and fiscal transfers are both determined by other characteristics of the provinces in a specific country. To obtain an improved estimate of the relationship between representation and redistribution, we collect and analyze provincial-level data from nine federations over several decades, taking advantage of the historical process through which federations formed and expanded. Controlling for a variety of country- and province-level factors and using a variety of estimation techniques, we show that overrepresented provinces in political unions around the world are rather dramatically favored in the distribution of resources.
International Nuclear Information System (INIS)
Ibort, A; Man'ko, V I; Marmo, G; Simoni, A; Ventriglia, F
2009-01-01
A natural extension of the Wigner function to the space of irreducible unitary representations of the Weyl-Heisenberg group is discussed. The action of the automorphisms group of the Weyl-Heisenberg group onto Wigner functions and their generalizations and onto symplectic tomograms is elucidated. Some examples of physical systems are considered to illustrate some aspects of the characterization of the Wigner functions as solutions of differential equations
State-space prediction model for chaotic time series
Alparslan, A. K.; Sayar, M.; Atilgan, A. R.
1998-08-01
A simple method for predicting the continuation of scalar chaotic time series ahead in time is proposed. The false nearest neighbors technique in connection with the time-delayed embedding is employed so as to reconstruct the state space. A local forecasting model based upon the time evolution of the topological neighboring in the reconstructed phase space is suggested. A moving root-mean-square error is utilized in order to monitor the error along the prediction horizon. The model is tested for the convection amplitude of the Lorenz model. The results indicate that for approximately 100 cycles of the training data, the prediction follows the actual continuation very closely about six cycles. The proposed model, like other state-space forecasting models, captures the long-term behavior of the system due to the use of spatial neighbors in the state space.
State Machine Modeling of the Space Launch System Solid Rocket Boosters
Harris, Joshua A.; Patterson-Hine, Ann
2013-01-01
The Space Launch System is a Shuttle-derived heavy-lift vehicle currently in development to serve as NASA's premiere launch vehicle for space exploration. The Space Launch System is a multistage rocket with two Solid Rocket Boosters and multiple payloads, including the Multi-Purpose Crew Vehicle. Planned Space Launch System destinations include near-Earth asteroids, the Moon, Mars, and Lagrange points. The Space Launch System is a complex system with many subsystems, requiring considerable systems engineering and integration. To this end, state machine analysis offers a method to support engineering and operational e orts, identify and avert undesirable or potentially hazardous system states, and evaluate system requirements. Finite State Machines model a system as a finite number of states, with transitions between states controlled by state-based and event-based logic. State machines are a useful tool for understanding complex system behaviors and evaluating "what-if" scenarios. This work contributes to a state machine model of the Space Launch System developed at NASA Ames Research Center. The Space Launch System Solid Rocket Booster avionics and ignition subsystems are modeled using MATLAB/Stateflow software. This model is integrated into a larger model of Space Launch System avionics used for verification and validation of Space Launch System operating procedures and design requirements. This includes testing both nominal and o -nominal system states and command sequences.
Reversibility and the structure of the local state space
International Nuclear Information System (INIS)
Al-Safi, Sabri W; Richens, Jonathan
2015-01-01
The richness of quantum theory’s reversible dynamics is one of its unique operational characteristics, with recent results suggesting deep links between the theory’s reversible dynamics, its local state space and the degree of non-locality it permits. We explore the delicate interplay between these features, demonstrating that reversibility places strong constraints on both the local and global state space. Firstly, we show that all reversible dynamics are trivial (composed of local transformations and permutations of subsytems) in maximally non-local theories whose local state spaces satisfy a dichotomy criterion; this applies to a range of operational models that have previously been studied, such as d-dimensional ‘hyperballs’ and almost all regular polytope systems. By separately deriving a similar result for odd-sided polygons, we show that classical systems are the only regular polytope state spaces whose maximally non-local composites allow for non-trivial reversible dynamics. Secondly, we show that non-trivial reversible dynamics do exist in maximally non-local theories whose state spaces are reducible into two or more smaller spaces. We conjecture that this is a necessary condition for the existence of such dynamics, but that reversible entanglement generation remains impossible even in this scenario. (paper)
Quantum magnification of classical sub-Planck phase space features
International Nuclear Information System (INIS)
Hensinger, W.K.; Heckenberg, N.; Rubinsztein-Dunlop, H.; Delande, D.
2002-01-01
Full text: To understand the relationship between quantum mechanics and classical physics a crucial question to be answered is how distinct classical dynamical phase space features translate into the quantum picture. This problem becomes even more interesting if these phase space features occupy a much smaller volume than ℎ in a phase space spanned by two non-commuting variables such as position and momentum. The question whether phase space structures in quantum mechanics associated with sub-Planck scales have physical signatures has recently evoked a lot of discussion. Here we will show that sub-Planck classical dynamical phase space structures, for example regions of regular motion, can give rise to states whose phase space representation is of size ℎ or larger. This is illustrated using period-1 regions of regular motion (modes of oscillatory motion of a particle in a modulated well) whose volume is distinctly smaller than Planck's constant. They are magnified in the quantum picture and appear as states whose phase space representation is of size h or larger. Cold atoms provide an ideal test bed to probe such fundamental aspects of quantum and classical dynamics. In the experiment a Bose-Einstein condensate is loaded into a far detuned optical lattice. The lattice depth is modulated resulting in the emergence of regions of regular motion surrounded by chaotic motion in the phase space spanned by position and momentum of the atoms along the standing wave. Sub-Planck scaled phase space features in the classical phase space are magnified and appear as distinct broad peaks in the atomic momentum distribution. The corresponding quantum analysis shows states of size Ti which can be associated with much smaller classical dynamical phase space features. This effect may considered as the dynamical equivalent of the Goldstone and Jaffe theorem which predicts the existence of at least one bound state at a bend in a two or three dimensional spatial potential
A simple and fast representation space for classifying complex time series
International Nuclear Information System (INIS)
Zunino, Luciano; Olivares, Felipe; Bariviera, Aurelio F.; Rosso, Osvaldo A.
2017-01-01
In the context of time series analysis considerable effort has been directed towards the implementation of efficient discriminating statistical quantifiers. Very recently, a simple and fast representation space has been introduced, namely the number of turning points versus the Abbe value. It is able to separate time series from stationary and non-stationary processes with long-range dependences. In this work we show that this bidimensional approach is useful for distinguishing complex time series: different sets of financial and physiological data are efficiently discriminated. Additionally, a multiscale generalization that takes into account the multiple time scales often involved in complex systems has been also proposed. This multiscale analysis is essential to reach a higher discriminative power between physiological time series in health and disease. - Highlights: • A bidimensional scheme has been tested for classification purposes. • A multiscale generalization is introduced. • Several practical applications confirm its usefulness. • Different sets of financial and physiological data are efficiently distinguished. • This multiscale bidimensional approach has high potential as discriminative tool.
A simple and fast representation space for classifying complex time series
Energy Technology Data Exchange (ETDEWEB)
Zunino, Luciano, E-mail: lucianoz@ciop.unlp.edu.ar [Centro de Investigaciones Ópticas (CONICET La Plata – CIC), C.C. 3, 1897 Gonnet (Argentina); Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900 La Plata (Argentina); Olivares, Felipe, E-mail: olivaresfe@gmail.com [Instituto de Física, Pontificia Universidad Católica de Valparaíso (PUCV), 23-40025 Valparaíso (Chile); Bariviera, Aurelio F., E-mail: aurelio.fernandez@urv.cat [Department of Business, Universitat Rovira i Virgili, Av. Universitat 1, 43204 Reus (Spain); Rosso, Osvaldo A., E-mail: oarosso@gmail.com [Instituto de Física, Universidade Federal de Alagoas (UFAL), BR 104 Norte km 97, 57072-970, Maceió, Alagoas (Brazil); Instituto Tecnológico de Buenos Aires (ITBA) and CONICET, C1106ACD, Av. Eduardo Madero 399, Ciudad Autónoma de Buenos Aires (Argentina); Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Av. Mons. Álvaro del Portillo 12.455, Las Condes, Santiago (Chile)
2017-03-18
In the context of time series analysis considerable effort has been directed towards the implementation of efficient discriminating statistical quantifiers. Very recently, a simple and fast representation space has been introduced, namely the number of turning points versus the Abbe value. It is able to separate time series from stationary and non-stationary processes with long-range dependences. In this work we show that this bidimensional approach is useful for distinguishing complex time series: different sets of financial and physiological data are efficiently discriminated. Additionally, a multiscale generalization that takes into account the multiple time scales often involved in complex systems has been also proposed. This multiscale analysis is essential to reach a higher discriminative power between physiological time series in health and disease. - Highlights: • A bidimensional scheme has been tested for classification purposes. • A multiscale generalization is introduced. • Several practical applications confirm its usefulness. • Different sets of financial and physiological data are efficiently distinguished. • This multiscale bidimensional approach has high potential as discriminative tool.
Non-commutative representation for quantum systems on Lie groups
Energy Technology Data Exchange (ETDEWEB)
Raasakka, Matti Tapio
2014-01-27
The topic of this thesis is a new representation for quantum systems on weakly exponential Lie groups in terms of a non-commutative algebra of functions, the associated non-commutative harmonic analysis, and some of its applications to specific physical systems. In the first part of the thesis, after a review of the necessary mathematical background, we introduce a {sup *}-algebra that is interpreted as the quantization of the canonical Poisson structure of the cotangent bundle over a Lie group. From the physics point of view, this represents the algebra of quantum observables of a physical system, whose configuration space is a Lie group. We then show that this quantum algebra can be represented either as operators acting on functions on the group, the usual group representation, or (under suitable conditions) as elements of a completion of the universal enveloping algebra of the Lie group, the algebra representation. We further apply the methods of deformation quantization to obtain a representation of the same algebra in terms of a non-commutative algebra of functions on a Euclidean space, which we call the non-commutative representation of the original quantum algebra. The non-commutative space that arises from the construction may be interpreted as the quantum momentum space of the physical system. We derive the transform between the group representation and the non-commutative representation that generalizes in a natural way the usual Fourier transform, and discuss key properties of this new non-commutative harmonic analysis. Finally, we exhibit the explicit forms of the non-commutative Fourier transform for three elementary Lie groups: R{sup d}, U(1) and SU(2). In the second part of the thesis, we consider application of the non-commutative representation and harmonic analysis to physics. First, we apply the formalism to quantum mechanics of a point particle on a Lie group. We define the dual non-commutative momentum representation, and derive the phase
Non-commutative representation for quantum systems on Lie groups
International Nuclear Information System (INIS)
Raasakka, Matti Tapio
2014-01-01
The topic of this thesis is a new representation for quantum systems on weakly exponential Lie groups in terms of a non-commutative algebra of functions, the associated non-commutative harmonic analysis, and some of its applications to specific physical systems. In the first part of the thesis, after a review of the necessary mathematical background, we introduce a * -algebra that is interpreted as the quantization of the canonical Poisson structure of the cotangent bundle over a Lie group. From the physics point of view, this represents the algebra of quantum observables of a physical system, whose configuration space is a Lie group. We then show that this quantum algebra can be represented either as operators acting on functions on the group, the usual group representation, or (under suitable conditions) as elements of a completion of the universal enveloping algebra of the Lie group, the algebra representation. We further apply the methods of deformation quantization to obtain a representation of the same algebra in terms of a non-commutative algebra of functions on a Euclidean space, which we call the non-commutative representation of the original quantum algebra. The non-commutative space that arises from the construction may be interpreted as the quantum momentum space of the physical system. We derive the transform between the group representation and the non-commutative representation that generalizes in a natural way the usual Fourier transform, and discuss key properties of this new non-commutative harmonic analysis. Finally, we exhibit the explicit forms of the non-commutative Fourier transform for three elementary Lie groups: R d , U(1) and SU(2). In the second part of the thesis, we consider application of the non-commutative representation and harmonic analysis to physics. First, we apply the formalism to quantum mechanics of a point particle on a Lie group. We define the dual non-commutative momentum representation, and derive the phase space path
Realization and elimination in rational representations of behaviors
Gottimukkala, Sasanka V.; Trentelman, Hendrikus; Fiaz, Shaik
This article deals with the relationship between rational representations of linear differential systems and their state representations. In particular we study the relationship between rational representations on the one hand, and output nulling and driving variable representations on the other. In
Simple derivation of magnetic space groups
International Nuclear Information System (INIS)
Bertaut, E.F.; CEA Centre d'Etudes Nucleaires de Grenoble, 38
1975-01-01
The magnetic translation lattices can be described by invariant wave vectors k. Advantages of the wave vector notation over the notations used by Belov et al. and Opechowski et al. are pointed out. In a one-dimensional real representation a space group element (α/tau(1)) has either the character +1 (symmetry element) or -1 (antisymmetry element). Thus the square of any space group operation must have the character +1 in a one-dimensional real representation. This simple ''square criterion'' is used to limit the admissible k-vectors and to derive the family of magnetic space groups, i.e. the set of all possible magnetic space groups, belonging to the same crystallographic space group. In the discussion some useful side results are obtained. Not only the real one-dimensional representations of point groups are connected to real one-dimensional representations of space groups, but a direct connection is shown to exist between one-dimensional complex representations of the point groups 3, 4 and 6 and one-dimensional real representations, belonging to P[001/2]=Psub(2c)(Psub(c))-lattices with screw axes 3 1 , 3 2 , 4 2 , 6 2 and 6 4 . Rules are derived for finding the Belov symbol when the Opechowski-Guccione symbol of the magnetic space group is known and this opportunity is used for correcting errors in the Opechowski-Guccione tables [fr
Identified state-space prediction model for aero-optical wavefronts
Faghihi, Azin; Tesch, Jonathan; Gibson, Steve
2013-07-01
A state-space disturbance model and associated prediction filter for aero-optical wavefronts are described. The model is computed by system identification from a sequence of wavefronts measured in an airborne laboratory. Estimates of the statistics and flow velocity of the wavefront data are shown and can be computed from the matrices in the state-space model without returning to the original data. Numerical results compare velocity values and power spectra computed from the identified state-space model with those computed from the aero-optical data.
Book, W. J.; Majett, M.
1982-01-01
The potential benefits of the ability to control more flexible mechanical arms are discussed. A justification is made in terms of speed of movement. A new controller design procedure is then developed to provide this capability. It uses both a frequency domain representation and a state variable representation of the arm model. The frequency domain model is used to update the modal state variable model to insure decoupled states. The technique is applied to a simple example with encouraging results.
Uncertainty evaluation for IIR (infinite impulse response) filtering using a state-space approach
International Nuclear Information System (INIS)
Link, Alfred; Elster, Clemens
2009-01-01
A novel method is proposed for evaluating the uncertainty associated with the output of a discrete-time IIR filter when the input signal is corrupted by additive noise and the filter coefficients are uncertain. This task arises, for instance, when the noise-corrupted output of a measurement system is compensated by a digital filter which has been designed on the basis of the characteristics of the measurement system. We assume that the noise is either stationary or uncorrelated, and we presume knowledge about its autocovariance function or its time-dependent variances, respectively. Uncertainty evaluation is considered in line with the 'Guide to the Expression of Uncertainty in Measurement'. A state-space representation is used to derive a calculation scheme which allows the uncertainties to be evaluated in an easy way and also enables real-time applications. The proposed procedure is illustrated by an example
Anharmonic potential in the oscillator representation
International Nuclear Information System (INIS)
Dineykhan, M.; Efimov, G.V.
1994-01-01
In the non relativistic and relativized Schroedinger equation the Wick ordering method called the oscillator representation is proposed to calculate the energy spectrum for a wide class of potentials allowing the existence of a bound state. The oscillator representation method gives a unique regular way to describe and calculate the energy levels of ground as well as orbital and radial excitation states for a wide class of potentials. The results of the zeroth approximation oscillator representation are in good agreement with the exact values for the anharmonic potentials. The oscillator representation method was applied to the relativized Schroedinger equation too. The perturbation series converges fairly fast, i.e., the highest perturbation corrections over the interaction Hamiltonian are small enough. 29 refs.; 4 tabs. (author)
Space groups for solid state scientists
Glazer, Michael; Glazer, Alexander N
2014-01-01
This Second Edition provides solid state scientists, who are not necessarily experts in crystallography, with an understandable and comprehensive guide to the new International Tables for Crystallography. The basic ideas of symmetry, lattices, point groups, and space groups are explained in a clear and detailed manner. Notation is introduced in a step-by-step way so that the reader is supplied with the tools necessary to derive and apply space group information. Of particular interest in this second edition are the discussions of space groups application to such timely topics as high-te
Peripersonal space in the brain.
di Pellegrino, Giuseppe; Làdavas, Elisabetta
2015-01-01
Research in neuroscience reveals that the brain constructs multiple representation of space. Here, we primarily focus on peripersonal space (PPS) representation, the region of space immediately surrounding our bodies and in which objects can be grasped and manipulated. We review convergent results from several generations of studies, including neurophysiological studies in animals, neuropsychological investigations in monkeys and brain-damaged patients with spatial cognition disorders, as well as recent neuroimaging experiments in neurologically normal individuals. Collectively, these studies show that the primate brain constructs multiple, rapidly modifiable representations of space, centered on different body parts (i.e., hand-centered, head-centered, and trunk-centered), which arise through extensive multisensory interactions within a set of interconnected parietal and frontal regions. PPS representations are pivotal in the sensory guidance of motor behavior, allowing us to interact with objects and, as demonstrated by recent studies, with other people in the space around us. Copyright © 2014 Elsevier Ltd. All rights reserved.
Quantization of Space-like States in Lorentz-Violating Theories
Colladay, Don
2018-01-01
Lorentz violation frequently induces modified dispersion relations that can yield space-like states that impede the standard quantization procedures. In certain cases, an extended Hamiltonian formalism can be used to define observer-covariant normalization factors for field expansions and phase space integrals. These factors extend the theory to include non-concordant frames in which there are negative-energy states. This formalism provides a rigorous way to quantize certain theories containing space-like states and allows for the consistent computation of Cherenkov radiation rates in arbitrary frames and avoids singular expressions.
Weighted -Integral Representations of -Functions in
Directory of Open Access Journals (Sweden)
Arman H. Karapetyan
2012-01-01
Full Text Available For 1-functions , given in the complex space , integral representations of the form =(−( are obtained. Here, is the orthogonal projector of the space 2{;−||||(} onto its subspace of entire functions and the integral operator appears by means of explicitly constructed kernel Φ which is investigated in detail.
Coherent states for quantum compact groups
International Nuclear Information System (INIS)
Jurco, B.; Stovicek, P.; CTU, Prague
1996-01-01
Coherent states are introduced and their properties are discussed for simple quantum compact groups A l , B l , C l and D l . The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested. (orig.)
System resiliency quantification using non-state-space and state-space analytic models
International Nuclear Information System (INIS)
Ghosh, Rahul; Kim, DongSeong; Trivedi, Kishor S.
2013-01-01
Resiliency is becoming an important service attribute for large scale distributed systems and networks. Key problems in resiliency quantification are lack of consensus on the definition of resiliency and systematic approach to quantify system resiliency. In general, resiliency is defined as the ability of (system/person/organization) to recover/defy/resist from any shock, insult, or disturbance [1]. Many researchers interpret resiliency as a synonym for fault-tolerance and reliability/availability. However, effect of failure/repair on systems is already covered by reliability/availability measures and that of on individual jobs is well covered under the umbrella of performability [2] and task completion time analysis [3]. We use Laprie [4] and Simoncini [5]'s definition in which resiliency is the persistence of service delivery that can justifiably be trusted, when facing changes. The changes we are referring to here are beyond the envelope of system configurations already considered during system design, that is, beyond fault tolerance. In this paper, we outline a general approach for system resiliency quantification. Using examples of non-state-space and state-space stochastic models, we analytically–numerically quantify the resiliency of system performance, reliability, availability and performability measures w.r.t. structural and parametric changes
Harvey, Ben M; Dumoulin, Serge O
2016-02-15
Several studies demonstrate that visual stimulus motion affects neural receptive fields and fMRI response amplitudes. Here we unite results of these two approaches and extend them by examining the effects of visual motion on neural position preferences throughout the hierarchy of human visual field maps. We measured population receptive field (pRF) properties using high-field fMRI (7T), characterizing position preferences simultaneously over large regions of the visual cortex. We measured pRFs properties using sine wave gratings in stationary apertures, moving at various speeds in either the direction of pRF measurement or the orthogonal direction. We find direction- and speed-dependent changes in pRF preferred position and size in all visual field maps examined, including V1, V3A, and the MT+ map TO1. These effects on pRF properties increase up the hierarchy of visual field maps. However, both within and between visual field maps the extent of pRF changes was approximately proportional to pRF size. This suggests that visual motion transforms the representation of visual space similarly throughout the visual hierarchy. Visual motion can also produce an illusory displacement of perceived stimulus position. We demonstrate perceptual displacements using the same stimulus configuration. In contrast to effects on pRF properties, perceptual displacements show only weak effects of motion speed, with far larger speed-independent effects. We describe a model where low-level mechanisms could underlie the observed effects on neural position preferences. We conclude that visual motion induces similar transformations of visuo-spatial representations throughout the visual hierarchy, which may arise through low-level mechanisms. Copyright © 2015 Elsevier Inc. All rights reserved.
Graded contractions of Jordan algebras and of their representations
International Nuclear Information System (INIS)
Kashuba, Iryna; Patera, JirI
2003-01-01
Contractions of Jordan algebras and Jordan superalgebras which preserve a chosen grading are defined and studied. Simultaneous grading of Jordan algebras and their representation spaces is used to develop a theory of grading, preserving contractions of representations of Jordan algebras
International Nuclear Information System (INIS)
Fan Hongyi; Wang Yong
2006-01-01
With the help of Bose operator identities and entangled state representation and based on our previous work [Phys. Lett. A 325 (2004) 188] we derive some new generalized Bessel equations which also have Bessel function as their solution. It means that for these intricate higher-order differential equations, we can get Bessel function solutions without using the expatiatory power-series expansion method.
States in the Hilbert space formulation and in the phase space formulation of quantum mechanics
International Nuclear Information System (INIS)
Tosiek, J.; Brzykcy, P.
2013-01-01
We consider the problem of testing whether a given matrix in the Hilbert space formulation of quantum mechanics or a function considered in the phase space formulation of quantum theory represents a quantum state. We propose several practical criteria for recognising states in these two versions of quantum physics. After minor modifications, they can be applied to check positivity of any operators acting in a Hilbert space or positivity of any functions from an algebra with a ∗-product of Weyl type. -- Highlights: ► Methods of testing whether a given matrix represents a quantum state. ► The Stratonovich–Weyl correspondence on an arbitrary symplectic manifold. ► Criteria for checking whether a function on a symplectic space is a Wigner function
International Nuclear Information System (INIS)
Amitabh, J.; Vaccaro, J.A.; Hill, K.E.
1998-01-01
We study the recently defined number-phase Wigner function S NP (n,θ) for a single-mode field considered to be in binomial and negative binomial states. These states interpolate between Fock and coherent states and coherent and quasi thermal states, respectively, and thus provide a set of states with properties ranging from uncertain phase and sharp photon number to sharp phase and uncertain photon number. The distribution function S NP (n,θ) gives a graphical representation of the complimentary nature of the number and phase properties of these states. We highlight important differences between Wigner's quasi probability function, which is associated with the position and momentum observables, and S NP (n,θ), which is associated directly with the photon number and phase observables. We also discuss the number-phase entropic uncertainty relation for the binomial and negative binomial states and we show that negative binomial states give a lower phase entropy than states which minimize the phase variance
How to upload a physical quantum state into correlation space
International Nuclear Information System (INIS)
Morimae, Tomoyuki
2011-01-01
In the framework of the computational tensor network [Phys. Rev. Lett. 98, 220503 (2007)], the quantum computation is performed in a virtual linear space called the correlation space. It was recently shown [Phys. Rev. Lett. 103, 050503 (2009)] that a state in a correlation space can be downloaded to the real physical space. In this paper, conversely, we study how to upload a state from a real physical space to the correlation space. After showing the impossibility of cloning a state between a real physical space and the correlation space, we propose a simple teleportation-like method of uploading. This method also enables the Gottesman-Chuang gate teleportation trick and entanglement swapping in the virtual-real hybrid setting. Furthermore, compared with the inverse of the downloading method by Cai et al. [Phys. Rev. Lett. 103, 050503 (2009)], which also works to upload, the proposed uploading method has several advantages.
State-space approach for evaluating the soil-plant-atmosphere system
International Nuclear Information System (INIS)
Timm, L.C.; Reichardt, K.; Cassaro, F.A.M.; Tominaga, T.T.; Bacchi, O.O.S.; Oliveira, J.C.M.; Dourado-Neto, D.
2004-01-01
Using as examples one sugarcane and one forage oat experiment, both carried out in the State of Sao Paulo, Brazil, this chapter presents recent state-space approaches used to evaluate the relation between soil and plant properties. A contrast is made between classical statistics methodologies that do not take into account the sampling position coordinates, and the more recently used methodologies which include the position coordinates, and allow a better interpretation of the field-sampled data. Classical concepts are first introduced, followed by spatially referenced methodologies like the autocorrelation function, the cross correlation function, and the state-space approach. Two variations of the state-space approach are given: one emphasizes the evolution of the state system while the other based on the bayesian formulation emphasizes the evolution of the estimated observations. It is concluded that these state-space analyses using dynamic regression models improve data analyses and are therefore recommended for analyzing time and space data series related to the performance of a given soil-plant-atmosphere system. (author)
The coherent state on SUq(2) homogeneous space
International Nuclear Information System (INIS)
Aizawa, N; Chakrabarti, R
2009-01-01
The generalized coherent states for quantum groups introduced by Jurco and StovIcek are studied for the simplest example SU q (2) in full detail. It is shown that the normalized SU q (2) coherent states enjoy the property of completeness, and allow a resolution of the unity. This feature is expected to play a key role in the application of these coherent states in physical models. The homogeneous space of SU q (2), i.e. the q-sphere of Podles, is reproduced in complex coordinates by using the coherent states. Differential calculus in the complex form on the homogeneous space is developed. The high spin limit of the SU q (2) coherent states is also discussed.
An Improved Treatment of AC Space Charge Fields in Large Signal Simulation Codes
National Research Council Canada - National Science Library
Dialetis, D; Chernin, D; Antonsen, Jr., T. M; Levush, B
2006-01-01
An accurate representation of the AC space charge electric field is required in order to be able to predict the performance of linear beam tubes, including TWT's and klystrons, using a steady state...
Motor and linguistic linking of space and time in the cerebellum.
Oliveri, Massimiliano; Bonnì, Sonia; Turriziani, Patrizia; Koch, Giacomo; Lo Gerfo, Emanuele; Torriero, Sara; Vicario, Carmelo Mario; Petrosini, Laura; Caltagirone, Carlo
2009-11-20
Recent literature documented the presence of spatial-temporal interactions in the human brain. The aim of the present study was to verify whether representation of past and future is also mapped onto spatial representations and whether the cerebellum may be a neural substrate for linking space and time in the linguistic domain. We asked whether processing of the tense of a verb is influenced by the space where response takes place and by the semantics of the verb. Responses to past tense were facilitated in the left space while responses to future tense were facilitated in the right space. Repetitive transcranial magnetic stimulation (rTMS) of the right cerebellum selectively slowed down responses to future tense of action verbs; rTMS of both cerebellar hemispheres decreased accuracy of responses to past tense in the left space and to future tense in the right space for non-verbs, and to future tense in the right space for state verbs. The results suggest that representation of past and future is mapped onto spatial formats and that motor action could represent the link between spatial and temporal dimensions. Right cerebellar, left motor brain networks could be part of the prospective brain, whose primary function is to use past experiences to anticipate future events. Both cerebellar hemispheres could play a role in establishing the grammatical rules for verb conjugation.
Dimensional reduction from entanglement in Minkowski space
International Nuclear Information System (INIS)
Brustein, Ram; Yarom, Amos
2005-01-01
Using a quantum field theoretic setting, we present evidence for dimensional reduction of any sub-volume of Minkowksi space. First, we show that correlation functions of a class of operators restricted to a sub-volume of D-dimensional Minkowski space scale as its surface area. A simple example of such area scaling is provided by the energy fluctuations of a free massless quantum field in its vacuum state. This is reminiscent of area scaling of entanglement entropy but applies to quantum expectation values in a pure state, rather than to statistical averages over a mixed state. We then show, in a specific case, that fluctuations in the bulk have a lower-dimensional representation in terms of a boundary theory at high temperature. (author)
Integral-spin fields on (3+2)-de Sitter space
International Nuclear Information System (INIS)
Gazeau, J.; Hans, M.
1988-01-01
Nowadays, (3+2)-de Sitter (or anti-de Sitter space) appears as a very attractive possibility at several levels of theoretical physics. The Wigner definition of an elementary system as associated to a unitary irreducible representation of the Poincare group may be extended to the de Sitter group SO(3,2) [or ∼(SO(3,2))] without great difficulty. The constant curvature, as small as it can be, is a natural candidate to play the role of a regularization parameter with respect to the flat-space limit. Massless particles in (3+2)-de Sitter theory are composite (singletons). On the other hand, supergravity theories necessitate a (large) constant curvature. The content of this paper is group theoretical. It attempts to continue the ''a la Wigner'' program for SO(3,2), already largely broached by Fronsdal. Three recurrence formulas are presented. They permit one to build up the carrier states for representations with arbitrary integral spin. Two of them are valid for the ''massive'' representations whereas the third one is applicable to the indecomposable massless representations. In addition, other presumably indecomposable, though nonphysical, representations are studied, in relation to the existence of ''generalized'' gauge fields and divergences. The recurrence formulas also allow one to build up the invariant two-point functions or homogeneous propagators
Representation theory a first course
Fulton, William
1991-01-01
The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for ...
Directory of Open Access Journals (Sweden)
Marcos Cueva Perus
2005-01-01
Full Text Available This article uses a comparative approach regarding frontier symbols and myths among the United States, Latin America and the Caribbean. Although wars fought over frontiers have greatly diminished throughout the world, the conception of frontier still held by the United States is that of a nationalist myth which embodies a semi-religious faith in the free market and democracy. On the other hand, Latin American and Caribbean countries, whose frontiers are far more complex, have shown extraordinary stability for several decades. This paper points out the risks involved in the spread of United States´ notions of frontier which, in addition, go hand-in-hand with the problem of multicultural segmentation. Although Latin American and Caribbean frontiers may be stable, they are vulnerable to the infiltration of foreing frontier representations.
Lifts of matroid representations over partial fields
Pendavingh, R.A.; Zwam, van S.H.M.
2010-01-01
There exist several theorems which state that when a matroid is representable over distinct fields F1,...,Fk , it is also representable over other fields. We prove a theorem, the Lift Theorem, that implies many of these results. First, parts of Whittle's characterization of representations of
Complexity in Simplicity: Flexible Agent-based State Space Exploration
DEFF Research Database (Denmark)
Rasmussen, Jacob Illum; Larsen, Kim Guldstrand
2007-01-01
In this paper, we describe a new flexible framework for state space exploration based on cooperating agents. The idea is to let various agents with different search patterns explore the state space individually and communicate information about fruitful subpaths of the search tree to each other...
Computer representation of molecular surfaces
International Nuclear Information System (INIS)
Max, N.L.
1981-01-01
This review article surveys recent work on computer representation of molecular surfaces. Several different algorithms are discussed for producing vector or raster drawings of space-filling models formed as the union of spheres. Other smoother surfaces are also considered
Global representations of the Heat and Schrodinger equation with singular potential
Directory of Open Access Journals (Sweden)
Jose A. Franco
2013-07-01
Full Text Available The n-dimensional Schrodinger equation with a singular potential $V_lambda(x=lambda |x|^{-2}$ is studied. Its solution space is studied as a global representation of $widetilde{SL(2,mathbb{R}}imes O(n$. A special subspace of solutions for which the action globalizes is constructed via nonstandard induction outside the semisimple category. The space of K-finite vectors is calculated, obtaining conditions for $lambda$ so that this space is non-empty. The direct sum of solution spaces over such admissible values of $lambda$ is studied as a representation of the (2n+1-dimensional Heisenberg group.
A representation theorem for linear discrete-space systems
Directory of Open Access Journals (Sweden)
Sandberg Irwin W.
1998-01-01
Full Text Available The cornerstone of the theory of discrete-time single-input single-output linear systems is the idea that every such system has an input–output map H that can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight which is corrected in this note by adding an additional term to the representation.
A Fröhlich effect and representational gravity in memory for auditory pitch.
Hubbard, Timothy L; Ruppel, Susan E
2013-08-01
Memory for the initial pitch of an auditory target that increased or decreased in auditory frequency was examined. Memory was displaced forward in the direction of pitch motion, and this is consistent with the Fröhlich effect previously observed for visual targets moving in visual physical space. The Fröhlich effect for pitch increased with faster target velocity and decreased if an auditory cue with the same pitch as the initial pitch of the target was presented before the target was presented. The Fröhlich effect was larger for descending pitch motion than for ascending pitch motion, and this is consistent with an influence of representational gravity. The data suggest that representation of auditory frequency space exhibits some of the same biases as representation of visual physical space, and implications for theories of attention in displacement and for crossmodal and multisensory representation of space are discussed. 2013 APA, all rights reserved
International Nuclear Information System (INIS)
Fechner, Susanne
2008-01-01
The von Neumann-representation introduced in this thesis describes each laser pulse in a one-to-one manner as a sum of bandwidth-limited, Gaussian laser pulses centered around different points in phase space. These pulses can be regarded as elementary building blocks from which every single laser pulse can be constructed. The von Neumann-representation combines different useful properties for applications in quantum control. First, it is a one-to-one map between the degrees of freedom of the pulse shaper and the phase-space representation of the corresponding shaped laser pulse. In other words: Every possible choice of pulse shaper parameters corresponds to exactly one von Neumann-representation and vice versa. Moreover, since temporal and spectral structures become immediately sizable, the von Neumann-representation, as well as the Husimi- or the Wigner-representations, allows for an intuitive interpretation of the represented laser pulse. (orig.)
Coherent states for quantum compact groups
Energy Technology Data Exchange (ETDEWEB)
Jurco, B. [European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.; Stovicek, P. [Ceske Vysoke Uceni Technicke, Prague (Czech Republic). Dept. of Mathematics]|[CTU, Prague (Czech Republic). Doppler Inst.
1996-12-01
Coherent states are introduced and their properties are discussed for simple quantum compact groups A{sub l}, B{sub l}, C{sub l} and D{sub l}. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested. (orig.)
Making Faces - State-Space Models Applied to Multi-Modal Signal Processing
DEFF Research Database (Denmark)
Lehn-Schiøler, Tue
2005-01-01
The two main focus areas of this thesis are State-Space Models and multi modal signal processing. The general State-Space Model is investigated and an addition to the class of sequential sampling methods is proposed. This new algorithm is denoted as the Parzen Particle Filter. Furthermore...... optimizer can be applied to speed up convergence. The linear version of the State-Space Model, the Kalman Filter, is applied to multi modal signal processing. It is demonstrated how a State-Space Model can be used to map from speech to lip movements. Besides the State-Space Model and the multi modal...... application an information theoretic vector quantizer is also proposed. Based on interactions between particles, it is shown how a quantizing scheme based on an analytic cost function can be derived....
Realizations of the canonical representation
Indian Academy of Sciences (India)
Traditionally, the canonical representation is realized on the Hilbert space ... Fix a decomposition R2n = Rn × Rn ..... to an orthonormal basis {ψ1,ψ2,. ..... [7] Vemuri M K, A non-commutative Sobolev inequality and its application to spectral.
Spatiotemporal representation of cardiac vectorcardiogram (VCG signals
Directory of Open Access Journals (Sweden)
Yang Hui
2012-03-01
Full Text Available Abstract Background Vectorcardiogram (VCG signals monitor both spatial and temporal cardiac electrical activities along three orthogonal planes of the body. However, the absence of spatiotemporal resolution in conventional VCG representations is a major impediment for medical interpretation and clinical usage of VCG. This is especially so because time-domain features of 12-lead ECG, instead of both spatial and temporal characteristics of VCG, are widely used for the automatic assessment of cardiac pathological patterns. Materials and methods We present a novel representation approach that captures critical spatiotemporal heart dynamics by displaying the real time motion of VCG cardiac vectors in a 3D space. Such a dynamic display can also be realized with only one lead ECG signal (e.g., ambulatory ECG through an alternative lag-reconstructed ECG representation from nonlinear dynamics principles. Furthermore, the trajectories are color coded with additional dynamical properties of space-time VCG signals, e.g., the curvature, speed, octant and phase angles to enhance the information visibility. Results In this investigation, spatiotemporal VCG signal representation is used to characterize various spatiotemporal pathological patterns for healthy control (HC, myocardial infarction (MI, atrial fibrillation (AF and bundle branch block (BBB. The proposed color coding scheme revealed that the spatial locations of the peak of T waves are in the Octant 6 for the majority (i.e., 74 out of 80 of healthy recordings in the PhysioNet PTB database. In contrast, the peak of T waves from 31.79% (117/368 of MI subjects are found to remain in Octant 6 and the rest (68.21% spread over all other octants. The spatiotemporal VCG signal representation is shown to capture the same important heart characteristics as the 12-lead ECG plots and more. Conclusions Spatiotemporal VCG signal representation is shown to facilitate the characterization of space-time cardiac
Volumes of conditioned bipartite state spaces
International Nuclear Information System (INIS)
Milz, Simon; Strunz, Walter T
2015-01-01
We analyze the metric properties of conditioned quantum state spaces M η (n×m) . These spaces are the convex sets of nm×nm density matrices that, when partially traced over m degrees of freedom, respectively yield the given n × n density matrix η. For the case n = 2, the volume of M η (2×m) equipped with the Hilbert–Schmidt measure can be conjectured to be a simple polynomial of the radius of η in the Bloch-ball. Remarkably, for m=2,3 we find numerically that the probability p sep (2×m) (η) to find a separable state in M η (2×m) is independent of η (except for η pure). For m>3, the same holds for p PosPart (2×m) (η), the probability to find a state with a positive partial transpose in M η (2×m) . These results are proven analytically for the case of the family of 4 × 4 X-states, and thoroughly numerically investigated for the general case. The important implications of these findings for the clarification of open problems in quantum theory are pointed out and discussed. (paper)
2010-01-01
... 5 Administrative Personnel 3 2010-01-01 2010-01-01 false Two-year restriction on any former employee's representations to United States concerning particular matter for which the employee had official responsibility. 2641.202 Section 2641.202 Administrative Personnel OFFICE OF GOVERNMENT ETHICS GOVERNMENT ETHICS POST-EMPLOYMENT CONFLICT OF...
Projective limits of state spaces II. Quantum formalism
Lanéry, Suzanne; Thiemann, Thomas
2017-06-01
In this series of papers, we investigate the projective framework initiated by Kijowski (1977) and Okołów (2009, 2014, 2013), which describes the states of a quantum theory as projective families of density matrices. A short reading guide to the series can be found in Lanéry (2016). After discussing the formalism at the classical level in a first paper (Lanéry, 2017), the present second paper is devoted to the quantum theory. In particular, we inspect in detail how such quantum projective state spaces relate to inductive limit Hilbert spaces and to infinite tensor product constructions (Lanéry, 2016, subsection 3.1) [1]. Regarding the quantization of classical projective structures into quantum ones, we extend the results by Okołów (2013), that were set up in the context of linear configuration spaces, to configuration spaces given by simply-connected Lie groups, and to holomorphic quantization of complex phase spaces (Lanéry, 2016, subsection 2.2) [1].
Quantum mechanics in coherent algebras on phase space
International Nuclear Information System (INIS)
Lesche, B.; Seligman, T.H.
1986-01-01
Quantum mechanics is formulated on a quantum mechanical phase space. The algebra of observables and states is represented by an algebra of functions on phase space that fulfills a certain coherence condition, expressing the quantum mechanical superposition principle. The trace operation is an integration over phase space. In the case where the canonical variables independently run from -infinity to +infinity the formalism reduces to the representation of quantum mechanics by Wigner distributions. However, the notion of coherent algebras allows to apply the formalism to spaces for which the Wigner mapping is not known. Quantum mechanics of a particle in a plane in polar coordinates is discussed as an example. (author)
International Nuclear Information System (INIS)
Snider, R.F.
1982-01-01
It is shown that the position and momentum directional representations of angular momentum states must satisfy Σ/sub lambdas/ = Σ/sub lambdas/(i)/sup lambda/Y/sub lambdas/(r)Y/sub lambdas/ (p)*. This imposes phase constraints on the relation between , , Y/sub lambdas/ (r), and Y/sub lambdas/(p). In the accompanying paper, it is shown that this resolves a problem in the centrifugal sudden approximation of molecular collision theory
Projective limits of state spaces IV. Fractal label sets
Lanéry, Suzanne; Thiemann, Thomas
2018-01-01
Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski (1977) to represent quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces (see Lanéry (2016) [1] for a concise introduction to this formalism). One can thus bypass the need to select a vacuum state for the theory, and still be provided with an explicit and constructive description of the quantum state space, at least as long as the label set indexing the projective structure is countable. Because uncountable label sets are much less practical in this context, we develop in the present article a general procedure to trim an originally uncountable label set down to countable cardinality. In particular, we investigate how to perform this tightening of the label set in a way that preserves both the physical content of the algebra of observables and its symmetries. This work is notably motivated by applications to the holonomy-flux algebra underlying Loop Quantum Gravity. Building on earlier work by Okołów (2013), a projective state space was introduced for this algebra in Lanéry and Thiemann (2016). However, the non-trivial structure of the holonomy-flux algebra prevents the construction of satisfactory semi-classical states (Lanéry and Thiemann, 2017). Implementing the general procedure just mentioned in the case of a one-dimensional version of this algebra, we show how a discrete subalgebra can be extracted without destroying universality nor diffeomorphism invariance. On this subalgebra, quantum states can then be constructed which are more regular than was possible on the original algebra. In particular, this allows the design of semi-classical states whose semi-classicality is enforced step by step, starting from collective, macroscopic degrees of freedom and going down progressively toward smaller and smaller scales.
A kernel-based multi-feature image representation for histopathology image classification
International Nuclear Information System (INIS)
Moreno J; Caicedo J Gonzalez F
2010-01-01
This paper presents a novel strategy for building a high-dimensional feature space to represent histopathology image contents. Histogram features, related to colors, textures and edges, are combined together in a unique image representation space using kernel functions. This feature space is further enhanced by the application of latent semantic analysis, to model hidden relationships among visual patterns. All that information is included in the new image representation space. Then, support vector machine classifiers are used to assign semantic labels to images. Processing and classification algorithms operate on top of kernel functions, so that; the structure of the feature space is completely controlled using similarity measures and a dual representation. The proposed approach has shown a successful performance in a classification task using a dataset with 1,502 real histopathology images in 18 different classes. The results show that our approach for histological image classification obtains an improved average performance of 20.6% when compared to a conventional classification approach based on SVM directly applied to the original kernel.
A KERNEL-BASED MULTI-FEATURE IMAGE REPRESENTATION FOR HISTOPATHOLOGY IMAGE CLASSIFICATION
Directory of Open Access Journals (Sweden)
J Carlos Moreno
2010-09-01
Full Text Available This paper presents a novel strategy for building a high-dimensional feature space to represent histopathology image contents. Histogram features, related to colors, textures and edges, are combined together in a unique image representation space using kernel functions. This feature space is further enhanced by the application of Latent Semantic Analysis, to model hidden relationships among visual patterns. All that information is included in the new image representation space. Then, Support Vector Machine classifiers are used to assign semantic labels to images. Processing and classification algorithms operate on top of kernel functions, so that, the structure of the feature space is completely controlled using similarity measures and a dual representation. The proposed approach has shown a successful performance in a classification task using a dataset with 1,502 real histopathology images in 18 different classes. The results show that our approach for histological image classification obtains an improved average performance of 20.6% when compared to a conventional classification approach based on SVM directly applied to the original kernel.
Tensor fields on orbits of quantum states and applications
Energy Technology Data Exchange (ETDEWEB)
Volkert, Georg Friedrich
2010-07-19
On classical Lie groups, which act by means of a unitary representation on finite dimensional Hilbert spaces H, we identify two classes of tensor field constructions. First, as pull-back tensor fields of order two from modified Hermitian tensor fields, constructed on Hilbert spaces by means of the property of having the vertical distributions of the C{sub 0}-principal bundle H{sub 0} {yields} P(H) over the projective Hilbert space P(H) in the kernel. And second, directly constructed on the Lie group, as left-invariant representation-dependent operator-valued tensor fields (LIROVTs) of arbitrary order being evaluated on a quantum state. Within the NP-hard problem of deciding whether a given state in a n-level bi-partite quantum system is entangled or separable (Gurvits, 2003), we show that both tensor field constructions admit a geometric approach to this problem, which evades the traditional ambiguity on defining metrical structures on the convex set of mixed states. In particular by considering manifolds associated to orbits passing through a selected state when acted upon by the local unitary group U(n) x U(n) of Schmidt coefficient decomposition inducing transformations, we find the following results: In the case of pure states we show that Schmidt-equivalence classes which are Lagrangian submanifolds define maximal entangled states. This implies a stronger statement as the one proposed by Bengtsson (2007). Moreover, Riemannian pull-back tensor fields split on orbits of separable states and provide a quantitative characterization of entanglement which recover the entanglement measure proposed by Schlienz and Mahler (1995). In the case of mixed states we highlight a relation between LIROVTs of order two and a class of computable separability criteria based on the Bloch-representation (de Vicente, 2007). (orig.)
Tensor fields on orbits of quantum states and applications
International Nuclear Information System (INIS)
Volkert, Georg Friedrich
2010-01-01
On classical Lie groups, which act by means of a unitary representation on finite dimensional Hilbert spaces H, we identify two classes of tensor field constructions. First, as pull-back tensor fields of order two from modified Hermitian tensor fields, constructed on Hilbert spaces by means of the property of having the vertical distributions of the C 0 -principal bundle H 0 → P(H) over the projective Hilbert space P(H) in the kernel. And second, directly constructed on the Lie group, as left-invariant representation-dependent operator-valued tensor fields (LIROVTs) of arbitrary order being evaluated on a quantum state. Within the NP-hard problem of deciding whether a given state in a n-level bi-partite quantum system is entangled or separable (Gurvits, 2003), we show that both tensor field constructions admit a geometric approach to this problem, which evades the traditional ambiguity on defining metrical structures on the convex set of mixed states. In particular by considering manifolds associated to orbits passing through a selected state when acted upon by the local unitary group U(n) x U(n) of Schmidt coefficient decomposition inducing transformations, we find the following results: In the case of pure states we show that Schmidt-equivalence classes which are Lagrangian submanifolds define maximal entangled states. This implies a stronger statement as the one proposed by Bengtsson (2007). Moreover, Riemannian pull-back tensor fields split on orbits of separable states and provide a quantitative characterization of entanglement which recover the entanglement measure proposed by Schlienz and Mahler (1995). In the case of mixed states we highlight a relation between LIROVTs of order two and a class of computable separability criteria based on the Bloch-representation (de Vicente, 2007). (orig.)
State-Space Modelling in Marine Science
DEFF Research Database (Denmark)
Albertsen, Christoffer Moesgaard
State-space models provide a natural framework for analysing time series that cannot be observed without error. This is the case for fisheries stock assessments and movement data from marine animals. In fisheries stock assessments, the aim is to estimate the stock size; however, the only data...... available is the number of fish removed from the population and samples on a small fraction of the population. In marine animal movement, accurate position systems such as GPS cannot be used. Instead, inaccurate alternative must be used yielding observations with large errors. Both assessment and individual...... animal movement models are important for management and conservation of marine animals. Consequently, models should be developed to be operational in a management context while adequately evaluating uncertainties in the models. This thesis develops state-space models using the Laplace approximation...
Manzungu, Emmanuel
In 1998 both South Africa and Zimbabwe promulgated new water laws to ensure that ownership and user-ship patterns of water resources match the new socio-political order. Integrated water resource management, incorporating among other things decentralized and democratized water management institutions and the principles of stakeholder participation, was regarded as the cornerstone of the reforms. This article examines how stakeholder representation, particularly of the formerly disadvantaged people, has been handled. It is observed that there has been too much effort dedicated to ensure a mere headcount of the stakeholders at the water table rather than on strategic representation. Strategic representation emphasizes stakeholder identity instead of consensus. Selective alliance building is important as is establishing genuine local level platforms with enough political space outside the state-tailored formal straight jackets. It is equally important to address developmental aspects of establishing catchment-wide bodies and structural problems such as access to land and financial resources. Without addressing these issues stakeholder representation will remain hamstrung in good intentions.
The wave equation on a curved space-time
International Nuclear Information System (INIS)
Friedlander, F.G.
1975-01-01
It is stated that chapters on differential geometry, distribution theory, and characteristics and the propagation of discontinuities are preparatory. The main matter is in three chapters, entitled: fundamental solutions, representation theorems, and wave equations on n-dimensional space-times. These deal with general construction of fundamental solutions and their application to the Cauchy problem. (U.K.)
Social representations about cancer
Directory of Open Access Journals (Sweden)
Andreja Cirila Škufca
2003-09-01
Full Text Available In this article we are presenting the results of the comparison study on social representations and causal attributions about cancer. We compared a breast cancer survivors group and control group without own experience of cancer of their own. Although social representations about cancer differ in each group, they are closely related to the concept of suffering, dying and death. We found differences in causal attribution of cancer. In both groups we found a category of risky behavior, which attributes a responsibility for a disease to an individual. Besides these factors we found predominate stress and psychological influences in cancer survivors group. On the other hand control group indicated factors outside the ones control e.g. heredity and environmental factors. Representations about a disease inside person's social space are important in co-shaping the individual process of coping with own disease. Since these representations are not always coherent with the knowledge of modern medicine their knowledge and appreciation in the course of treatment is of great value. We find the findingss of applied social psychology important as starting points in the therapeutic work with patients.
Path representation of su-hat (2){sub k} states I: Operators and particles for k=1,2
Energy Technology Data Exchange (ETDEWEB)
Lamy-Poirier, Joel, E-mail: jlamypoirier@perimeterinstitute.c [Departement de physique, de genie physique et d' optique, Universite Laval, Quebec, G1K 7P4 (Canada); Mathieu, Pierre, E-mail: pmathieu@phy.ulaval.c [Departement de physique, de genie physique et d' optique, Universite Laval, Quebec, G1K 7P4 (Canada)
2011-04-11
This is the first of two articles devoted to the analysis of the path description of the states in su-hat (2){sub k} WZW models, a representation well suited for constructive derivations of the fermionic characters. In this first article, the cases k=1,2 are treated in detail, emphasizing a different description in each case (operators vs particles). For k=1, we first prove, as a side result, the equivalence of two known path representations for the finitized su-hat (2){sub 1} states by displaying an explicit bijection. An immediate offshoot is the gain of a new and simple weighting for the (Kyoto) path representation that generalizes to level k. The bijection also suggests two operator constructions for the su-hat (2){sub 1} paths, a local and a nonlocal one, both interrelated. These are formal operators that map a path to another path, so that any path can be obtained by successive applications of these operators on a simple reference (ground-state) path. The nonlocal operator description is the starting point for a direct and elementary derivation of the su-hat (2){sub 1} spinon character. The second part presents an extensive study of the su-hat (2){sub 2} paths from their particle point of view, where the particles are defined as the path building blocks. The resulting generating functions appear to provide new (at least superficially) fermionic forms of the characters. In particular, a nice relationship between the sum of the j=0,1 characters at k=2 and the two ones at k=1 is unraveled.
QED representation for the net of causal loops
Ciolli, Fabio; Ruzzi, Giuseppe; Vasselli, Ezio
2015-06-01
The present work tackles the existence of local gauge symmetries in the setting of Algebraic Quantum Field Theory (AQFT). The net of causal loops, previously introduced by the authors, is a model independent construction of a covariant net of local C*-algebras on any 4-dimensional globally hyperbolic space-time, aimed to capture structural properties of any reasonable quantum gauge theory. Representations of this net can be described by causal and covariant connection systems, and local gauge transformations arise as maps between equivalent connection systems. The present paper completes these abstract results, realizing QED as a representation of the net of causal loops in Minkowski space-time. More precisely, we map the quantum electromagnetic field Fμν, not free in general, into a representation of the net of causal loops and show that the corresponding connection system and the local gauge transformations find a counterpart in terms of Fμν.
Energy Technology Data Exchange (ETDEWEB)
Olsen, Seth, E-mail: seth.olsen@uq.edu.au [School of Mathematics and Physics, The University of Queensland, Brisbane QLD 4072 (Australia)
2015-01-28
This paper reviews basic results from a theory of the a priori classical probabilities (weights) in state-averaged complete active space self-consistent field (SA-CASSCF) models. It addresses how the classical probabilities limit the invariance of the self-consistency condition to transformations of the complete active space configuration interaction (CAS-CI) problem. Such transformations are of interest for choosing representations of the SA-CASSCF solution that are diabatic with respect to some interaction. I achieve the known result that a SA-CASSCF can be self-consistently transformed only within degenerate subspaces of the CAS-CI ensemble density matrix. For uniformly distributed (“microcanonical”) SA-CASSCF ensembles, self-consistency is invariant to any unitary CAS-CI transformation that acts locally on the ensemble support. Most SA-CASSCF applications in current literature are microcanonical. A problem with microcanonical SA-CASSCF models for problems with “more diabatic than adiabatic” states is described. The problem is that not all diabatic energies and couplings are self-consistently resolvable. A canonical-ensemble SA-CASSCF strategy is proposed to solve the problem. For canonical-ensemble SA-CASSCF, the equilibrated ensemble is a Boltzmann density matrix parametrized by its own CAS-CI Hamiltonian and a Lagrange multiplier acting as an inverse “temperature,” unrelated to the physical temperature. Like the convergence criterion for microcanonical-ensemble SA-CASSCF, the equilibration condition for canonical-ensemble SA-CASSCF is invariant to transformations that act locally on the ensemble CAS-CI density matrix. The advantage of a canonical-ensemble description is that more adiabatic states can be included in the support of the ensemble without running into convergence problems. The constraint on the dimensionality of the problem is relieved by the introduction of an energy constraint. The method is illustrated with a complete active space
Diffeomorphism Group Representations in Relativistic Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Goldin, Gerald A. [Rutgers Univ., Piscataway, NJ (United States); Sharp, David H. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-12-20
We explore the role played by the di eomorphism group and its unitary representations in relativistic quantum eld theory. From the quantum kinematics of particles described by representations of the di eomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar eld in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to elds whose quanta are spatially extended objects.
Silva, H G; Lopes, I
Heliospheric modulation of galactic cosmic rays links solar cycle activity with neutron monitor count rate on earth. A less direct relation holds between neutron monitor count rate and atmospheric electric field because different atmospheric processes, including fluctuations in the ionosphere, are involved. Although a full quantitative model is still lacking, this link is supported by solid statistical evidence. Thus, a connection between the solar cycle activity and atmospheric electric field is expected. To gain a deeper insight into these relations, sunspot area (NOAA, USA), neutron monitor count rate (Climax, Colorado, USA), and atmospheric electric field (Lisbon, Portugal) are presented here in a phase space representation. The period considered covers two solar cycles (21, 22) and extends from 1978 to 1990. Two solar maxima were observed in this dataset, one in 1979 and another in 1989, as well as one solar minimum in 1986. Two main observations of the present study were: (1) similar short-term topological features of the phase space representations of the three variables, (2) a long-term phase space radius synchronization between the solar cycle activity, neutron monitor count rate, and potential gradient (confirmed by absolute correlation values above ~0.8). Finally, the methodology proposed here can be used for obtaining the relations between other atmospheric parameters (e.g., solar radiation) and solar cycle activity.
Quantum control and representation theory
International Nuclear Information System (INIS)
Ibort, A; Perez-Pardo, J M
2009-01-01
A new notion of controllability for quantum systems that takes advantage of the linear superposition of quantum states is introduced. We call such a notion von Neumann controllability, and it is shown that it is strictly weaker than the usual notion of pure state and operator controllability. We provide a simple and effective characterization of it by using tools from the theory of unitary representations of Lie groups. In this sense, we are able to approach the problem of control of quantum states from a new perspective, that of the theory of unitary representations of Lie groups. A few examples of physical interest and the particular instances of compact and nilpotent dynamical Lie groups are discussed
Non-discriminatory Rules and Ethnic Representation: The Election of the Bosnian State Presidency
DEFF Research Database (Denmark)
Bochsler, Daniel
2012-01-01
. Following the 2009 judgment of the European Court of Human Rights, Bosnia was urged to reform its electoral law. This paper discusses alternative practices of ethnically based political representation and their possible application in the Bosnian state presidency elections. Several innovative electoral...... models that satisfy fair political and legal criteria for desirable electoral dynamics in divided societies can be envisaged in the Bosnian context. Specifically, these are: the introduction of a single countrywide electoral district, the adoption of the single non-transferable vote, and the application...
Multivariate time series with linear state space structure
Gómez, Víctor
2016-01-01
This book presents a comprehensive study of multivariate time series with linear state space structure. The emphasis is put on both the clarity of the theoretical concepts and on efficient algorithms for implementing the theory. In particular, it investigates the relationship between VARMA and state space models, including canonical forms. It also highlights the relationship between Wiener-Kolmogorov and Kalman filtering both with an infinite and a finite sample. The strength of the book also lies in the numerous algorithms included for state space models that take advantage of the recursive nature of the models. Many of these algorithms can be made robust, fast, reliable and efficient. The book is accompanied by a MATLAB package called SSMMATLAB and a webpage presenting implemented algorithms with many examples and case studies. Though it lays a solid theoretical foundation, the book also focuses on practical application, and includes exercises in each chapter. It is intended for researchers and students wor...
Svensson, Andreas; Schön, Thomas B.; Lindsten, Fredrik
2018-05-01
Probabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems. Some problems of this type that were previously intractable can now be solved on standard personal computers thanks to recent advances in Monte Carlo methods. In particular, for learning of unknown parameters in nonlinear state-space models, methods based on the particle filter (a Monte Carlo method) have proven very useful. A notoriously challenging problem, however, still occurs when the observations in the state-space model are highly informative, i.e. when there is very little or no measurement noise present, relative to the amount of process noise. The particle filter will then struggle in estimating one of the basic components for probabilistic learning, namely the likelihood p (data | parameters). To this end we suggest an algorithm which initially assumes that there is substantial amount of artificial measurement noise present. The variance of this noise is sequentially decreased in an adaptive fashion such that we, in the end, recover the original problem or possibly a very close approximation of it. The main component in our algorithm is a sequential Monte Carlo (SMC) sampler, which gives our proposed method a clear resemblance to the SMC2 method. Another natural link is also made to the ideas underlying the approximate Bayesian computation (ABC). We illustrate it with numerical examples, and in particular show promising results for a challenging Wiener-Hammerstein benchmark problem.
State-Space Realization of the Wave-Radiation Force within FAST: Preprint
Energy Technology Data Exchange (ETDEWEB)
Duarte, T.; Sarmento, A.; Alves, M.; Jonkman, J.
2013-06-01
Several methods have been proposed in the literature to find a state-space model for the wave-radiation forces. In this paper, four methods were compared, two in the frequency domain and two in the time domain. The frequency-response function and the impulse response of the resulting state-space models were compared against the ones derived by the numerical code WAMIT. The implementation of the state-space module within the FAST offshore wind turbine computer-aided engineering (CAE) tool was verified, comparing the results against the previously implemented numerical convolution method. The results agreed between the two methods, with a significant reduction in required computational time when using the state-space module.
The probability representation as a new formulation of quantum mechanics
International Nuclear Information System (INIS)
Man'ko, Margarita A; Man'ko, Vladimir I
2012-01-01
We present a new formulation of conventional quantum mechanics, in which the notion of a quantum state is identified via a fair probability distribution of the position measured in a reference frame of the phase space with rotated axes. In this formulation, the quantum evolution equation as well as the equation for finding energy levels are expressed as linear equations for the probability distributions that determine the quantum states. We also give the integral transforms relating the probability distribution (called the tomographic-probability distribution or the state tomogram) to the density matrix and the Wigner function and discuss their connection with the Radon transform. Qudit states are considered and the invertible map of the state density operators onto the probability vectors is discussed. The tomographic entropies and entropic uncertainty relations are reviewed. We demonstrate the uncertainty relations for the position and momentum and the entropic uncertainty relations in the tomographic-probability representation, which is suitable for an experimental check of the uncertainty relations.
Analytic factorization of Lie group representations
DEFF Research Database (Denmark)
Gimperlein, Heiko; Krötz, Bernhard; Lienau, Christoph
2012-01-01
For every moderate growth representation (p,E)(p,E) of a real Lie group G on a Fréchet space, we prove a factorization theorem of Dixmier–Malliavin type for the space of analytic vectors E¿E¿. There exists a natural algebra of superexponentially decreasing analytic functions A(G)A(G), such that E......¿=¿(A(G))E¿E¿=¿(A(G))E¿. As a corollary we obtain that E¿E¿ coincides with the space of analytic vectors for the Laplace–Beltrami operator on G....
Interior Space: Representation, Occupation, Well-Being and Interiority
Power, Jacqueline
2014-01-01
This article will provide an overview of space as it is understood and engaged with from within the discipline of interior design/interior architecture. Firstly, the term interior will be described. Secondly, the paper will discuss space as a general concept, before exploring what space is speifically for the interior design/interior architecture discipline. How is space understood? What does space "look" like for interuior designers/interior architects?.
Emerging Object Representations in the Visual System Predict Reaction Times for Categorization
Ritchie, J. Brendan; Tovar, David A.; Carlson, Thomas A.
2015-01-01
Recognizing an object takes just a fraction of a second, less than the blink of an eye. Applying multivariate pattern analysis, or “brain decoding”, methods to magnetoencephalography (MEG) data has allowed researchers to characterize, in high temporal resolution, the emerging representation of object categories that underlie our capacity for rapid recognition. Shortly after stimulus onset, object exemplars cluster by category in a high-dimensional activation space in the brain. In this emerging activation space, the decodability of exemplar category varies over time, reflecting the brain’s transformation of visual inputs into coherent category representations. How do these emerging representations relate to categorization behavior? Recently it has been proposed that the distance of an exemplar representation from a categorical boundary in an activation space is critical for perceptual decision-making, and that reaction times should therefore correlate with distance from the boundary. The predictions of this distance hypothesis have been born out in human inferior temporal cortex (IT), an area of the brain crucial for the representation of object categories. When viewed in the context of a time varying neural signal, the optimal time to “read out” category information is when category representations in the brain are most decodable. Here, we show that the distance from a decision boundary through activation space, as measured using MEG decoding methods, correlates with reaction times for visual categorization during the period of peak decodability. Our results suggest that the brain begins to read out information about exemplar category at the optimal time for use in choice behaviour, and support the hypothesis that the structure of the representation for objects in the visual system is partially constitutive of the decision process in recognition. PMID:26107634
Advanced Solid State Lighting for AES Deep Space Hab
National Aeronautics and Space Administration — The advanced Solid State Lighting (SSL) assemblies augmented 2nd generation modules under development for the Advanced Exploration Systems Deep Space Habitat in...
A dynamical topology for the space of states
International Nuclear Information System (INIS)
Dittrich, J.
1979-01-01
A new topology is introduced for the space of states of a physical system. This topology is given by dynamics, every state has a neighbourhood consisting of states connected by the time evolution only. With respect to the new topology, all conservation laws can be treated as topological laws. (author)
Space Sciences Education and Outreach Project of Moscow State University
Krasotkin, S.
2006-11-01
sergekras@mail.ru The space sciences education and outreach project was initiated at Moscow State University in order to incorporate modern space research into the curriculum popularize the basics of space physics, and enhance public interest in space exploration. On 20 January 2005 the first Russian University Satellite “Universitetskiy-Tatyana” was launched into circular polar orbit (inclination 83 deg., altitude 940-980 km). The onboard scientific complex “Tatyana“, as well as the mission control and information receiving centre, was designed and developed at Moscow State University. The scientific programme of the mission includes measurements of space radiation in different energy channels and Earth UV luminosity and lightning. The current education programme consists of basic multimedia lectures “Life of the Earth in the Solar Atmosphere” and computerized practice exercises “Space Practice” (based on the quasi-real-time data obtained from “Universitetskiy-Tatyana” satellite and other Internet resources). A multimedia lectures LIFE OF EARTH IN THE SOLAR ATMOSPHERE containing the basic information and demonstrations of heliophysics (including Sun structure and solar activity, heliosphere and geophysics, solar-terrestrial connections and solar influence on the Earth’s life) was created for upper high-school and junior university students. For the upper-university students there a dozen special computerized hands-on exercises were created based on the experimental quasi-real-time data obtained from our satellites. Students specializing in space physics from a few Russian universities are involved in scientific work. Educational materials focus on upper high school, middle university and special level for space physics students. Moscow State University is now extending its space science education programme by creating multimedia lectures on remote sensing, space factors and materials study, satellite design and development, etc. The space
State space modeling of Memristor-based Wien oscillator
Talukdar, Abdul Hafiz Ibne; Radwan, Ahmed G.; Salama, Khaled N.
2011-01-01
State space modeling of Memristor based Wien 'A' oscillator has been demonstrated for the first time considering nonlinear ion drift in Memristor. Time dependant oscillating resistance of Memristor is reported in both state space solution and SPICE simulation which plausibly provide the basis of realizing parametric oscillation by Memristor based Wien oscillator. In addition to this part Memristor is shown to stabilize the final oscillation amplitude by means of its nonlinear dynamic resistance which hints for eliminating diode in the feedback network of conventional Wien oscillator. © 2011 IEEE.
State space modeling of Memristor-based Wien oscillator
Talukdar, Abdul Hafiz Ibne
2011-12-01
State space modeling of Memristor based Wien \\'A\\' oscillator has been demonstrated for the first time considering nonlinear ion drift in Memristor. Time dependant oscillating resistance of Memristor is reported in both state space solution and SPICE simulation which plausibly provide the basis of realizing parametric oscillation by Memristor based Wien oscillator. In addition to this part Memristor is shown to stabilize the final oscillation amplitude by means of its nonlinear dynamic resistance which hints for eliminating diode in the feedback network of conventional Wien oscillator. © 2011 IEEE.
Coherent and squeezed states in phase space
International Nuclear Information System (INIS)
Jannussis, A.; Bartzis, V.; Vlahos, E.
1990-01-01
In the present paper, the coherent and the squeezed states in phase space have been studied. From the wave functions of the coherent and the squeezed state, their corresponding Wigner distribution functions are calculated. Especially the calculation of the corresponding Wigner functions for the above states permits the determination of the mean values of position and momentum and thus the Heisenberg uncertainty relation. In fact, from the related results, it is concluded that the uncertainty relation of the coherent and associated squeezed states is the same
Rothman, Adam E.; Mazziotti, David A.
2010-03-01
We study molecular conductivity for a one-electron, bath-molecule-bath model Hamiltonian. The primary quantum-mechanical variable is the one-electron reduced density matrix (1-RDM). By identifying similarities between the steady-state Liouville equation and the anti-Hermitian contracted Schrödinger equation (ACSE) [D. A. Mazziotti, Phys. Rev. A 75, 022505 (2007)], we develop a way of enforcing nonequilibrium, steady-state behavior in a time-independent theory. Our results illustrate the relationship between current and voltage in molecular junctions assuming that the total number of electrons under consideration can be fixed across all driving potentials. The impetus for this work is a recent study by Subotnik et al. that also uses the 1-RDM to study molecular conductivity under different assumptions regarding the total number of electrons [J. E. Subotnik et al., J. Chem. Phys. 130, 144105 (2009)]. Unlike calculations in the previous study, our calculations result in 1-RDMs that are fully N-representable. The present work maintains N-representability through a bath-bath mixing that is related to a time-independent relaxation of the baths in the absence of the molecule, as governed by the ACSE. A lack of N-representability can be important since it corresponds to occupying energy states in the molecule or baths with more than one electron or hole (the absence of an electron) in violation of the Pauli principle. For this reason the present work may serve as an important, albeit preliminary, step in designing a 2-RDM/ACSE method for studying steady-state molecular conductivity with an explicit treatment of electron correlation.
Bargmann representation for Landau levels in two dimensions
Energy Technology Data Exchange (ETDEWEB)
Rohringer, Nina [Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstr. 8-10, A-1040 Vienna (Austria); Burgdoerfer, Joachim [Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstr. 8-10, A-1040 Vienna (Austria); Macris, Nicolas [Institut de Physique Theorique, Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne (Switzerland)
2003-04-11
We present a formulation of the quantum mechanics of an electron gas confined to two dimensions in a strong magnetic field within the framework of the Hilbert space of analytic functions (Bargmann's space). Our approach extends the representation introduced by Girvin and Jach for the ground state to arbitrary Landau levels and to the regime of coupling between Landau levels. By projecting out the rapid cyclotron motion, the quantum mechanics of the slow guiding centre motion is converted into a system of coupled-channel equations describing the coupling between Landau levels due to the (disorder) potentials. In the limit of strong fields, the coupled-channel equations can be solved perturbatively. For the single-channel case we derive a WKB-like quantization condition for the one-dimensional motion along equipotential lines for arbitrary Landau levels. Two applications of this formalism are discussed: the weak-levitation problem in quantum Hall systems and a two-electron quantum dot in a strong magnetic field.
Bargmann representation for Landau levels in two dimensions
International Nuclear Information System (INIS)
Rohringer, Nina; Burgdoerfer, Joachim; Macris, Nicolas
2003-01-01
We present a formulation of the quantum mechanics of an electron gas confined to two dimensions in a strong magnetic field within the framework of the Hilbert space of analytic functions (Bargmann's space). Our approach extends the representation introduced by Girvin and Jach for the ground state to arbitrary Landau levels and to the regime of coupling between Landau levels. By projecting out the rapid cyclotron motion, the quantum mechanics of the slow guiding centre motion is converted into a system of coupled-channel equations describing the coupling between Landau levels due to the (disorder) potentials. In the limit of strong fields, the coupled-channel equations can be solved perturbatively. For the single-channel case we derive a WKB-like quantization condition for the one-dimensional motion along equipotential lines for arbitrary Landau levels. Two applications of this formalism are discussed: the weak-levitation problem in quantum Hall systems and a two-electron quantum dot in a strong magnetic field
Bargmann representation for Landau levels in two dimensions
Rohringer, N; Macris, N
2003-01-01
We present a formulation of the quantum mechanics of an electron gas confined to two dimensions in a strong magnetic field within the framework of the Hilbert space of analytic functions (Bargmann's space). Our approach extends the representation introduced by Girvin and Jach for the ground state to arbitrary Landau levels and to the regime of coupling between Landau levels. By projecting out the rapid cyclotron motion, the quantum mechanics of the slow guiding centre motion is converted into a system of coupled-channel equations describing the coupling between Landau levels due to the (disorder) potentials. In the limit of strong fields, the coupled-channel equations can be solved perturbatively. For the single-channel case we derive a WKB-like quantization condition for the one-dimensional motion along equipotential lines for arbitrary Landau levels. Two applications of this formalism are discussed: the weak-levitation problem in quantum Hall systems and a two-electron quantum dot in a strong magnetic field...
Hramov, Alexander; Musatov, Vyacheslav Yu.; Runnova, Anastasija E.; Efremova, Tatiana Yu.; Koronovskii, Alexey A.; Pisarchik, Alexander N.
2018-04-01
In the paper we propose an approach based on artificial neural networks for recognition of different human brain states associated with distinct visual stimulus. Based on the developed numerical technique and the analysis of obtained experimental multichannel EEG data, we optimize the spatiotemporal representation of multichannel EEG to provide close to 97% accuracy in recognition of the EEG brain states during visual perception. Different interpretations of an ambiguous image produce different oscillatory patterns in the human EEG with similar features for every interpretation. Since these features are inherent to all subjects, a single artificial network can classify with high quality the associated brain states of other subjects.
Formulating state space models in R with focus on longitudinal regression models
DEFF Research Database (Denmark)
Dethlefsen, Claus; Lundbye-Christensen, Søren
We provide a language for formulating a range of state space models. The described methodology is implemented in the R -package sspir available from cran.r-project.org . A state space model is specified similarly to a generalized linear model in R , by marking the time-varying terms in the form...... We provide a language for formulating a range of state space models. The described methodology is implemented in the R -package sspir available from cran.r-project.org . A state space model is specified similarly to a generalized linear model in R , by marking the time-varying terms...
Modeling volatility using state space models.
Timmer, J; Weigend, A S
1997-08-01
In time series problems, noise can be divided into two categories: dynamic noise which drives the process, and observational noise which is added in the measurement process, but does not influence future values of the system. In this framework, we show that empirical volatilities (the squared relative returns of prices) exhibit a significant amount of observational noise. To model and predict their time evolution adequately, we estimate state space models that explicitly include observational noise. We obtain relaxation times for shocks in the logarithm of volatility ranging from three weeks (for foreign exchange) to three to five months (for stock indices). In most cases, a two-dimensional hidden state is required to yield residuals that are consistent with white noise. We compare these results with ordinary autoregressive models (without a hidden state) and find that autoregressive models underestimate the relaxation times by about two orders of magnitude since they do not distinguish between observational and dynamic noise. This new interpretation of the dynamics of volatility in terms of relaxators in a state space model carries over to stochastic volatility models and to GARCH models, and is useful for several problems in finance, including risk management and the pricing of derivative securities. Data sets used: Olsen & Associates high frequency DEM/USD foreign exchange rates (8 years). Nikkei 225 index (40 years). Dow Jones Industrial Average (25 years).
Topological Schemas of Memory Spaces
Babichev, Andrey; Dabaghian, Yuri A.
2018-01-01
Hippocampal cognitive map—a neuronal representation of the spatial environment—is widely discussed in the computational neuroscience literature for decades. However, more recent studies point out that hippocampus plays a major role in producing yet another cognitive framework—the memory space—that incorporates not only spatial, but also non-spatial memories. Unlike the cognitive maps, the memory spaces, broadly understood as “networks of interconnections among the representations of events,” have not yet been studied from a theoretical perspective. Here we propose a mathematical approach that allows modeling memory spaces constructively, as epiphenomena of neuronal spiking activity and thus to interlink several important notions of cognitive neurophysiology. First, we suggest that memory spaces have a topological nature—a hypothesis that allows treating both spatial and non-spatial aspects of hippocampal function on equal footing. We then model the hippocampal memory spaces in different environments and demonstrate that the resulting constructions naturally incorporate the corresponding cognitive maps and provide a wider context for interpreting spatial information. Lastly, we propose a formal description of the memory consolidation process that connects memory spaces to the Morris' cognitive schemas-heuristic representations of the acquired memories, used to explain the dynamics of learning and memory consolidation in a given environment. The proposed approach allows evaluating these constructs as the most compact representations of the memory space's structure. PMID:29740306
Topological Schemas of Memory Spaces
Directory of Open Access Journals (Sweden)
Andrey Babichev
2018-04-01
Full Text Available Hippocampal cognitive map—a neuronal representation of the spatial environment—is widely discussed in the computational neuroscience literature for decades. However, more recent studies point out that hippocampus plays a major role in producing yet another cognitive framework—the memory space—that incorporates not only spatial, but also non-spatial memories. Unlike the cognitive maps, the memory spaces, broadly understood as “networks of interconnections among the representations of events,” have not yet been studied from a theoretical perspective. Here we propose a mathematical approach that allows modeling memory spaces constructively, as epiphenomena of neuronal spiking activity and thus to interlink several important notions of cognitive neurophysiology. First, we suggest that memory spaces have a topological nature—a hypothesis that allows treating both spatial and non-spatial aspects of hippocampal function on equal footing. We then model the hippocampal memory spaces in different environments and demonstrate that the resulting constructions naturally incorporate the corresponding cognitive maps and provide a wider context for interpreting spatial information. Lastly, we propose a formal description of the memory consolidation process that connects memory spaces to the Morris' cognitive schemas-heuristic representations of the acquired memories, used to explain the dynamics of learning and memory consolidation in a given environment. The proposed approach allows evaluating these constructs as the most compact representations of the memory space's structure.
DEFF Research Database (Denmark)
Raahauge, Kirsten Marie
2008-01-01
This article deals with representations of one specific city, Århus, Denmark, especially its central district. The analysis is based on anthropological fieldwork conducted in Skåde Bakker and Fedet, two well-off neighborhoods. The overall purpose of the project is to study perceptions of space...... and the interaction of cultural, social, and spatial organizations, as seen from the point of view of people living in Skåde Bakker and Fedet. The focus is on the city dwellers’ representations of the central district of Århus with specific reference to the concept of transit space. When applied to various Århusian...
State Space Reduction for Model Checking Agent Programs
S.-S.T.Q. Jongmans (Sung-Shik); K.V. Hindriks; M.B. van Riemsdijk; L. Dennis; O. Boissier; R.H. Bordini (Rafael)
2012-01-01
htmlabstractState space reduction techniques have been developed to increase the efficiency of model checking in the context of imperative programming languages. Unfortunately, these techniques cannot straightforwardly be applied to agents: the nature of states in the two programming paradigms
An XML Representation for Crew Procedures
Simpson, Richard C.
2005-01-01
NASA ensures safe operation of complex systems through the use of formally-documented procedures, which encode the operational knowledge of the system as derived from system experts. Crew members use procedure documentation on the ground for training purposes and on-board space shuttle and space station to guide their activities. Investigators at JSC are developing a new representation for procedures that is content-based (as opposed to display-based). Instead of specifying how a procedure should look on the printed page, the content-based representation will identify the components of a procedure and (more importantly) how the components are related (e.g., how the activities within a procedure are sequenced; what resources need to be available for each activity). This approach will allow different sets of rules to be created for displaying procedures on a computer screen, on a hand-held personal digital assistant (PDA), verbally, or on a printed page, and will also allow intelligent reasoning processes to automatically interpret and use procedure definitions. During his NASA fellowship, Dr. Simpson examined how various industries represent procedures (also called business processes or workflows), in areas such as manufacturing, accounting, shipping, or customer service. A useful method for designing and evaluating workflow representation languages is by determining their ability to encode various workflow patterns, which depict abstract relationships between the components of a procedure removed from the context of a specific procedure or industry. Investigators have used this type of analysis to evaluate how well-suited existing workflow representation languages are for various industries based on the workflow patterns that commonly arise across industry-specific procedures. Based on this type of analysis, it is already clear that existing workflow representations capture discrete flow of control (i.e., when one activity should start and stop based on when other
Semantic Representations in 3D Perceptual Space
Directory of Open Access Journals (Sweden)
Suncica Zdravkovic
2011-05-01
Full Text Available Barsalou's (1999 perceptual theory of knowledge echoes the pre-20th century tradition of conceptualizing all knowledge as inherently perceptual. Hence conceptual space has an infinite number of dimensions and heavily relies on perceptual experience. Osgood's (1952 semantic differential technique was developed as a bridge between perception and semantics. We updated Osgood's methodology in order to investigate current issues in visual cognition by: (1 using a 2D rather than a 1D space to place the concepts, (2 having dimensions that were perceptual while the targets were conceptual, (3 coupling visual experience with another two perceptual domains (audition and touch, (4 analyzing the data using MDS (not factor analysis. In three experiments, subjects (N = 57 judged five concrete and five abstract words on seven bipolar scales in three perceptual modalities. The 2D space led to different patterns of response compared to the classic 1D space. MDS revealed that perceptual modalities are not equally informative for mapping word-meaning distances (Mantel min = −.23; Mantel max = .88. There was no reliable differences due to test administration modality (paper vs. computer, nor scale orientation. The present findings are consistent with multidimensionality of conceptual space, a perceptual basis for knowledge, and dynamic characteristics of concepts discussed in contemporary theories.
Automatic Design of a Maglev Controller in State Space
1991-12-01
Design of a Maglev Controller in State Space Feng Zhao Richard Thornton Abstract We describe the automatic synthesis of a global nonlinear controller for...the global switching points of the controller is presented. The synthesized control system can stabilize the maglev vehicle with large initial displace...NUMBERS Automation Desing of a Maglev Controller in State Space N00014-89-J-3202 MIP-9001651 6. AUTHOR(S) Feng Zhao and Richard Thornton 7. PERFORMING
Transformation of Socioeconomic Space: The Role of the State
Directory of Open Access Journals (Sweden)
Alexander Nikolaevich Shvetsov
2015-03-01
Full Text Available Modern Russia is traditionally characterized by a special and strong public participation in solving problems of spatial development. Thus, the state has following diverse roles: 1 the creator of the modern space configuration; 2 the mastermind and main driving force of modern spatial transformations; 3 the regulator and investor of these processes; 4 the main sponsor and beneficiary of space transformation; and, finally, the hostage of its own dominance in the processes of spatial transformation. However, stereotypes are being gradually overcome and public policy in the area of spatial transformations focuses not only on «public projects» but also on self-development of regions, combined with the interests of big business which plays an increasing role in the transformation of socioeconomic space. The article reveals the meaning and content of the problem of systemic interaction between the state and space concerning the modernization of the country. The author explores the range of fundamental research and applied issues resulting from the contradictory combination of traditional (historical stereotypes and the latest Russian circumstances. These issues determine the background, nature and consequences of state impacts on socio-economic space, as well as the composition, content and validity of the used instruments
Information Theoretic Characterization of Physical Theories with Projective State Space
Zaopo, Marco
2015-08-01
Probabilistic theories are a natural framework to investigate the foundations of quantum theory and possible alternative or deeper theories. In a generic probabilistic theory, states of a physical system are represented as vectors of outcomes probabilities and state spaces are convex cones. In this picture the physics of a given theory is related to the geometric shape of the cone of states. In quantum theory, for instance, the shape of the cone of states corresponds to a projective space over complex numbers. In this paper we investigate geometric constraints on the state space of a generic theory imposed by the following information theoretic requirements: every non completely mixed state of a system is perfectly distinguishable from some other state in a single shot measurement; information capacity of physical systems is conserved under making mixtures of states. These assumptions guarantee that a generic physical system satisfies a natural principle asserting that the more a state of the system is mixed the less information can be stored in the system using that state as logical value. We show that all theories satisfying the above assumptions are such that the shape of their cones of states is that of a projective space over a generic field of numbers. Remarkably, these theories constitute generalizations of quantum theory where superposition principle holds with coefficients pertaining to a generic field of numbers in place of complex numbers. If the field of numbers is trivial and contains only one element we obtain classical theory. This result tells that superposition principle is quite common among probabilistic theories while its absence gives evidence of either classical theory or an implausible theory.
Reinforcement learning in continuous state and action spaces
H. P. van Hasselt (Hado); M.A. Wiering; M. van Otterlo
2012-01-01
textabstractMany traditional reinforcement-learning algorithms have been designed for problems with small finite state and action spaces. Learning in such discrete problems can been difficult, due to noise and delayed reinforcements. However, many real-world problems have continuous state or action
Learning Visual Representations for Perception-Action Systems
DEFF Research Database (Denmark)
Piater, Justus; Jodogne, Sebastien; Detry, Renaud
2011-01-01
and RLJC, our second method learns structural object models for robust object detection and pose estimation by probabilistic inference. To these models, the method associates grasp experiences autonomously learned by trial and error. These experiences form a nonparametric representation of grasp success......We discuss vision as a sensory modality for systems that effect actions in response to perceptions. While the internal representations informed by vision may be arbitrarily complex, we argue that in many cases it is advantageous to link them rather directly to action via learned mappings....... These arguments are illustrated by two examples of our own work. First, our RLVC algorithm performs reinforcement learning directly on the visual input space. To make this very large space manageable, RLVC interleaves the reinforcement learner with a supervised classification algorithm that seeks to split...
Construction of spaces of kinematic quantum states for field theories via projective techniques
International Nuclear Information System (INIS)
Okołów, Andrzej
2013-01-01
We present a method of constructing a space of quantum states for a field theory: given phase space of a theory, we define a family of physical systems each possessing a finite number of degrees of freedom, next we define a space of quantum states for each finite system, finally using projective techniques we organize all these spaces into a space of quantum states which corresponds to the original phase space. This construction is kinematic in this sense that it bases merely on the structure of the phase space of a theory and does not take into account possible constraints on the space. The construction is a generalization of a construction by Kijowski—the latter one is limited to theories of linear phase spaces, while the former one is free of this limitation. The method presented in this paper enables to construct a space of quantum states for the teleparallel equivalent of general relativity. (paper)
Integrability and nonintegrability of quantum systems. II. Dynamics in quantum phase space
Zhang, Wei-Min; Feng, Da Hsuan; Yuan, Jian-Min
1990-12-01
Based on the concepts of integrability and nonintegrability of a quantum system presented in a previous paper [Zhang, Feng, Yuan, and Wang, Phys. Rev. A 40, 438 (1989)], a realization of the dynamics in the quantum phase space is now presented. For a quantum system with dynamical group scrG and in one of its unitary irreducible-representation carrier spaces gerhΛ, the quantum phase space is a 2MΛ-dimensional topological space, where MΛ is the quantum-dynamical degrees of freedom. This quantum phase space is isomorphic to a coset space scrG/scrH via the unitary exponential mapping of the elementary excitation operator subspace of scrg (algebra of scrG), where scrH (⊂scrG) is the maximal stability subgroup of a fixed state in gerhΛ. The phase-space representation of the system is realized on scrG/scrH, and its classical analogy can be obtained naturally. It is also shown that there is consistency between quantum and classical integrability. Finally, a general algorithm for seeking the manifestation of ``quantum chaos'' via the classical analogy is provided. Illustrations of this formulation in several important quantum systems are presented.
Public Library Representations and Internet Appropriations
Directory of Open Access Journals (Sweden)
Paula Sequeiros
2013-11-01
Full Text Available May the changes in the representations of the public library be propitiated by readers' appropriations of the Internet? To answer this question, a theoretically-driven and empirically-based research was developed in a public library in Portugal, combining the analysis of documents uses, the ethnography of space and Internet use, of social relations developed while reading, with the analysis of representations of the public library. No clear-cut association emerged between social-demographics or user profiles, and representations, in general. No disruptive Internet "impact" was found: Internet use may contribute to reinforce traditional representations of the library, while it may also update and democratise other representations. If the library and the Internet are represented as synonymous, the former does not make sense without the latter; but an Internet widespread and intensive use conflicts with the image of an institution dedicated to high-brow culture. Changes in uses of the public library are, instead, clearly associated with new types of readers, which in their turn reflect changes in urban social composition. URN: http://nbn-resolving.de/urn:nbn:de:0114-fqs1401141
Problem of short-term forecasting of near-earth space state
International Nuclear Information System (INIS)
Eselevich, V.G.; Ashmanets, V.I.; Startsev, S.A.
1996-01-01
The paper deals with actual and practically important problem of investigation and forecasting of state condition during magnetic storms. The available methods of forecasting of near-earth space state are analyzed. Forecasting of magnetic storms was conducted for control of space vehicles. Quasi-determinate method of magnetic storm forecasting is suggested. 13 refs., 3 figs
Energy Technology Data Exchange (ETDEWEB)
Lamy-Poirier, Joel, E-mail: jlamypoirier@perimeterinstitute.c [Departement de Physique, de Genie Physique et d' Optique, Universite Laval, Quebec, Canada, G1V 0A6 (Canada); Mathieu, Pierre, E-mail: pmathieu@phy.ulaval.c [Departement de Physique, de Genie Physique et d' Optique, Universite Laval, Quebec, Canada, G1V 0A6 (Canada)
2011-06-01
This is the second of two articles (independent of each other) devoted to the analysis of the path description of the states in su-hat (2){sub k} WZW models. Here we present a constructive derivation of the fermionic character at level k based on these paths. The starting point is the expression of a path in terms of a sequence of nonlocal (formal) operators acting on the vacuum ground-state path. Within this framework, the key step is the construction of the level-k operator sequences out of those at level-1 by the action of a new type of operators. These actions of operators on operators turn out to have a path interpretation: these paths are precisely the finitized RSOS paths related to the unitary minimal models M(k+1,k+2). We thus unravel - at the level of the path representation of the states - a direct factorization into a k=1 spinon part times a RSOS factor. It is also pointed out that since there are two fermionic forms describing these finite RSOS paths, the resulting fermionic su-hat (2){sub k} characters arise in two versions. Finally, the relation between the present construction and the Nagoya spectral decomposition of the path space is sketched.
Diatomic molecule vibrational potentials: Accuracy of representations
International Nuclear Information System (INIS)
Engelke, R.
1978-01-01
A method is presented for increasing the radius of convergence of certain representations of diatomic molecule vibrational potentials. The method relies on using knowledge of the analytic structure of such potentials to the maximum when attempting to approximate them. The known singular point (due to the centrifugal and/or Coulomb potentials) at zero internuclear separation should be included in its exact form in an approximate representation. The efficacy of this idea is tested [using Peek's ''exact'' numerical Born-Oppenheimer potential for the (1ssigma/sub g/) 2 Σ + /sub g/ state of H + 2 as a test problem] when the representational form is the series of (1) Dunham, (2) Simons, Parr, and Finlan, (3) Thakkar, and (4) Ogilvie-Tipping, and also (5) when the form is a [2, 2] or a [3, 3] Pade approximant. Significant improvements in accuracy are obtained in some of these cases, particularly on the inner wall of the potential. A comparison of the effectiveness of the five methods is made both with and without the origin behavior being included exactly. This is useful in itself as no comprehensive accuracy comparison of the standard representations seems to have appeared in the literature. The Ogilvie-Tipping series, corrected at the origin for singular behavior, is the best representation presently available for states analogous to the (1ssigma/sub g/) 2 Σ + /sub g/ state of H + 2
International Nuclear Information System (INIS)
Garcia-Vela, A.
2002-01-01
A new quantum-type phase-space distribution is proposed in order to sample initial conditions for classical trajectory simulations. The phase-space distribution is obtained as the modulus of a quantum phase-space state of the system, defined as the direct product of the coordinate and momentum representations of the quantum initial state. The distribution is tested by sampling initial conditions which reproduce the initial state of the Ar-HCl cluster prepared by ultraviolet excitation, and by simulating the photodissociation dynamics by classical trajectories. The results are compared with those of a wave packet calculation, and with a classical simulation using an initial phase-space distribution recently suggested. A better agreement is found between the classical and the quantum predictions with the present phase-space distribution, as compared with the previous one. This improvement is attributed to the fact that the phase-space distribution propagated classically in this work resembles more closely the shape of the wave packet propagated quantum mechanically
Neurofeedback and the Neural Representation of Self: Lessons From Awake State and Sleep.
Ioannides, Andreas A
2018-01-01
Neurofeedback has been around for half a century, but despite some promising results it is not yet widely appreciated. Recently, some of the concerns about neurofeedback have been addressed with functional magnetic resonance imaging and magnetoencephalography adding their contributions to the long history of neurofeedback with electroencephalography. Attempts to address other concerns related to methodological issues with new experiments and meta-analysis of earlier studies, have opened up new questions about its efficacy. A key concern about neurofeedback is the missing framework to explain how improvements in very different and apparently unrelated conditions are achieved. Recent advances in neuroscience begin to address this concern. A particularly promising approach is the analysis of resting state of fMRI data, which has revealed robust covariations in brain networks that maintain their integrity in sleep and even anesthesia. Aberrant activity in three brain wide networks (i.e., the default mode, central executive and salience networks) has been associated with a number of psychiatric disorders. Recent publications have also suggested that neurofeedback guides the restoration of "normal" activity in these three networks. Using very recent results from our analysis of whole night MEG sleep data together with key concepts from developmental psychology, cloaked in modern neuroscience terms, a theoretical framework is proposed for a neural representation of the self, located at the core of a double onion-like structure of the default mode network. This framework fits a number of old and recent neuroscientific findings, and unites the way attention and memory operate in awake state and during sleep. In the process, safeguards are uncovered, put in place by evolution, before any interference with the core representation of self can proceed. Within this framework, neurofeedback is seen as set of methods for restoration of aberrant activity in large scale networks
Neurofeedback and the Neural Representation of Self: Lessons From Awake State and Sleep
Directory of Open Access Journals (Sweden)
Andreas A. Ioannides
2018-04-01
Full Text Available Neurofeedback has been around for half a century, but despite some promising results it is not yet widely appreciated. Recently, some of the concerns about neurofeedback have been addressed with functional magnetic resonance imaging and magnetoencephalography adding their contributions to the long history of neurofeedback with electroencephalography. Attempts to address other concerns related to methodological issues with new experiments and meta-analysis of earlier studies, have opened up new questions about its efficacy. A key concern about neurofeedback is the missing framework to explain how improvements in very different and apparently unrelated conditions are achieved. Recent advances in neuroscience begin to address this concern. A particularly promising approach is the analysis of resting state of fMRI data, which has revealed robust covariations in brain networks that maintain their integrity in sleep and even anesthesia. Aberrant activity in three brain wide networks (i.e., the default mode, central executive and salience networks has been associated with a number of psychiatric disorders. Recent publications have also suggested that neurofeedback guides the restoration of “normal” activity in these three networks. Using very recent results from our analysis of whole night MEG sleep data together with key concepts from developmental psychology, cloaked in modern neuroscience terms, a theoretical framework is proposed for a neural representation of the self, located at the core of a double onion-like structure of the default mode network. This framework fits a number of old and recent neuroscientific findings, and unites the way attention and memory operate in awake state and during sleep. In the process, safeguards are uncovered, put in place by evolution, before any interference with the core representation of self can proceed. Within this framework, neurofeedback is seen as set of methods for restoration of aberrant activity in
Visual Working Memory Is Independent of the Cortical Spacing Between Memoranda.
Harrison, William J; Bays, Paul M
2018-03-21
The sensory recruitment hypothesis states that visual short-term memory is maintained in the same visual cortical areas that initially encode a stimulus' features. Although it is well established that the distance between features in visual cortex determines their visibility, a limitation known as crowding, it is unknown whether short-term memory is similarly constrained by the cortical spacing of memory items. Here, we investigated whether the cortical spacing between sequentially presented memoranda affects the fidelity of memory in humans (of both sexes). In a first experiment, we varied cortical spacing by taking advantage of the log-scaling of visual cortex with eccentricity, presenting memoranda in peripheral vision sequentially along either the radial or tangential visual axis with respect to the fovea. In a second experiment, we presented memoranda sequentially either within or beyond the critical spacing of visual crowding, a distance within which visual features cannot be perceptually distinguished due to their nearby cortical representations. In both experiments and across multiple measures, we found strong evidence that the ability to maintain visual features in memory is unaffected by cortical spacing. These results indicate that the neural architecture underpinning working memory has properties inconsistent with the known behavior of sensory neurons in visual cortex. Instead, the dissociation between perceptual and memory representations supports a role of higher cortical areas such as posterior parietal or prefrontal regions or may involve an as yet unspecified mechanism in visual cortex in which stimulus features are bound to their temporal order. SIGNIFICANCE STATEMENT Although much is known about the resolution with which we can remember visual objects, the cortical representation of items held in short-term memory remains contentious. A popular hypothesis suggests that memory of visual features is maintained via the recruitment of the same neural
Directory of Open Access Journals (Sweden)
Myrna V. Casillas
2015-03-01
Full Text Available In this paper, an original model-based scheme for leak location using pressure sensors in water distribution networks is introduced. The proposed approach is based on a new representation called the Leak Signature Space (LSS that associates a specific signature to each leak location being minimally affected by leak magnitude. The LSS considers a linear model approximation of the relation between pressure residuals and leaks that is projected onto a selected hyperplane. This new approach allows to infer the location of a given leak by comparing the position of its signature with other leak signatures. Moreover, two ways of improving the method’s robustness are proposed. First, by associating a domain of influence to each signature and second, through a time horizon analysis. The efficiency of the method is highlighted by means of a real network using several scenarios involving different number of sensors and considering the presence of noise in the measurements.
Field, F.; Goodbun, J.; Watson, V.
Architects have a role to play in interplanetary space that has barely yet been explored. The architectural community is largely unaware of this new territory, for which there is still no agreed method of practice. There is moreover a general confusion, in scientific and related fields, over what architects might actually do there today. Current extra-planetary designs generally fail to explore the dynamic and relational nature of space-time, and often reduce human habitation to a purely functional problem. This is compounded by a crisis over the representation (drawing) of space-time. The present work returns to first principles of architecture in order to realign them with current socio-economic and technological trends surrounding the space industry. What emerges is simultaneously the basis for an ecological space architecture, and the representational strategies necessary to draw it. We explore this approach through a work of design-based research that describes the construction of Ocean; a huge body of water formed by the collision of two asteroids at the Translunar Lagrange Point (L2), that would serve as a site for colonisation, and as a resource to fuel future missions. Ocean is an experimental model for extra-planetary space design and its representation, within the autonomous discipline of architecture.
A Sweep-Line Method for State Space Exploration
DEFF Research Database (Denmark)
Christensen, Søren; Kristensen, Lars Michael; Mailund, Thomas
2001-01-01
generation, since these states can never be reached again. This in turn reduces the memory used for state space storage during the task of verification. Examples of progress measures are sequence numbers in communication protocols and time in certain models with time. We illustrate the application...
Extended representations of observables and states for a noncontextual reinterpretation of QM
International Nuclear Information System (INIS)
Garola, Claudio; Sozzo, Sandro
2012-01-01
A crucial and problematical feature of quantum mechanics (QM) is nonobjectivity of properties. The ESR model restores objectivity reinterpreting quantum probabilities as conditional on detection and embodying the mathematical formalism of QM into a broader noncontextual (hence local) framework. We propose here an improved presentation of the ESR model containing a more complete mathematical representation of the basic entities of the model. We also extend the model to mixtures showing that the mathematical representations of proper mixtures do not coincide with the mathematical representation of mixtures provided by QM, while the representation of improper mixtures does. This feature of the ESR model entails that some interpretative problems raising in QM when dealing with mixtures are avoided. From an empirical point of view, the predictions of the ESR model depend on some parameters which may be such that they are very close to the predictions of QM in most cases. But the nonstandard representation of proper mixtures allows us to propose the scheme of an experiment that could check whether the predictions of QM or the predictions of the ESR model are correct. (paper)
Westheimer, Gerald
2008-09-01
Differences between the geometrical properties of simple configurations and their visual percept are called geometrical-optical illusions. They can be differentiated from illusions in the brightness or color domains, from ambiguous figures and impossible objects, from trompe l'oeil and perspective drawing with perfectly valid views, and from illusory contours. They were discovered independently by several scientists in a short time span in the 1850's. The clear distinction between object and visual space that they imply allows the question to be raised whether the transformation between the two spaces can be productively investigated in terms of differential geometry and metrical properties. Perceptual insight and psychophysical research prepares the ground for investigation of the neural representation of space but, because visual attributes are processed separately in parallel, one looks in vain for a neural map that is isomorphic with object space or even with individual forms it contains. Geometrical-optical illusions help reveal parsing rules for sensory signals by showing how conflicts are resolved when there is mismatch in the output of the processing modules for various primitives as a perceptual pattern's unitary structure is assembled. They point to a hierarchical ordering of spatial primitives: cardinal directions and explicit contours predominate over oblique orientation and implicit contours (Poggendorff illusion); rectilinearity yields to continuity (Hering illusion), point position and line length to contour orientation (Ponzo). Hence the geometrical-optical illusions show promise as analytical tools in unraveling neural processing in vision.
Parallel symbolic state-space exploration is difficult, but what is the alternative?
Directory of Open Access Journals (Sweden)
Gianfranco Ciardo
2009-12-01
Full Text Available State-space exploration is an essential step in many modeling and analysis problems. Its goal is to find the states reachable from the initial state of a discrete-state model described. The state space can used to answer important questions, e.g., "Is there a dead state?" and "Can N become negative?", or as a starting point for sophisticated investigations expressed in temporal logic. Unfortunately, the state space is often so large that ordinary explicit data structures and sequential algorithms cannot cope, prompting the exploration of (1 parallel approaches using multiple processors, from simple workstation networks to shared-memory supercomputers, to satisfy large memory and runtime requirements and (2 symbolic approaches using decision diagrams to encode the large structured sets and relations manipulated during state-space generation. Both approaches have merits and limitations. Parallel explicit state-space generation is challenging, but almost linear speedup can be achieved; however, the analysis is ultimately limited by the memory and processors available. Symbolic methods are a heuristic that can efficiently encode many, but not all, functions over a structured and exponentially large domain; here the pitfalls are subtler: their performance varies widely depending on the class of decision diagram chosen, the state variable order, and obscure algorithmic parameters. As symbolic approaches are often much more efficient than explicit ones for many practical models, we argue for the need to parallelize symbolic state-space generation algorithms, so that we can realize the advantage of both approaches. This is a challenging endeavor, as the most efficient symbolic algorithm, Saturation, is inherently sequential. We conclude by discussing challenges, efforts, and promising directions toward this goal.
Wigner function for the generalized excited pair coherent state
International Nuclear Information System (INIS)
Meng Xiangguo; Wang Jisuo; Liang Baolong; Li Hongqi
2008-01-01
This paper introduces the generalized excited pair coherent state (GEPCS). Using the entangled state |η> representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, the variations of the Wigner function distributions with the parameters q, α, k and l are discussed. The tomogram of the GEPCS is calculated with the help of the Radon transform between the Wigner operator and the projection operator of the entangled state |η 1 , η 2 , τ 1 , τ 2 >. The entangled states |η> and η 1 , η 2 , τ 1 , τ 2 > provide two good representative space for studying the Wigner functions and tomograms of various two-mode correlated quantum states
State-space modeling of the relationship between air quality and mortality.
Murray, C J; Nelson, C R
2000-07-01
A portion of a population is assumed to be at risk, with the mortality hazard varying with atmospheric conditions including total suspended particulates (TSP). This at-risk population is not observed and the hazard function is unknown; we wish to estimate these from mortality count and atmospheric variables. Consideration of population dynamics leads to a state-space representation, allowing the Kalman Filter (KF) to be used for estimation. A harvesting effect is thus implied; high mortality is followed by lower mortality until the population is replenished by new arrivals. The model is applied to daily data for Philadelphia, PA, 1973-1990. The estimated hazard function rises with the level of TSP and at extremes of temperature and also reflects a positive interaction between TSP and temperature. The estimated at-risk population averages about 480 and varies seasonally. We find that lags of TSP are statistically significant, but the presence of negative coefficients suggests their role may be partially statistical rather than biological. In the population dynamics framework, the natural metric for health damage from air pollution is its impact on life expectancy. The range of hazard rates over the sample period is 0.07 to 0.085, corresponding to life expectancies of 14.3 and 11.8 days, respectively.
Adaptive importance sampling of random walks on continuous state spaces
International Nuclear Information System (INIS)
Baggerly, K.; Cox, D.; Picard, R.
1998-01-01
The authors consider adaptive importance sampling for a random walk with scoring in a general state space. Conditions under which exponential convergence occurs to the zero-variance solution are reviewed. These results generalize previous work for finite, discrete state spaces in Kollman (1993) and in Kollman, Baggerly, Cox, and Picard (1996). This paper is intended for nonstatisticians and includes considerable explanatory material
Operator Representations of Frames: Boundedness, Duality, and Stability
DEFF Research Database (Denmark)
Christensen, Ole; Hasannasab, Marzieh
2017-01-01
The purpose of the paper is to analyze frames (Formula presented.) having the form (Formula presented.) for some linear operator (Formula presented.). A key result characterizes boundedness of the operator T in terms of shift-invariance of a certain sequence space. One of the consequences is a ch...... in frame theory. Various ways of avoiding this problem will be discussed. Throughout the paper the results will be connected with the operators and function systems appearing in applied harmonic analysis, as well as with general group representations.......The purpose of the paper is to analyze frames (Formula presented.) having the form (Formula presented.) for some linear operator (Formula presented.). A key result characterizes boundedness of the operator T in terms of shift-invariance of a certain sequence space. One of the consequences...... is a characterization of the case where the representation (Formula presented.) can be achieved for an operator T that has an extension to a bounded bijective operator (Formula presented.) In this case we also characterize all the dual frames that are representable in terms of iterations of an operator V; in particular...
Some nonunitary, indecomposable representations of the Euclidean algebra e(3)
International Nuclear Information System (INIS)
Douglas, Andrew; De Guise, Hubert
2010-01-01
The Euclidean group E(3) is the noncompact, semidirect product group E(3)≅R 3 x SO(3). It is the Lie group of orientation-preserving isometries of three-dimensional Euclidean space. The Euclidean algebra e(3) is the complexification of the Lie algebra of E(3). We construct three distinct families of finite-dimensional, nonunitary representations of e(3) and show that each representation is indecomposable. The representations of the first family are explicitly realized as subspaces of the polynomial ring F[X,Y,Z] with the action of e(3) given by differential operators. The other families are constructed via duals and tensor products of the representations within the first family. We describe subrepresentations, quotients and duals of these indecomposable representations.
Interactive Space(s) -- the CTSG: bridging the real and virtual
Eliëns, A.P.W.; Mao, W.; Vermeersch, L
2010-01-01
In this paper, ideas will be presented how to realize games or playful activities in interactive space(s), having a real (spatial) component as well as a representation in virtual 2D or 3D space, by means of web pages and/or online games. Apart from general design criteria, the paper discusses a
SLE local martingales in logarithmic representations
International Nuclear Information System (INIS)
Kytölä, Kalle
2009-01-01
A space of local martingales of SLE-type growth processes forms a representation of Virasoro algebra, but apart from a few simplest cases, not much is known about this representation. The purpose of this paper is to exhibit examples of representations where L 0 is not diagonalizable—a phenomenon characteristic of logarithmic conformal field theory. Furthermore, we observe that the local martingales bear a close relation to the fusion product of the boundary changing fields. Our examples reproduce first of all many familiar logarithmic representations at certain rational values of the central charge. In particular we discuss the case of SLE κ=6 describing the exploration path in critical percolation and its relation to the question of operator content of the appropriate conformal field theory of zero central charge. In this case one encounters logarithms in a probabilistically transparent way, through conditioning on a crossing event. But we also observe that some quite natural SLE variants exhibit logarithmic behavior at all values of κ, thus at all central charges and not only at specific rational values
Symposium on Singularities, Representation of Algebras, and Vector Bundles
Trautmann, Günther
1987-01-01
It is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction. These relations however cannot be considered to be either completely understood or fully exploited. These proceedings document recent developments in the area. The questions and methods of representation theory have applications to singularities and to vector bundles. Representation theory itself, which had primarily developed its methods for Artinian algebras, starts to investigate algebras of higher dimension partly because of these applications. Future research in representation theory may be spurred by the classification of singularities and the highly developed theory of moduli for vector bundles. The volume contains 3 survey articles on the 3 main topics mentioned, stressing their interrelationships, as well as original research papers.
U-duality multiplets and nonperturbative superstring states
International Nuclear Information System (INIS)
Bars, I.; Yankielowicz, S.
1996-01-01
We employ an algebraic approach for unifying perturbative and nonperturbative superstring states on an equal footing, in the form of U-duality multiplets, at all excited string levels. In compactified type-IIA supertring theory we present evidence that the multiplet is labeled by two spaces, open-quote open-quote index close-quote close-quote space and open-quote open-quote base close-quote close-quote space, on which U acts without mixing them. Both spaces are nonperturbative extensions of similar spaces that label perturbative T-duality multiplets. Base space consists of all the central charges of the 11D SUSY algebra, while index space corresponds to representations of the maximal compact subgroup K improper-subset U. This structure predicts the quantum numbers of the nonperturbative states. We also discuss whether and how U multiplets may coexist with 11-dimensional multiplets that are associated with an additional nonperturbative 11D structure that seems to be lurking behind in the underlying theory. copyright 1996 The American Physical Society
Black, R. X.
2017-12-01
We summarize results from a project focusing on regional temperature and precipitation extremes over the continental United States. Our project introduces a new framework for evaluating these extremes emphasizing their (a) large-scale organization, (b) underlying physical sources (including remote-excitation and scale-interaction) and (c) representation in climate models. Results to be reported include the synoptic-dynamic behavior, seasonality and secular variability of cold waves, dry spells and heavy rainfall events in the observational record. We also study how the characteristics of such extremes are systematically related to Northern Hemisphere planetary wave structures and thus planetary- and hemispheric-scale forcing (e.g., those associated with major El Nino events and Arctic sea ice change). The underlying physics of event onset are diagnostically quantified for different categories of events. Finally, the representation of these extremes in historical coupled climate model simulations is studied and the origins of model biases are traced using new metrics designed to assess the large-scale atmospheric forcing of local extremes.
Building blocks of topological quantum chemistry: Elementary band representations
Cano, Jennifer; Bradlyn, Barry; Wang, Zhijun; Elcoro, L.; Vergniory, M. G.; Felser, C.; Aroyo, M. I.; Bernevig, B. Andrei
2018-01-01
The link between chemical orbitals described by local degrees of freedom and band theory, which is defined in momentum space, was proposed by Zak several decades ago for spinless systems with and without time reversal in his theory of "elementary" band representations. In a recent paper [Bradlyn et al., Nature (London) 547, 298 (2017), 10.1038/nature23268] we introduced the generalization of this theory to the experimentally relevant situation of spin-orbit coupled systems with time-reversal symmetry and proved that all bands that do not transform as band representations are topological. Here we give the full details of this construction. We prove that elementary band representations are either connected as bands in the Brillouin zone and are described by localized Wannier orbitals respecting the symmetries of the lattice (including time reversal when applicable), or, if disconnected, describe topological insulators. We then show how to generate a band representation from a particular Wyckoff position and determine which Wyckoff positions generate elementary band representations for all space groups. This theory applies to spinful and spinless systems, in all dimensions, with and without time reversal. We introduce a homotopic notion of equivalence and show that it results in a finer classification of topological phases than approaches based only on the symmetry of wave functions at special points in the Brillouin zone. Utilizing a mapping of the band connectivity into a graph theory problem, we show in companion papers which Wyckoff positions can generate disconnected elementary band representations, furnishing a natural avenue for a systematic materials search.
The Extent of Membership Representation and Non-Representation on the IASB
Directory of Open Access Journals (Sweden)
Alistair Brown
2008-06-01
affiliation of members, Internet access, and gender composition over a five-year period. The results of the study show that over the period 2001-2005 representation on a four IASB committees was dominated by male members from high Internet access regions of the United States of America.
Non-commutative phase space and its space-time symmetry
International Nuclear Information System (INIS)
Li Kang; Dulat Sayipjamal
2010-01-01
First a description of 2+1 dimensional non-commutative (NC) phase space is presented, and then we find that in this formulation the generalized Bopp's shift has a symmetric representation and one can easily and straightforwardly define the star product on NC phase space. Then we define non-commutative Lorentz transformations both on NC space and NC phase space. We also discuss the Poincare symmetry. Finally we point out that our NC phase space formulation and the NC Lorentz transformations are applicable to any even dimensional NC space and NC phase space. (authors)
Matrix product representation of the stationary state of the open zero range process
Bertin, Eric; Vanicat, Matthieu
2018-06-01
Many one-dimensional lattice particle models with open boundaries, like the paradigmatic asymmetric simple exclusion process (ASEP), have their stationary states represented in the form of a matrix product, with matrices that do not explicitly depend on the lattice site. In contrast, the stationary state of the open 1D zero-range process (ZRP) takes an inhomogeneous factorized form, with site-dependent probability weights. We show that in spite of the absence of correlations, the stationary state of the open ZRP can also be represented in a matrix product form, where the matrices are site-independent, non-commuting and determined from algebraic relations resulting from the master equation. We recover the known distribution of the open ZRP in two different ways: first, using an explicit representation of the matrices and boundary vectors; second, from the sole knowledge of the algebraic relations satisfied by these matrices and vectors. Finally, an interpretation of the relation between the matrix product form and the inhomogeneous factorized form is proposed within the framework of hidden Markov chains.
3D hierarchical spatial representation and memory of multimodal sensory data
Khosla, Deepak; Dow, Paul A.; Huber, David J.
2009-04-01
This paper describes an efficient method and system for representing, processing and understanding multi-modal sensory data. More specifically, it describes a computational method and system for how to process and remember multiple locations in multimodal sensory space (e.g., visual, auditory, somatosensory, etc.). The multimodal representation and memory is based on a biologically-inspired hierarchy of spatial representations implemented with novel analogues of real representations used in the human brain. The novelty of the work is in the computationally efficient and robust spatial representation of 3D locations in multimodal sensory space as well as an associated working memory for storage and recall of these representations at the desired level for goal-oriented action. We describe (1) A simple and efficient method for human-like hierarchical spatial representations of sensory data and how to associate, integrate and convert between these representations (head-centered coordinate system, body-centered coordinate, etc.); (2) a robust method for training and learning a mapping of points in multimodal sensory space (e.g., camera-visible object positions, location of auditory sources, etc.) to the above hierarchical spatial representations; and (3) a specification and implementation of a hierarchical spatial working memory based on the above for storage and recall at the desired level for goal-oriented action(s). This work is most useful for any machine or human-machine application that requires processing of multimodal sensory inputs, making sense of it from a spatial perspective (e.g., where is the sensory information coming from with respect to the machine and its parts) and then taking some goal-oriented action based on this spatial understanding. A multi-level spatial representation hierarchy means that heterogeneous sensory inputs (e.g., visual, auditory, somatosensory, etc.) can map onto the hierarchy at different levels. When controlling various machine
SEVERAL REPRESENTATIONS OF THE FOREIGNER IN ROMANIAN POPULAR EPICS NOTES FOR A FOLKLORIC IMAGOLOGY
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Corina Daniela POPESCU
2015-05-01
Full Text Available From the perspective of the anthropology of space, the problem of perception and representation of the alien remains a fertile subject of research, nevertheless inevitably interfering with imagology, in the sense assigned to the concept of image as any representation of a cultural r eality through which the individual or the group translate the cultural, social, ideological space in which they are located Identity does not justify an existence in itself, but only in relation to alterity The imagological perspective of the foreigner in Romanian traditional culture proves rich in categories of representation dictated inevitably by reference to spatiality
International Nuclear Information System (INIS)
Stulpe, Werner
2014-01-01
The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is revisited, and its limitation in view of a classical reformulation of the statistical scheme of quantum mechanics is discussed. In particular, on the basis of a theorem concerning a non-denseness property of a set of coexistent effects, it is shown that an injective classical embedding of the quantum states cannot be supplemented by an at least approximate classical description of the quantum mechanical effects. As an alternative approach, the concept of quasi-probability representations of quantum mechanics is considered
Learning of Multimodal Representations With Random Walks on the Click Graph.
Wu, Fei; Lu, Xinyan; Song, Jun; Yan, Shuicheng; Zhang, Zhongfei Mark; Rui, Yong; Zhuang, Yueting
2016-02-01
In multimedia information retrieval, most classic approaches tend to represent different modalities of media in the same feature space. With the click data collected from the users' searching behavior, existing approaches take either one-to-one paired data (text-image pairs) or ranking examples (text-query-image and/or image-query-text ranking lists) as training examples, which do not make full use of the click data, particularly the implicit connections among the data objects. In this paper, we treat the click data as a large click graph, in which vertices are images/text queries and edges indicate the clicks between an image and a query. We consider learning a multimodal representation from the perspective of encoding the explicit/implicit relevance relationship between the vertices in the click graph. By minimizing both the truncated random walk loss as well as the distance between the learned representation of vertices and their corresponding deep neural network output, the proposed model which is named multimodal random walk neural network (MRW-NN) can be applied to not only learn robust representation of the existing multimodal data in the click graph, but also deal with the unseen queries and images to support cross-modal retrieval. We evaluate the latent representation learned by MRW-NN on a public large-scale click log data set Clickture and further show that MRW-NN achieves much better cross-modal retrieval performance on the unseen queries/images than the other state-of-the-art methods.
Faithful representation of similarities among three-dimensional shapes in human vision.
Cutzu, F; Edelman, S
1996-01-01
Efficient and reliable classification of visual stimuli requires that their representations reside a low-dimensional and, therefore, computationally manageable feature space. We investigated the ability of the human visual system to derive such representations from the sensory input-a highly nontrivial task, given the million or so dimensions of the visual signal at its entry point to the cortex. In a series of experiments, subjects were presented with sets of parametrically defined shapes; the points in the common high-dimensional parameter space corresponding to the individual shapes formed regular planar (two-dimensional) patterns such as a triangle, a square, etc. We then used multidimensional scaling to arrange the shapes in planar configurations, dictated by their experimentally determined perceived similarities. The resulting configurations closely resembled the original arrangements of the stimuli in the parameter space. This achievement of the human visual system was replicated by a computational model derived from a theory of object representation in the brain, according to which similarities between objects, and not the geometry of each object, need to be faithfully represented. Images Fig. 3 PMID:8876260
Estimation methods for nonlinear state-space models in ecology
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Berg, Casper Willestofte; Thygesen, Uffe Høgsbro
2011-01-01
The use of nonlinear state-space models for analyzing ecological systems is increasing. A wide range of estimation methods for such models are available to ecologists, however it is not always clear, which is the appropriate method to choose. To this end, three approaches to estimation in the theta...... logistic model for population dynamics were benchmarked by Wang (2007). Similarly, we examine and compare the estimation performance of three alternative methods using simulated data. The first approach is to partition the state-space into a finite number of states and formulate the problem as a hidden...... Markov model (HMM). The second method uses the mixed effects modeling and fast numerical integration framework of the AD Model Builder (ADMB) open-source software. The third alternative is to use the popular Bayesian framework of BUGS. The study showed that state and parameter estimation performance...
Wirth, Sylvia; Baraduc, Pierre; Planté, Aurélie; Pinède, Serge; Duhamel, Jean-René
2017-01-01
To elucidate how gaze informs the construction of mental space during wayfinding in visual species like primates, we jointly examined navigation behavior, visual exploration, and hippocampal activity as macaque monkeys searched a virtual reality maze for a reward. Cells sensitive to place also responded to one or more variables like head direction, point of gaze, or task context. Many cells fired at the sight (and in anticipation) of a single landmark in a viewpoint- or task-dependent manner, simultaneously encoding the animal’s logical situation within a set of actions leading to the goal. Overall, hippocampal activity was best fit by a fine-grained state space comprising current position, view, and action contexts. Our findings indicate that counterparts of rodent place cells in primates embody multidimensional, task-situated knowledge pertaining to the target of gaze, therein supporting self-awareness in the construction of space. PMID:28241007
The Representation of Fatherhood by the Arab Diaspora in the United States
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Marta Bosch
2008-01-01
Full Text Available This article1 analyzes three debut novels –Alicia Erian’s Towelhead (2005, Laila Halaby’s West of the Jordan (2003, and Diana Abu-Jaber’s Arabian Jazz (1993– in order to explore the representation of fatherhood by the Arab diaspora in the United States. To do so, it will draw on Ralph La Rossa’s notion of “new father”, and on Julie Peteet’s and Daniel Monterescu’s ideas about Arab masculinity. It will then analyze the main father figures in the novels under the light of these concepts. It will finally conclude that the different existing models of Arab fatherhood move from traditionalism to liberalism, and that allows the possibility of “new fatherhoods” to emerge.
Approximate representations of propagators in an external field
International Nuclear Information System (INIS)
Fried, H.M.
1979-01-01
A method of forming approximate representations for propagators with external field dependence is suggested and discussed in the context of potential scattering. An integro-differential equation in D+1 variables, where D represents the dimensionality of Euclidian space-time, is replaced by a Volterra equation in one variable. Approximate solutions to the latter provide a generalization of the Bloch-Nordsieck representation, containing the effects of all powers of hard-potential interactions, each modified by a characteristic soft-potential dependence [fr
Multimedia Mapping using Continuous State Space Models
DEFF Research Database (Denmark)
Lehn-Schiøler, Tue
2004-01-01
In this paper a system that transforms speech waveforms to animated faces are proposed. The system relies on continuous state space models to perform the mapping, this makes it possible to ensure video with no sudden jumps and allows continuous control of the parameters in 'face space'. Simulations...... are performed on recordings of 3-5 sec. video sequences with sentences from the Timit database. The model is able to construct an image sequence from an unknown noisy speech sequence fairly well even though the number of training examples are limited....
Berberian, S K
2002-01-01
A detailed exposition of G.W. Mackey's theory of Borel spaces (standard, substandard, analytic), based on results in Chapter 9 of Bourbaki's General Topology. Appended are five informal lectures on the subject (given at the CIMPA/ICPAM Summer School, Nice, 1986), sketching the connection between Borel spaces and representations of operator algebras.
Linguistic and Perceptual Mapping in Spatial Representations: An Attentional Account.
Valdés-Conroy, Berenice; Hinojosa, José A; Román, Francisco J; Romero-Ferreiro, Verónica
2018-03-01
Building on evidence for embodied representations, we investigated whether Spanish spatial terms map onto the NEAR/FAR perceptual division of space. Using a long horizontal display, we measured congruency effects during the processing of spatial terms presented in NEAR or FAR space. Across three experiments, we manipulated the task demands in order to investigate the role of endogenous attention in linguistic and perceptual space mapping. We predicted congruency effects only when spatial properties were relevant for the task (reaching estimation task, Experiment 1) but not when attention was allocated to other features (lexical decision, Experiment 2; and color, Experiment 3). Results showed faster responses for words presented in Near-space in all experiments. Consistent with our hypothesis, congruency effects were observed only when a reaching estimate was requested. Our results add important evidence for the role of top-down processing in congruency effects from embodied representations of spatial terms. Copyright © 2017 Cognitive Science Society, Inc.
Active Affordance Learning in Continuous State and Action Spaces
Wang, C.; Hindriks, K.V.; Babuska, R.
2014-01-01
Learning object affordances and manipulation skills is essential for developing cognitive service robots. We propose an active affordance learning approach in continuous state and action spaces without manual discretization of states or exploratory motor primitives. During exploration in the action
Cruz-Roa, Angel; Arevalo, John; Basavanhally, Ajay; Madabhushi, Anant; González, Fabio
2015-01-01
Learning data representations directly from the data itself is an approach that has shown great success in different pattern recognition problems, outperforming state-of-the-art feature extraction schemes for different tasks in computer vision, speech recognition and natural language processing. Representation learning applies unsupervised and supervised machine learning methods to large amounts of data to find building-blocks that better represent the information in it. Digitized histopathology images represents a very good testbed for representation learning since it involves large amounts of high complex, visual data. This paper presents a comparative evaluation of different supervised and unsupervised representation learning architectures to specifically address open questions on what type of learning architectures (deep or shallow), type of learning (unsupervised or supervised) is optimal. In this paper we limit ourselves to addressing these questions in the context of distinguishing between anaplastic and non-anaplastic medulloblastomas from routine haematoxylin and eosin stained images. The unsupervised approaches evaluated were sparse autoencoders and topographic reconstruct independent component analysis, and the supervised approach was convolutional neural networks. Experimental results show that shallow architectures with more neurons are better than deeper architectures without taking into account local space invariances and that topographic constraints provide useful invariant features in scale and rotations for efficient tumor differentiation.
A Distributional Representation Model For Collaborative Filtering
Junlin, Zhang; Heng, Cai; Tongwen, Huang; Huiping, Xue
2015-01-01
In this paper, we propose a very concise deep learning approach for collaborative filtering that jointly models distributional representation for users and items. The proposed framework obtains better performance when compared against current state-of-art algorithms and that made the distributional representation model a promising direction for further research in the collaborative filtering.
The Bohr-Heisenberg correspondence principle viewed from phase space
DEFF Research Database (Denmark)
Dahl, Jens Peder
2002-01-01
Phase-space representations play an increasingly important role in several branches of physics. Here, we review the author's studies of the Bohr-Heisenberg correspondence principle within the Weyl-Wigner phase-space representation. The analysis leads to refined correspondence rules that can...
Path integral representations on the complex sphere
International Nuclear Information System (INIS)
Grosche, C.
2007-08-01
In this paper we discuss the path integral representations for the coordinate systems on the complex sphere S 3C . The Schroedinger equation, respectively the path integral, separates in exactly 21 orthogonal coordinate systems. We enumerate these coordinate systems and we are able to present the path integral representations explicitly in the majority of the cases. In each solution the expansion into the wave-functions is stated. Also, the kernel and the corresponding Green function can be stated in closed form in terms of the invariant distance on the sphere, respectively on the hyperboloid. (orig.)
International Nuclear Information System (INIS)
Mlinar, Vladan
2015-01-01
To facilitate the design and optimization of nanomaterials for a given application it is necessary to understand the relationship between structure and physical properties. For large nanomaterials, there is imprecise structural information so the full structure is only resolved at the level of partial representations. Here we show how to reconcile partial structural representations using constraints from structural characterization measurements and theory to maximally exploit the limited amount of data available from experiment. We determine a range of parameter space where predictive theory can be used to design and optimize the structure. Using an example of variation of chemical composition profile across the interface of two nanomaterials, we demonstrate how, given experimental and theoretical constraints, to find a region of structure-parameter space within which computationally explored partial representations of the full structure will have observable real-world counterparts. (paper)
Khaligh-Razavi, Seyed-Mahdi; Henriksson, Linda; Kay, Kendrick; Kriegeskorte, Nikolaus
2017-02-01
Studies of the primate visual system have begun to test a wide range of complex computational object-vision models. Realistic models have many parameters, which in practice cannot be fitted using the limited amounts of brain-activity data typically available. Task performance optimization (e.g. using backpropagation to train neural networks) provides major constraints for fitting parameters and discovering nonlinear representational features appropriate for the task (e.g. object classification). Model representations can be compared to brain representations in terms of the representational dissimilarities they predict for an image set. This method, called representational similarity analysis (RSA), enables us to test the representational feature space as is (fixed RSA) or to fit a linear transformation that mixes the nonlinear model features so as to best explain a cortical area's representational space (mixed RSA). Like voxel/population-receptive-field modelling, mixed RSA uses a training set (different stimuli) to fit one weight per model feature and response channel (voxels here), so as to best predict the response profile across images for each response channel. We analysed response patterns elicited by natural images, which were measured with functional magnetic resonance imaging (fMRI). We found that early visual areas were best accounted for by shallow models, such as a Gabor wavelet pyramid (GWP). The GWP model performed similarly with and without mixing, suggesting that the original features already approximated the representational space, obviating the need for mixing. However, a higher ventral-stream visual representation (lateral occipital region) was best explained by the higher layers of a deep convolutional network and mixing of its feature set was essential for this model to explain the representation. We suspect that mixing was essential because the convolutional network had been trained to discriminate a set of 1000 categories, whose frequencies
The kinematical Hilbert space of loop quantum gravity from BF theories
International Nuclear Information System (INIS)
Cianfrani, Francesco
2011-01-01
In this work, it is demonstrated how the kinematical Hilbert space of loop quantum gravity (LQG) can be inferred from the configuration space of BF theories via the imposition of the Hamiltonian constraints. In particular, it is outlined how the projection to the representations associated with Ashtekar-Barbero connections provides the correct procedure to implement second-class constraints and the corresponding nontrivial induced symplectic structure. Then, the reduction to SU(2) invariant intertwiners is analyzed and the properties of LQG states under Lorentz transformations are discussed.
Clifford Algebras and Spinorial Representation of Linear Canonical Transformations in Quantum Theory
International Nuclear Information System (INIS)
Raoelina Andriambololona; Ranaivoson, R.T.R.; Rakotoson, H.
2017-11-01
This work is a continuation of previous works that we have done concerning linear canonical transformations and a phase space representation of quantum theory. It is mainly focused on the description of an approach which permits to establish spinorial representation of linear canonical transformations. It begins with an introduction section in which the reason and context of the content are discussed. The introduction section is followed by a brief recall about Clifford algebra and spin group. The description of the approach is started with the presentation of an adequate parameterization of linear canonical transformations which permits to represent them with special pseudo-orthogonal transformations in an operators space. The establishment of the spinorial representation is deduced using relation between special pseudo-orthogonal groups and spin groups. The cases of one dimension quantum mechanics and general multidimensional theory are both studied. The case of linear canonical transformation related to Minkowski space is particularly studied and it is shown that Lorentz transformation may be considered as particular case of linear canonical transformation. Some results from the spinorial representation are also exploited to define operators which may be used to establish equations for fields if one considers the possibility of envisaging a field theory which admits as main symmetry group the group constituted by linear canonical transformations.
METHODS FOR THE REPRESENTATION OF THE HELICOIDAL SURFACE
Directory of Open Access Journals (Sweden)
SCURTU Liviu-Iacob
2017-05-01
Full Text Available In this paper there are presented the graphical methods to determine the parameters of an helicoidal stairs. The first part of this paper shows the used methods to generate the helicoidal curves using descriptive geometry methods. It has represented the state of the art of the generation of a helical surface studies. The second part of this study shows the helical stairs surface representation using descriptive geometry methods. For the representation of the helicoidal stairs are used two projections, the front and top view. A method of the stairs representation is solved using CAD modelling dedicated software. Following the helical surface representation in both methods, has been achieved a comparative study by using two representation methods. Conclusions about these two representation methods are presented in the end of this paper.
Visual Representations on High School Biology, Chemistry, Earth Science, and Physics Assessments
LaDue, Nicole D.; Libarkin, Julie C.; Thomas, Stephen R.
2015-01-01
The pervasive use of visual representations in textbooks, curricula, and assessments underscores their importance in K-12 science education. For example, visual representations figure prominently in the recent publication of the Next Generation Science Standards (NGSS Lead States in Next generation science standards: for states, by states.…
Pure state consciousness and its local reduction to neuronal space
Duggins, A. J.
2013-01-01
The single neuronal state can be represented as a vector in a complex space, spanned by an orthonormal basis of integer spike counts. In this model a scalar element of experience is associated with the instantaneous firing rate of a single sensory neuron over repeated stimulus presentations. Here the model is extended to composite neural systems that are tensor products of single neuronal vector spaces. Depiction of the mental state as a vector on this tensor product space is intended to capture the unity of consciousness. The density operator is introduced as its local reduction to the single neuron level, from which the firing rate can again be derived as the objective correlate of a subjective element. However, the relational structure of perceptual experience only emerges when the non-local mental state is considered. A metric of phenomenal proximity between neuronal elements of experience is proposed, based on the cross-correlation function of neurophysiology, but constrained by the association of theoretical extremes of correlation/anticorrelation in inseparable 2-neuron states with identical and opponent elements respectively.
DEFF Research Database (Denmark)
Pinto Coelho Muniz Vinhal, Andre; Yan, Wei; Kontogeorgis, Georgios
2017-01-01
of the Cubic-Plus-Association (CPA) equation of state (EoS). We obtained new parameters for methanol and alkanes from n-hexane to n-decane. The comparison with the original parameters showed that this procedure is important for associating compounds, since for inert species the equation reduces to the Soave......-Redlich-Kwong (SRK) EoS. The application of the rescaled parameters improved the critical point representation of pure fluids at the expense of the saturated liquid phase volume description. In the case of binary mixtures containing methanol and n-alkanes, the association model with the new parameters satisfactorily...
The semantic representation of prejudice and stereotypes.
Bhatia, Sudeep
2017-07-01
We use a theory of semantic representation to study prejudice and stereotyping. Particularly, we consider large datasets of newspaper articles published in the United States, and apply latent semantic analysis (LSA), a prominent model of human semantic memory, to these datasets to learn representations for common male and female, White, African American, and Latino names. LSA performs a singular value decomposition on word distribution statistics in order to recover word vector representations, and we find that our recovered representations display the types of biases observed in human participants using tasks such as the implicit association test. Importantly, these biases are strongest for vector representations with moderate dimensionality, and weaken or disappear for representations with very high or very low dimensionality. Moderate dimensional LSA models are also the best at learning race, ethnicity, and gender-based categories, suggesting that social category knowledge, acquired through dimensionality reduction on word distribution statistics, can facilitate prejudiced and stereotyped associations. Copyright © 2017 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Benny Liebold
2013-03-01
Full Text Available Recently, cinemas, home theater systems and game consoles have undergone a rapid evolution towards stereoscopic representation with recipients gradually becoming accustomed to these changes. Stereoscopy techniques in most media present two offset images separately to the left and right eye of the viewer (usually with the help of glasses separating both images resulting in the perception of three-dimensional depth. In contrast to these mass market techniques, true 3D volumetric displays or holograms that display an image in three full dimensions are relatively uncommon. The visual quality and visual comfort of stereoscopic representation is constantly being improved by the industry.
State-space Manifold and Rotating Black Holes
Bellucci, Stefano
2010-01-01
We study a class of fluctuating higher dimensional black hole configurations obtained in string theory/ $M$-theory compactifications. We explore the intrinsic Riemannian geometric nature of Gaussian fluctuations arising from the Hessian of the coarse graining entropy, defined over an ensemble of brane microstates. It has been shown that the state-space geometry spanned by the set of invariant parameters is non-degenerate, regular and has a negative scalar curvature for the rotating Myers-Perry black holes, Kaluza-Klein black holes, supersymmetric $AdS_5$ black holes, $D_1$-$D_5$ configurations and the associated BMPV black holes. Interestingly, these solutions demonstrate that the principal components of the state-space metric tensor admit a positive definite form, while the off diagonal components do not. Furthermore, the ratio of diagonal components weakens relatively faster than the off diagonal components, and thus they swiftly come into an equilibrium statistical configuration. Novel aspects of the scali...
Identification of a class of nonlinear state-space models using RPE techniques
DEFF Research Database (Denmark)
Zhou, W. W.; Blanke, Mogens
1986-01-01
The recursive prediction error methods in state-space form have been efficiently used as parameter identifiers for linear systems, and especially Ljung's innovations filter using a Newton search direction has proved to be quite ideal. In this paper, the RPE method in state-space form is developed...... a quite convincing performance of the filter as combined parameter and state estimator....
Concepts, ontologies, and knowledge representation
Jakus, Grega; Omerovic, Sanida; Tomažic, Sašo
2013-01-01
Recording knowledge in a common framework that would make it possible to seamlessly share global knowledge remains an important challenge for researchers. This brief examines several ideas about the representation of knowledge addressing this challenge. A widespread general agreement is followed that states uniform knowledge representation should be achievable by using ontologies populated with concepts. A separate chapter is dedicated to each of the three introduced topics, following a uniform outline: definition, organization, and use. This brief is intended for those who want to get to know
Coherent states on horospheric three-dimensional Lobachevsky space
Energy Technology Data Exchange (ETDEWEB)
Kurochkin, Yu., E-mail: y.kurochkin@ifanbel.bas-net.by; Shoukavy, Dz., E-mail: shoukavy@ifanbel.bas-net.by [Institute of Physics, National Academy of Sciences of Belarus, 68 Nezalezhnasci Ave., Minsk 220072 (Belarus); Rybak, I., E-mail: Ivan.Rybak@astro.up.pt [Institute of Physics, National Academy of Sciences of Belarus, 68 Nezalezhnasci Ave., Minsk 220072 (Belarus); Instituto de Astrofísica e Ciências do Espaço, CAUP, Rua das Estrelas, 4150-762 Porto (Portugal); Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal)
2016-08-15
In the paper it is shown that due to separation of variables in the Laplace-Beltrami operator (Hamiltonian of a free quantum particle) in horospheric and quasi-Cartesian coordinates of three dimensional Lobachevsky space, it is possible to introduce standard (“conventional” according to Perelomov [Generalized Coherent States and Their Applications (Springer-Verlag, 1986), p. 320]) coherent states. Some problems (oscillator on horosphere, charged particle in analogy of constant uniform magnetic field) where coherent states are suitable for treating were considered.
Wang, Yang; Wu, Lin
2018-07-01
Low-Rank Representation (LRR) is arguably one of the most powerful paradigms for Multi-view spectral clustering, which elegantly encodes the multi-view local graph/manifold structures into an intrinsic low-rank self-expressive data similarity embedded in high-dimensional space, to yield a better graph partition than their single-view counterparts. In this paper we revisit it with a fundamentally different perspective by discovering LRR as essentially a latent clustered orthogonal projection based representation winged with an optimized local graph structure for spectral clustering; each column of the representation is fundamentally a cluster basis orthogonal to others to indicate its members, which intuitively projects the view-specific feature representation to be the one spanned by all orthogonal basis to characterize the cluster structures. Upon this finding, we propose our technique with the following: (1) We decompose LRR into latent clustered orthogonal representation via low-rank matrix factorization, to encode the more flexible cluster structures than LRR over primal data objects; (2) We convert the problem of LRR into that of simultaneously learning orthogonal clustered representation and optimized local graph structure for each view; (3) The learned orthogonal clustered representations and local graph structures enjoy the same magnitude for multi-view, so that the ideal multi-view consensus can be readily achieved. The experiments over multi-view datasets validate its superiority, especially over recent state-of-the-art LRR models. Copyright © 2018 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Borstnik, N. Mankoc; Nielsen, H.B.
2002-01-01
We present a technique to construct a spinor space basis as products of certain nilpotents and projections formed from γ a for which we only need to know that they obey the Clifford algebra. The technique works for all dimensions and signatures. We use this technique to deliver a concrete choice of γ-matrices and Lorentz group generators for (fundamental representations of) spinors in a rather systematic and transparent way. We further develop the formalism by proposing the corresponding graphic presentation of basic states, which offers an easy way to see all the quantum numbers of states with respect to the generators of the Lorentz group, as well as transformation properties of the states under any element of the Clifford algebra
Generalized hypergeometric coherent states
International Nuclear Information System (INIS)
Appl, Thomas; Schiller, Diethard H
2004-01-01
We introduce a large class of holomorphic quantum states by choosing their normalization functions to be given by generalized hypergeometric functions. We call them generalized hypergeometric states in general, and generalized hypergeometric coherent states in particular, if they allow a resolution of unity. Depending on the domain of convergence of the generalized hypergeometric functions, we distinguish generalized hypergeometric states on the plane, the open unit disc and the unit circle. All states are eigenstates of suitably defined lowering operators. We then study their photon number statistics and phase properties as revealed by the Husimi and Pegg-Barnett phase distributions. On the basis of the generalized hypergeometric coherent states we introduce new analytic representations of arbitrary quantum states in Bargmann and Hardy spaces as well as generalized hypergeometric Husimi distributions and corresponding phase distributions
Probabilistic Q-function distributions in fermionic phase-space
International Nuclear Information System (INIS)
Rosales-Zárate, Laura E C; Drummond, P D
2015-01-01
We obtain a positive probability distribution or Q-function for an arbitrary fermionic many-body system. This is different to previous Q-function proposals, which were either restricted to a subspace of the overall Hilbert space, or used Grassmann methods that do not give probabilities. The fermionic Q-function obtained here is constructed using normally ordered Gaussian operators, which include both non-interacting thermal density matrices and BCS states. We prove that the Q-function exists for any density matrix, is real and positive, and has moments that correspond to Fermi operator moments. It is defined on a finite symmetric phase-space equivalent to the space of real, antisymmetric matrices. This has the natural SO(2M) symmetry expected for Majorana fermion operators. We show that there is a physical interpretation of the Q-function: it is the relative probability for observing a given Gaussian density matrix. The distribution has a uniform probability across the space at infinite temperature, while for pure states it has a maximum value on the phase-space boundary. The advantage of probabilistic representations is that they can be used for computational sampling without a sign problem. (fast track communication)
Dynamic State Space Partitioning for External Memory Model Checking
DEFF Research Database (Denmark)
Evangelista, Sami; Kristensen, Lars Michael
2009-01-01
We describe a dynamic partitioning scheme usable by model checking techniques that divide the state space into partitions, such as most external memory and distributed model checking algorithms. The goal of the scheme is to reduce the number of transitions that link states belonging to different...
Coding space-time stimulus dynamics in auditory brain maps
Directory of Open Access Journals (Sweden)
Yunyan eWang
2014-04-01
Full Text Available Sensory maps are often distorted representations of the environment, where ethologically-important ranges are magnified. The implication of a biased representation extends beyond increased acuity for having more neurons dedicated to a certain range. Because neurons are functionally interconnected, non-uniform representations influence the processing of high-order features that rely on comparison across areas of the map. Among these features are time-dependent changes of the auditory scene generated by moving objects. How sensory representation affects high order processing can be approached in the map of auditory space of the owl’s midbrain, where locations in the front are over-represented. In this map, neurons are selective not only to location but also to location over time. The tuning to space over time leads to direction selectivity, which is also topographically organized. Across the population, neurons tuned to peripheral space are more selective to sounds moving into the front. The distribution of direction selectivity can be explained by spatial and temporal integration on the non-uniform map of space. Thus, the representation of space can induce biased computation of a second-order stimulus feature. This phenomenon is likely observed in other sensory maps and may be relevant for behavior.
Unitary group representations in Fock spaces with generalized exchange properties
International Nuclear Information System (INIS)
Liguori, A.
1994-09-01
The notion of second R-quantization is investigated, - a suitable deformation of the standard second quantization which properly takes into account the non-trivial exchange properties characterizing generalized statistics. The R-quantization of a class of unitary one-particle representations relevant for the description of symmetries is also performed. The Euclidean covariance of anyons is analyzed in this context. (author). 11 refs
Limits on nonlocal correlations from the structure of the local state space
International Nuclear Information System (INIS)
Janotta, Peter; Gogolin, Christian; Barrett, Jonathan; Brunner, Nicolas
2011-01-01
The outcomes of measurements on entangled quantum systems can be nonlocally correlated. However, while it is easy to write down toy theories allowing arbitrary nonlocal correlations, those allowed in quantum mechanics are limited. Quantum correlations cannot, for example, violate a principle known as macroscopic locality, which implies that they cannot violate Tsirelson's bound. This paper shows that there is a connection between the strength of nonlocal correlations in a physical theory and the structure of the state spaces of individual systems. This is illustrated by a family of models in which local state spaces are regular polygons, where a natural analogue of a maximally entangled state of two systems exists. We characterize the nonlocal correlations obtainable from such states. The family allows us to study the transition between classical, quantum and super-quantum correlations by varying only the local state space. We show that the strength of nonlocal correlations - in particular whether the maximally entangled state violates Tsirelson's bound or not-depends crucially on a simple geometric property of the local state space, known as strong self-duality. This result is seen to be a special case of a general theorem, which states that a broad class of entangled states in probabilistic theories-including, by extension, all bipartite classical and quantum states-cannot violate macroscopic locality. Finally, our results show that models exist that are locally almost indistinguishable from quantum mechanics, but can nevertheless generate maximally nonlocal correlations.
Global Linear Representations of Nonlinear Systems and the Adjoint Map
Banks, S.P.
1988-01-01
In this paper we shall study the global linearization of nonlinear systems on a manifold by two methods. The first consists of an expansion of the vector field in the space of square integrable vector fields. In the second method we use the adjoint representation of the Lie algebra vector fields to obtain an infinite-dimensional matrix representation of the system. A connection between the two approaches will be developed.
State-Space Modelling of Loudspeakers using Fractional Derivatives
DEFF Research Database (Denmark)
King, Alexander Weider; Agerkvist, Finn T.
2015-01-01
This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response of a fractio......This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response...... of a fractional harmonic oscillator, representing the mechanical part of a loudspeaker, showing the effect of the fractional derivative and its relationship to viscoelasticity. Finally, a loudspeaker model with a fractional order viscoelastic suspension and fractional order voice coil is fit to measurement data...
Two problems from the theory of semiotic control models. I. Representations of semiotic models
Energy Technology Data Exchange (ETDEWEB)
Osipov, G S
1981-11-01
Two problems from the theory of semiotic control models are being stated, in particular the representation of models and the semantic analysis of themtheory of semiotic control models are being stated, in particular the representation of models and the semantic analysis of them. Algebraic representation of semiotic models, covering of representations, their reduction and equivalence are discussed. The interrelations between functional and structural characteristics of semiotic models are investigated. 20 references.
Caspar Wessel. On the Analytical Representation of Direction
DEFF Research Database (Denmark)
This book contains the first complete English translation of Caspar Wessel's paper from 1797 "On the Analytical Representation of Direction". The paper has become famous because it gives the first geometric interpretation of the complex numbers. As the complete translation will show, it is also...... remarkable for the analytical representation of directions (vectors) in space and the elegant analytic solution of plane and spherical polygons. Wessel's essay is prefaced by two historical papers on the person Caspar Wessel and his work. They shed much new light on this first important Norwegian...
Path integral representations on the complex sphere
Energy Technology Data Exchange (ETDEWEB)
Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2007-08-15
In this paper we discuss the path integral representations for the coordinate systems on the complex sphere S{sub 3C}. The Schroedinger equation, respectively the path integral, separates in exactly 21 orthogonal coordinate systems. We enumerate these coordinate systems and we are able to present the path integral representations explicitly in the majority of the cases. In each solution the expansion into the wave-functions is stated. Also, the kernel and the corresponding Green function can be stated in closed form in terms of the invariant distance on the sphere, respectively on the hyperboloid. (orig.)
Parent Trigger Policies, Representation, and the Public Good
Allen, Ann; Saultz, Andrew
2015-01-01
Using theories of representation and democratic education, this article examines the impetus of parent trigger policies in the United States and their potential effects on public good goals for public education. The article also uses theories of representation and responsible democratic governance to assess the parent trigger policies, or what are…
International Nuclear Information System (INIS)
Gessner, W.; Ernst, V.
1980-01-01
The indefinite metric space O/sub M/ of the covariant form of the quantized Maxwell field M is analyzed in some detail. S/sub M/ contains not only the pre-Hilbert space X 0 of states of transverse photons which occurs in the Gupta--Bleuler formalism of the free M, but a whole rosette of continuously many, isomorphic, complete, pre-Hilbert spaces L/sup q/ disjunct up to the zero element o of S/sub M/. The L/sup q/ are the maximal subspaces of S/sub M/ which allow the usual statistical interpretation. Each L/sup q/ corresponds uniquely to one square integrable, spatial distribution j/sup o/(x) of the total charge Q=0. If M is in any state from L/sup q/, the bare charge j 0 (x) appears to be inseparably dressed by the quantum equivalent of its proper, classical Coulomb field E(x). The vacuum occurs only in the state space L 0 of the free Maxwell field. Each L/sup q/ contains a secondary rosette of continuously many, up to o disjunct, isomorphic Hilbert spaces H/sub g//sup q/ related to different electromagnetic gauges. The space H/sub o//sup q/, which corresponds to the Coulomb gauge within the Lorentz gauge, plays a physically distinguished role in that only it leads to the usual concept of energy. If M is in any state from H/sub g//sup q/, the bare 4-current j 0 (x), j(x), where j(x) is any square integrable, transverse current density in space, is endowed with its proper 4-potential which depends on the chosen gauge, and with its proper, gauge independent, Coulomb--Oersted field E(x), B(x). However, these fields exist only in the sense of quantum mechanical expectation values equipped with the corresponding field fluctuations. So they are basically different from classical electromagnetic fields
Formulating state space models in R with focus on longitudinal regression models
DEFF Research Database (Denmark)
Dethlefsen, Claus; Lundbye-Christensen, Søren
2006-01-01
We provide a language for formulating a range of state space models with response densities within the exponential family. The described methodology is implemented in the R-package sspir. A state space model is specified similarly to a generalized linear model in R, and then the time-varying terms...
An application of gain-scheduled control using state-space interpolation to hydroactive gas bearings
DEFF Research Database (Denmark)
Theisen, Lukas Roy Svane; Camino, Juan F.; Niemann, Hans Henrik
2016-01-01
with a gain-scheduling strategy using state-space interpolation, which avoids both the performance loss and the increase of controller order associated to the Youla parametrisation. The proposed state-space interpolation for gain-scheduling is applied for mass imbalance rejection for a controllable gas...... bearing scheduled in two parameters. Comparisons against the Youla-based scheduling demonstrate the superiority of the state-space interpolation....
Reference Frame Fields based on Quantum Theory Representations of Real and Complex Numbers
Benioff, Paul
2007-01-01
A quantum theory representations of real (R) and complex (C) numbers is given that is based on states of single, finite strings of qukits for any base k > 1. Both unary representations and the possibility that qukits with k a prime number are elementary and the rest composite are discussed. Cauchy sequences of qukit string states are defined from the arithmetic properties. The representations of R and C, as equivalence classes of these sequences, differ from classical kit string state represe...
Visions and Representations of the Urban Transformation of Buga (Colombia, 1900-1937
Directory of Open Access Journals (Sweden)
Héctor Manuel Cuevas Arenas
2016-07-01
Full Text Available This article offers an interpretation of the representations that make the elites in the Buga City (Colombia regarding the process of transformation in its urban setting in the early twentieth century. This problem is addressed to investigate modernization, changes and receptions within the elites of this locality. This paper investigates the valuations made regarding betterment of space through the modernization of the city and improvement of its inhabitants in the moral, cultural and hygienic. To explore these research problems were used concepts as Bourdieu´s "symbolic capital", the Moscovici´s definition of "social representation" and contributions of authors like Geertz, Chartier, Kingman and others. Urban change in the press and the minutes of the City Council was explored as spaces of expectations and experiences that stimulated speeches, debates and representations. This work relativized the opposition between the modern and the traditional in the locality, because the representations realized the ability of elites to involve the universal with their specific needs of social distinction, creation of civility and morality, as well as the creation of identity referents.
Implicit geometric representations for optimal design of gas turbine blades
International Nuclear Information System (INIS)
Mansour, T.; Ghaly, W.
2004-01-01
Shape optimization requires a proper geometric representation of the blade profile; the parameters of such a representation are usually taken as design variables in the optimization process. This implies that the model must possess three specific features: flexibility, efficiency, and accuracy. For the specific task of aerodynamic optimization for turbine blades, it is critical to have flexibility in both the global and local design spaces in order to obtain a successful optimization. This work is concerned with the development of two geometric representations of turbine blade profiles that are appropriate for aerodynamic optimization: the Modified Rapid Axial Turbine Design (MRATD) model where the blade is represented by five low-order curves that satisfy eleven designer parameters; this model is suitable for a global search of the design space. The second model is NURBS parameterization of the blade profile that can be used for a local refinement. The two models are presented and are assessed for flexibility and accuracy when representing several typical turbine blade profiles. The models will be further discussed in terms of curve smoothness and blade shape representation with a multi-NURBS curve versus one curve and its effect on the flow field, in particular the pressure distribution along the blade surfaces, will be elaborated. (author)
Space-time complexity in solid state models
International Nuclear Information System (INIS)
Bishop, A.R.
1985-01-01
In this Workshop on symmetry-breaking it is appropriate to include the evolving fields of nonlinear-nonequilibrium systems in which transitions to and between various degrees of ''complexity'' (including ''chaos'') occur in time or space or both. These notions naturally bring together phenomena of pattern formation and chaos and therefore have ramifications for a huge array of natural sciences - astrophysics, plasmas and lasers, hydrodynamics, field theory, materials and solid state theory, optics and electronics, biology, pattern recognition and evolution, etc. Our particular concerns here are with examples from solid state and condensed matter
Solution of the nonrelativistic wave equation using the tridiagonal representation approach
Alhaidari, A. D.
2017-07-01
We choose a complete set of square integrable functions as a basis for the expansion of the wavefunction in configuration space such that the matrix representation of the nonrelativistic time-independent linear wave operator is tridiagonal and symmetric. Consequently, the matrix wave equation becomes a symmetric three-term recursion relation for the expansion coefficients of the wavefunction. The recursion relation is then solved exactly in terms of orthogonal polynomials in the energy. Some of these polynomials are not found in the mathematics literature. The asymptotics of these polynomials give the phase shift for the continuous energy scattering states and the spectrum for the discrete energy bound states. Depending on the space and boundary conditions, the basis functions are written in terms of either the Laguerre or Jacobi polynomials. The tridiagonal requirement limits the number of potential functions that yield exact solutions of the wave equation. Nonetheless, the class of exactly solvable problems in this approach is larger than the conventional class (see, for example, Table XII in the text). We also give very accurate results for cases where the wave operator matrix is not tridiagonal but its elements could be evaluated either exactly or numerically with high precision.
Abelian faces of state spaces of C*-algebras
International Nuclear Information System (INIS)
Batty, C.J.K.
1980-01-01
Let F be a closed face of the weak* compact convex state space of a unital C*-algebra A. The class of F-abelian states, introduced earlier by the author, is studied further. It is shown (without any restriction on A or F) that F is a Choquet simplex if and only if every state in F is F-abelian, and that it is sufficient for this that every pure state in F is F-abelian. As a corollary, it is deduced that an arbitrary C*-dynamical system (A,G,α) is G-abelian if and only if every ergodic state is weakly clustering. Nevertheless the set of all F-abelian (or even G-abelian) states is not necessarily weak* compact. (orig.)
General regression and representation model for classification.
Directory of Open Access Journals (Sweden)
Jianjun Qian
Full Text Available Recently, the regularized coding-based classification methods (e.g. SRC and CRC show a great potential for pattern classification. However, most existing coding methods assume that the representation residuals are uncorrelated. In real-world applications, this assumption does not hold. In this paper, we take account of the correlations of the representation residuals and develop a general regression and representation model (GRR for classification. GRR not only has advantages of CRC, but also takes full use of the prior information (e.g. the correlations between representation residuals and representation coefficients and the specific information (weight matrix of image pixels to enhance the classification performance. GRR uses the generalized Tikhonov regularization and K Nearest Neighbors to learn the prior information from the training data. Meanwhile, the specific information is obtained by using an iterative algorithm to update the feature (or image pixel weights of the test sample. With the proposed model as a platform, we design two classifiers: basic general regression and representation classifier (B-GRR and robust general regression and representation classifier (R-GRR. The experimental results demonstrate the performance advantages of proposed methods over state-of-the-art algorithms.
Directory of Open Access Journals (Sweden)
Daniel Durstewitz
2017-06-01
Full Text Available The computational and cognitive properties of neural systems are often thought to be implemented in terms of their (stochastic network dynamics. Hence, recovering the system dynamics from experimentally observed neuronal time series, like multiple single-unit recordings or neuroimaging data, is an important step toward understanding its computations. Ideally, one would not only seek a (lower-dimensional state space representation of the dynamics, but would wish to have access to its statistical properties and their generative equations for in-depth analysis. Recurrent neural networks (RNNs are a computationally powerful and dynamically universal formal framework which has been extensively studied from both the computational and the dynamical systems perspective. Here we develop a semi-analytical maximum-likelihood estimation scheme for piecewise-linear RNNs (PLRNNs within the statistical framework of state space models, which accounts for noise in both the underlying latent dynamics and the observation process. The Expectation-Maximization algorithm is used to infer the latent state distribution, through a global Laplace approximation, and the PLRNN parameters iteratively. After validating the procedure on toy examples, and using inference through particle filters for comparison, the approach is applied to multiple single-unit recordings from the rodent anterior cingulate cortex (ACC obtained during performance of a classical working memory task, delayed alternation. Models estimated from kernel-smoothed spike time data were able to capture the essential computational dynamics underlying task performance, including stimulus-selective delay activity. The estimated models were rarely multi-stable, however, but rather were tuned to exhibit slow dynamics in the vicinity of a bifurcation point. In summary, the present work advances a semi-analytical (thus reasonably fast maximum-likelihood estimation framework for PLRNNs that may enable to recover
Directory of Open Access Journals (Sweden)
Aksjonov Andrei
2015-12-01
Full Text Available The mathematical model of the three-dimensional crane using the Euler-Lagrange approach is derived. A state-space representation of the derived model is proposed and explored in the Simulink® environment and on the laboratory stand. The obtained control design was simulated, analyzed and compared with existing encoder-based system provided by the three-dimensional (3D Crane manufacturer Inteco®. As well, an anti-swing fuzzy logic control has been developed, simulated, and analyzed. Obtained control algorithm is compared with the existing anti-swing proportional-integral controller designed by the 3D crane manufacturer Inteco®. 5-degree of freedom (5DOF control schemes are designed, examined and compared with the various load masses. The topicality of the problem is due to the wide usage of gantry cranes in industry. The solution is proposed for the future research in sensorless and intelligent control of complex motor driven application.
Sum-over-histories representation for the causal Green function of free scalar field theory
International Nuclear Information System (INIS)
Rudolph, O.
1993-10-01
A set of Green functions G α (x-y), α element of [0, 2π], for free scalar field theory is introduced, varying between the Hadamard Green function Δ 1 (x-y) triple bond 0vertical stroke {φ(x), φ(y)}vertical stroke 0> and the causal Green function G π (x-y)=iΔ(x-y) triple bond [φ(x), φ(y)]. For every α element of [0, 2π] a path-integral representation for G α is obtained both in the configuration space and in the phase space of the classical relativistic particle. Especially setting α=π a sum-over-histories representation for the causal Green function is obtained. Furthermore using BRST theory an alternative path-integral representation for G α is presented. From these path integral representations the composition laws for the G α 's are derived using a modified path decomposition expansion. (orig.)
Three-dimensional image capturing and representation for multimedia ambiance communication
Ichikawa, Tadashi; Iwasawa, Shoichiro; Yamada, Kunio; Kanamaru, Toshifumi; Naemura, Takeshi; Aizawa, Kiyoharu; Morishima, Shigeo; Saito, Takahiro
2001-02-01
Multimedia Ambiance Communication is as a means of achieving shared-space communication in an immersive environment consisting of an arch-type stereoscopic projection display. Our goal is to enable shared-space communication by creating a photo-realistic three-dimensional (3D) image space that users can feel a part of. The concept of a layered structure defined for painting, such as long-range, mid-range, and short-range views, can be applied to a 3D image space. New techniques, such as two-plane expression, high quality panorama image generation and setting representation for image processing, 3D image representation and generation for photo- realistic 3D image space have been developed. Also, we propose a life-like avatar within the 3D image space. To obtain the characteristics of user's body, a human subject is scanned using a CyberwareTM whole body scanner. The output from the scanner, a range image, is a good start for modeling the avatar's geometric shape. A generic human surface model is fitted to the range image. The obtained model is topologically equivalent even if our method is applied to another subject. If a generic model with motion definitions is employed, and common motion rules can be applied to all models made from the generic model.
Approximate representation of optimal strategies from influence diagrams
DEFF Research Database (Denmark)
Jensen, Finn V.
2008-01-01
, and where the policy functions for the decisions have so large do- mains that they cannot be represented directly in a strategy tree. The approach is to have separate ID representations for each decision variable. In each representation the actual information is fully exploited, however the representation...... of policies for future decisions are approximations. We call the approximation information abstraction. It consists in introducing a dummy structure connecting the past with the decision. We study how to specify, implement and learn information abstraction.......There are three phases in the life of a decision problem, specification, solution, and rep- resentation of solution. The specification and solution phases are off-line, while the rep- resention of solution often shall serve an on-line situation with rather tough constraints on time and space. One...
Directory of Open Access Journals (Sweden)
Carlos Alberto de Oliveira Magalhães Júnior
2012-05-01
Full Text Available The Perobas Biological Reserve is situated in the Brazilian municipalities of Tuneiras do Oeste and Cianorte, State of Paraná. Prior to the foundation, the local and state communities’ representatives manifested different standpoints, favorable and unfavorable, concerning the establishment of this environmental protection area. Considering the importance of comprehending social representations that students from the City of Tuneiras do Oeste have concerning the Perobas Biological Reserve, the present study aimed at investigating Basic Education students, as well as indicating ways for an environmental education development. We used the Free Evocation of Words technique and the analysis of composition contents. We identified that representations of the analyzed group are based on the Nature components present in the Reserve and on the role of the local inhabitants for their conservation, however such knowledge is not well-founded. We understand that educative actions must be initiated in order to proportionate the construction of knowledge concerning the Reserve´s Nature components and the mutual interactions involved. This knowledge can, subsequently, lead students to comprehend that a role is ascribed to them in the protection and the co-responsibility for the preservation of the protected area.
Schermerhorn, Alice C; Cummings, E Mark; Davies, Patrick T
2008-02-01
The authors examine mutual family influence processes at the level of children's representations of multiple family relationships, as well as the structure of those representations. From a community sample with 3 waves, each spaced 1 year apart, kindergarten-age children (105 boys and 127 girls) completed a story-stem completion task, tapping representations of multiple family relationships. Structural equation modeling with autoregressive controls indicated that representational processes involving different family relationships were interrelated over time, including links between children's representations of marital conflict and reactions to conflict, between representations of security about marital conflict and parent-child relationships, and between representations of security in father-child and mother-child relationships. Mixed support was found for notions of increasing stability in representations during this developmental period. Results are discussed in terms of notions of transactional family dynamics, including family-wide perspectives on mutual influence processes attributable to multiple family relationships.
Coherent states for FLRW space-times in loop quantum gravity
International Nuclear Information System (INIS)
Magliaro, Elena; Perini, Claudio; Marciano, Antonino
2011-01-01
We construct a class of coherent spin-network states that capture properties of curved space-times of the Friedmann-Lamaitre-Robertson-Walker type on which they are peaked. The data coded by a coherent state are associated to a cellular decomposition of a spatial (t=const) section with a dual graph given by the complete five-vertex graph, though the construction can be easily generalized to other graphs. The labels of coherent states are complex SL(2,C) variables, one for each link of the graph, and are computed through a smearing process starting from a continuum extrinsic and intrinsic geometry of the canonical surface. The construction covers both Euclidean and Lorentzian signatures; in the Euclidean case and in the limit of flat space we reproduce the simplicial 4-simplex semiclassical states used in spin foams.
The Wigner distribution function for squeezed vacuum superposed state
International Nuclear Information System (INIS)
Zayed, E.M.E.; Daoud, A.S.; AL-Laithy, M.A.; Naseem, E.N.
2005-01-01
In this paper, we construct the Wigner distribution function for a single-mode squeezed vacuum mixed-state which is a superposition of the squeezed vacuum state. This state is defined as a P-representation for the density operator. The obtained Wigner function depends, beside the phase-space variables, on the mean number of photons occupied by the coherent state of the mode. This mean number relates to the mean free path through a given relation, which enables us to measure this number experimentally by measuring the mean free path
Spacetime representation of topological phononics
Deymier, Pierre A.; Runge, Keith; Lucas, Pierre; Vasseur, Jérôme O.
2018-05-01
Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein–Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.
Hybrid Histogram Descriptor: A Fusion Feature Representation for Image Retrieval.
Feng, Qinghe; Hao, Qiaohong; Chen, Yuqi; Yi, Yugen; Wei, Ying; Dai, Jiangyan
2018-06-15
Currently, visual sensors are becoming increasingly affordable and fashionable, acceleratingly the increasing number of image data. Image retrieval has attracted increasing interest due to space exploration, industrial, and biomedical applications. Nevertheless, designing effective feature representation is acknowledged as a hard yet fundamental issue. This paper presents a fusion feature representation called a hybrid histogram descriptor (HHD) for image retrieval. The proposed descriptor comprises two histograms jointly: a perceptually uniform histogram which is extracted by exploiting the color and edge orientation information in perceptually uniform regions; and a motif co-occurrence histogram which is acquired by calculating the probability of a pair of motif patterns. To evaluate the performance, we benchmarked the proposed descriptor on RSSCN7, AID, Outex-00013, Outex-00014 and ETHZ-53 datasets. Experimental results suggest that the proposed descriptor is more effective and robust than ten recent fusion-based descriptors under the content-based image retrieval framework. The computational complexity was also analyzed to give an in-depth evaluation. Furthermore, compared with the state-of-the-art convolutional neural network (CNN)-based descriptors, the proposed descriptor also achieves comparable performance, but does not require any training process.
Invariant subspaces in some function spaces on symmetric spaces. II
International Nuclear Information System (INIS)
Platonov, S S
1998-01-01
Let G be a semisimple connected Lie group with finite centre, K a maximal compact subgroup of G, and M=G/K a Riemannian symmetric space of non-compact type. We study the problem of describing the structure of closed linear subspaces in various function spaces on M that are invariant under the quasiregular representation of the group G. We consider the case when M is a symplectic symmetric space of rank 1
An elementary aspect of the Weyl-Wigner representation
DEFF Research Database (Denmark)
Dahl, Jens Peder; Schleich, W.P.
2003-01-01
It is an elementary aspect of the Weyl-Wigner representation of quantum mechanics that the dynamical phase-space function corresponding to the square of a quantum-mechanical operator is, in general, different from the square of the function representing the operator itself. We call attention...
Thinking Egyptian: Active Models for Understanding Spatial Representation.
Schiferl, Ellen
This paper highlights how introductory textbooks on Egyptian art inhibit understanding by reinforcing student preconceptions, and demonstrates another approach to discussing space with a classroom exercise and software. The alternative approach, an active model for spatial representation, introduced here was developed by adapting classroom…
Classical representations for quantum-like systems through an axiomatics for context dependence
International Nuclear Information System (INIS)
Coecke, B.
1997-01-01
We introduce a definition for a 'hidden measurement system', i.e., a physical entity for which there exist: (i) 'a set of non-contextual states of the entity under study' and (ii) 'a set of states of the measurement context', and which are such that all uncertainties are due to a lack of knowledge on the actual state of the measurement context. First we identify an explicit criterion that enables us to verify whether a given hidden measurement system is a representation of a given couple Σ, ε consisting of a set of states Σ and a set of measurements ε (= measurement system). Then we prove for every measurement system that there exists at least one representation as a hidden measurement system with [0, 1] as set of states of the measurement context. Thus, we can apply this definition of a hidden measurement system to impose an axiomatics for context dependence. We show that in this way we always find classical representations (hidden measurement representations) for general non-classical entities (e.g. quantum entities). (orig.)
Weighted Discriminative Dictionary Learning based on Low-rank Representation
International Nuclear Information System (INIS)
Chang, Heyou; Zheng, Hao
2017-01-01
Low-rank representation has been widely used in the field of pattern classification, especially when both training and testing images are corrupted with large noise. Dictionary plays an important role in low-rank representation. With respect to the semantic dictionary, the optimal representation matrix should be block-diagonal. However, traditional low-rank representation based dictionary learning methods cannot effectively exploit the discriminative information between data and dictionary. To address this problem, this paper proposed weighted discriminative dictionary learning based on low-rank representation, where a weighted representation regularization term is constructed. The regularization associates label information of both training samples and dictionary atoms, and encourages to generate a discriminative representation with class-wise block-diagonal structure, which can further improve the classification performance where both training and testing images are corrupted with large noise. Experimental results demonstrate advantages of the proposed method over the state-of-the-art methods. (paper)
Representation properties, Racah sum rule, and Biedenharn - Elliott identity for Uq(osp(1|2))
International Nuclear Information System (INIS)
Minnaert, P.; Mozrzymas, M.
1998-01-01
It is shown that the universal R matrix in the tensor product of two irreducible representation spaces of the quantum superalgebra U q (osp(1|2)) can be expressed by Clebsch - Gordan coefficients. The Racah sum rule satisfied by U q (osp(1|2)) Racah coefficients and 6-j symbols is derived from the properties of the universal R matrix in the tensor product of three representation spaces. Considering the tensor product of four irreducible representations, it is shown that Biedenharn - Elliott identity holds for U q (osp(1|2)) Racah coefficients and 6-j symbols. A recursion relation for U q (osp(1|2)) 6-j symbols is derived from the Biedenharn endash Elliott identity. copyright 1998 American Institute of Physics
Kraus representation of a damped harmonic oscillator and its application
International Nuclear Information System (INIS)
Liu Yuxi; Oezdemir, Sahin K.; Miranowicz, Adam; Imoto, Nobuyuki
2004-01-01
By definition, the Kraus representation of a harmonic oscillator suffering from the environment effect, modeled as the amplitude damping or the phase damping, is directly given by a simple operator algebra solution. As examples and applications, we first give a Kraus representation of a single qubit whose computational basis states are defined as bosonic vacuum and single particle number states. We further discuss the environment effect on qubits whose computational basis states are defined as the bosonic odd and even coherent states. The environment effects on entangled qubits defined by two different kinds of computational basis are compared with the use of fidelity
Filtering and smoothing of stae vector for diffuse state space models
Koopman, S.J.; Durbin, J.
2003-01-01
This paper presents exact recursions for calculating the mean and mean square error matrix of the state vector given the observations for the multi-variate linear Gaussian state-space model in the case where the initial state vector is (partially) diffuse.
International Nuclear Information System (INIS)
Wu Chunfeng; Chen Jingling; Oh, C.H.; Kwek, L.C.; Xue Kang
2005-01-01
We construct an explicit Wigner function for the N-mode squeezed state. Based on a previous observation that the Wigner function describes correlations in the joint measurement of the phase-space displaced parity operator, we investigate the nonlocality of the multipartite entangled state by the violation of the Zukowski-Brukner N-qubit Bell inequality. We find that quantum predictions for such a squeezed state violate these inequalities by an amount that grows with the number N
International Nuclear Information System (INIS)
Koronovskij, A.A.; Rempen, I.S.; Khramov, A.E.
2003-01-01
The set of the unstable periodic space-time states, characterizing the chaotic space-time dynamics of the electron beam with the supercritical current in the Pierce diode is discussed. The Lyapunov indicators of the revealed instable space-time states of the chaotic dynamics of the distributed self-excited system are calculated. It is shown that change in the set of the unstable periodic states in dependence on the Pierce parameter is determined by change in the various orbits stability, which is demonstrated by the values of senior Lyapunov unstable state index [ru
On the problem of representability and the Bogolyubov-Hartree-Fock theory
Energy Technology Data Exchange (ETDEWEB)
Knoerr, Hans Konrad
2013-11-22
The general topic of this thesis is an approximation of the ground state energy for many-particle quantum systems. In particular the Bogolyubov-Hartree-Fock theory and the representability of one- and two-particle density matrices are studied. After an introductory chapter we specify some basic notation of many-body quantum mechanics in Chapter 2. In Chapter 3 we consider boson, as well as fermion systems. We first tackle the question of representability for bosons, i.e., the question which conditions a one- and a two-particle operator must satisfy to ensure that they are the one- and the two-particle density matrix of a state. For a particle number-conserving system, the representability conditions up to second order for bosons are well-known and called admissibility, P-, and G-conditions. Since, however, most physical systems consisting of bosons are not particle number-conserving, we give an alternative for such systems: Generalizing the two-particle density matrix, we observe that the representability conditions up to second order hold if and only if this generalized two-particle density matrix is positive semi-definite and the one- and the two-particle density matrices fulfill trace class and symmetry conditions. Moreover, we study the Bogolyubov-Hartree-Fock energy of boson and fermion systems. We generalize Lieb's variational principle which in its original formulation holds for purely repulsive particle interactions for fermions only. Our second main result is the following: for bosons, as well as for fermions the infimum of the energy for a variation over pure quasifree states coincides with the one for a variation over all quasifree states under the assumption that the Hamiltonian is bounded below. In the last section of Chapter 3 we specify the relation between centered quasifree states and their corresponding generalized one-particle density matrix, which finds an application in the variational process in the Bogolyubov-Hartree-Fock theory. It is
On the problem of representability and the Bogolyubov-Hartree-Fock theory
International Nuclear Information System (INIS)
Knoerr, Hans Konrad
2013-01-01
The general topic of this thesis is an approximation of the ground state energy for many-particle quantum systems. In particular the Bogolyubov-Hartree-Fock theory and the representability of one- and two-particle density matrices are studied. After an introductory chapter we specify some basic notation of many-body quantum mechanics in Chapter 2. In Chapter 3 we consider boson, as well as fermion systems. We first tackle the question of representability for bosons, i.e., the question which conditions a one- and a two-particle operator must satisfy to ensure that they are the one- and the two-particle density matrix of a state. For a particle number-conserving system, the representability conditions up to second order for bosons are well-known and called admissibility, P-, and G-conditions. Since, however, most physical systems consisting of bosons are not particle number-conserving, we give an alternative for such systems: Generalizing the two-particle density matrix, we observe that the representability conditions up to second order hold if and only if this generalized two-particle density matrix is positive semi-definite and the one- and the two-particle density matrices fulfill trace class and symmetry conditions. Moreover, we study the Bogolyubov-Hartree-Fock energy of boson and fermion systems. We generalize Lieb's variational principle which in its original formulation holds for purely repulsive particle interactions for fermions only. Our second main result is the following: for bosons, as well as for fermions the infimum of the energy for a variation over pure quasifree states coincides with the one for a variation over all quasifree states under the assumption that the Hamiltonian is bounded below. In the last section of Chapter 3 we specify the relation between centered quasifree states and their corresponding generalized one-particle density matrix, which finds an application in the variational process in the Bogolyubov-Hartree-Fock theory. It is
Relan, Rishi; Tiels, Koen; Marconato, Anna; Dreesen, Philippe; Schoukens, Johan
2018-05-01
Many real world systems exhibit a quasi linear or weakly nonlinear behavior during normal operation, and a hard saturation effect for high peaks of the input signal. In this paper, a methodology to identify a parsimonious discrete-time nonlinear state space model (NLSS) for the nonlinear dynamical system with relatively short data record is proposed. The capability of the NLSS model structure is demonstrated by introducing two different initialisation schemes, one of them using multivariate polynomials. In addition, a method using first-order information of the multivariate polynomials and tensor decomposition is employed to obtain the parsimonious decoupled representation of the set of multivariate real polynomials estimated during the identification of NLSS model. Finally, the experimental verification of the model structure is done on the cascaded water-benchmark identification problem.
A unified development of several techniques for the representation of random vectors and data sets
Bundick, W. T.
1973-01-01
Linear vector space theory is used to develop a general representation of a set of data vectors or random vectors by linear combinations of orthonormal vectors such that the mean squared error of the representation is minimized. The orthonormal vectors are shown to be the eigenvectors of an operator. The general representation is applied to several specific problems involving the use of the Karhunen-Loeve expansion, principal component analysis, and empirical orthogonal functions; and the common properties of these representations are developed.
Directory of Open Access Journals (Sweden)
Mohammed Daoud
2018-04-01
Full Text Available A relation is established in the present paper between Dicke states in a d-dimensional space and vectors in the representation space of a generalized Weyl–Heisenberg algebra of finite dimension d. This provides a natural way to deal with the separable and entangled states of a system of N = d − 1 symmetric qubit states. Using the decomposition property of Dicke states, it is shown that the separable states coincide with the Perelomov coherent states associated with the generalized Weyl–Heisenberg algebra considered in this paper. In the so-called Majorana scheme, the qudit (d-level states are represented by N points on the Bloch sphere; roughly speaking, it can be said that a qudit (in a d-dimensional space is describable by a N-qubit vector (in a N-dimensional space. In such a scheme, the permanent of the matrix describing the overlap between the N qubits makes it possible to measure the entanglement between the N qubits forming the qudit. This is confirmed by a Fubini–Study metric analysis. A new parameter, proportional to the permanent and called perma-concurrence, is introduced for characterizing the entanglement of a symmetric qudit arising from N qubits. For d = 3 ( ⇔ N = 2 , this parameter constitutes an alternative to the concurrence for two qubits. Other examples are given for d = 4 and 5. A connection between Majorana stars and zeros of a Bargmmann function for qudits closes this article.
Secondary structure classification of amino-acid sequences using state-space modeling
Brunnert, Marcus; Krahnke, Tillmann; Urfer, Wolfgang
2001-01-01
The secondary structure classification of amino acid sequences can be carried out by a statistical analysis of sequence and structure data using state-space models. Aiming at this classification, a modified filter algorithm programmed in S is applied to data of three proteins. The application leads to correct classifications of two proteins even when using relatively simple estimation methods for the parameters of the state-space models. Furthermore, it has been shown that the assumed initial...
State-Space Geometry, Statistical Fluctuations, and Black Holes in String Theory
Directory of Open Access Journals (Sweden)
Stefano Bellucci
2014-01-01
Full Text Available We study the state-space geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a state-space perspective to the black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic geometric meaning of the statistical fluctuations, local and global stability conditions, and long range statistical correlations. We provide a set of physical motivations pertaining to the extremal and nonextremal black holes, namely, the meaning of the chemical geometry and physics of correlation. We illustrate the state-space configurations for general charge extremal black holes. In sequel, we extend our analysis for various possible charge and anticharge nonextremal black holes. From the perspective of statistical fluctuation theory, we offer general remarks, future directions, and open issues towards the intrinsic geometric understanding of the vacuum fluctuations and black holes in string theory.
Phase-space quantum control; Quantenkontrolle im Zeit-Frequenz-Phasenraum
Energy Technology Data Exchange (ETDEWEB)
Fechner, Susanne
2008-08-06
The von Neumann-representation introduced in this thesis describes each laser pulse in a one-to-one manner as a sum of bandwidth-limited, Gaussian laser pulses centered around different points in phase space. These pulses can be regarded as elementary building blocks from which every single laser pulse can be constructed. The von Neumann-representation combines different useful properties for applications in quantum control. First, it is a one-to-one map between the degrees of freedom of the pulse shaper and the phase-space representation of the corresponding shaped laser pulse. In other words: Every possible choice of pulse shaper parameters corresponds to exactly one von Neumann-representation and vice versa. Moreover, since temporal and spectral structures become immediately sizable, the von Neumann-representation, as well as the Husimi- or the Wigner-representations, allows for an intuitive interpretation of the represented laser pulse. (orig.)
Unbounded representations of symmetry groups in gauge quantum field theory. II. Integration
International Nuclear Information System (INIS)
Voelkel, A.H.
1986-01-01
Within the gauge quantum field theory of the Wightman--Garding type, the integration of representations of Lie algebras is investigated. By means of the covariance condition (substitution rules) for the basic fields, it is shown that a form skew-symmetric representation of a Lie algebra can be integrated to a form isometric and in general unbounded representation of the universal covering group of a corresponding Lie group provided the conditions (Nelson, Sternheimer, etc.), which are well known for the case of Hilbert or Banach representations, hold. If a form isometric representation leaves the subspace from which the physical Hilbert space is obtained via factorization and completion invariant, then the same is proved to be true for its differential. Conversely, a necessary and sufficient condition is derived for the transmission of the invariance of this subspace under a form skew-symmetric representation of a Lie algebra to its integral
A Markovian state-space framework for integrating flexibility into space system design decisions
Lafleur, Jarret M.
The past decades have seen the state of the art in aerospace system design progress from a scope of simple optimization to one including robustness, with the objective of permitting a single system to perform well even in off-nominal future environments. Integrating flexibility, or the capability to easily modify a system after it has been fielded in response to changing environments, into system design represents a further step forward. One challenge in accomplishing this rests in that the decision-maker must consider not only the present system design decision, but also sequential future design and operation decisions. Despite extensive interest in the topic, the state of the art in designing flexibility into aerospace systems, and particularly space systems, tends to be limited to analyses that are qualitative, deterministic, single-objective, and/or limited to consider a single future time period. To address these gaps, this thesis develops a stochastic, multi-objective, and multi-period framework for integrating flexibility into space system design decisions. Central to the framework are five steps. First, system configuration options are identified and costs of switching from one configuration to another are compiled into a cost transition matrix. Second, probabilities that demand on the system will transition from one mission to another are compiled into a mission demand Markov chain. Third, one performance matrix for each design objective is populated to describe how well the identified system configurations perform in each of the identified mission demand environments. The fourth step employs multi-period decision analysis techniques, including Markov decision processes from the field of operations research, to find efficient paths and policies a decision-maker may follow. The final step examines the implications of these paths and policies for the primary goal of informing initial system selection. Overall, this thesis unifies state-centric concepts of
International Nuclear Information System (INIS)
Paz, Juan Pablo; Roncaglia, Augusto Jose; Saraceno, Marcos
2005-01-01
We analyze and further develop a method to represent the quantum state of a system of n qubits in a phase-space grid of NxN points (where N=2 n ). The method, which was recently proposed by Wootters and co-workers (Gibbons et al., Phys. Rev. A 70, 062101 (2004).), is based on the use of the elements of the finite field GF(2 n ) to label the phase-space axes. We present a self-contained overview of the method, we give insights into some of its features, and we apply it to investigate problems which are of interest for quantum-information theory: We analyze the phase-space representation of stabilizer states and quantum error-correction codes and present a phase-space solution to the so-called mean king problem
Neural Representation. A Survey-Based Analysis of the Notion
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Oscar Vilarroya
2017-08-01
Full Text Available The word representation (as in “neural representation”, and many of its related terms, such as to represent, representational and the like, play a central explanatory role in neuroscience literature. For instance, in “place cell” literature, place cells are extensively associated with their role in “the representation of space.” In spite of its extended use, we still lack a clear, universal and widely accepted view on what it means for a nervous system to represent something, on what makes a neural activity a representation, and on what is re-presented. The lack of a theoretical foundation and definition of the notion has not hindered actual research. My aim here is to identify how active scientists use the notion of neural representation, and eventually to list a set of criteria, based on actual use, that can help in distinguishing between genuine or non-genuine neural-representation candidates. In order to attain this objective, I present first the results of a survey of authors within two domains, place-cell and multivariate pattern analysis (MVPA research. Based on the authors’ replies, and on a review of neuroscientific research, I outline a set of common properties that an account of neural representation seems to require. I then apply these properties to assess the use of the notion in two domains of the survey, place-cell and MVPA studies. I conclude by exploring a shift in the notion of representation suggested by recent literature.
A state space algorithm for the spectral factorization
Kraffer, F.; Kraffer, F.; Kwakernaak, H.
1997-01-01
This paper presents an algorithm for the spectral factorization of a para-Hermitian polynomial matrix. The algorithm is based on polynomial matrix to state space and vice versa conversions, and avoids elementary polynomial operations in computations; It relies on well-proven methods of numerical
International Nuclear Information System (INIS)
Oeckl, Robert
2012-01-01
We establish a precise isomorphism between the Schrödinger representation and the holomorphic representation in linear and affine field theory. In the linear case, this isomorphism is induced by a one-to-one correspondence between complex structures and Schrödinger vacua. In the affine case we obtain similar results, with the role of the vacuum now taken by a whole family of coherent states. In order to establish these results we exhibit a rigorous construction of the Schrödinger representation and use a suitable generalization of the Segal-Bargmann transform. Our construction is based on geometric quantization and applies to any real polarization and its pairing with any Kähler polarization.
Embedding a State Space Model Into a Markov Decision Process
DEFF Research Database (Denmark)
Nielsen, Lars Relund; Jørgensen, Erik; Højsgaard, Søren
2011-01-01
In agriculture Markov decision processes (MDPs) with finite state and action space are often used to model sequential decision making over time. For instance, states in the process represent possible levels of traits of the animal and transition probabilities are based on biological models...
Bayesian state space models for dynamic genetic network construction across multiple tissues.
Liang, Yulan; Kelemen, Arpad
2016-08-01
Construction of gene-gene interaction networks and potential pathways is a challenging and important problem in genomic research for complex diseases while estimating the dynamic changes of the temporal correlations and non-stationarity are the keys in this process. In this paper, we develop dynamic state space models with hierarchical Bayesian settings to tackle this challenge for inferring the dynamic profiles and genetic networks associated with disease treatments. We treat both the stochastic transition matrix and the observation matrix time-variant and include temporal correlation structures in the covariance matrix estimations in the multivariate Bayesian state space models. The unevenly spaced short time courses with unseen time points are treated as hidden state variables. Hierarchical Bayesian approaches with various prior and hyper-prior models with Monte Carlo Markov Chain and Gibbs sampling algorithms are used to estimate the model parameters and the hidden state variables. We apply the proposed Hierarchical Bayesian state space models to multiple tissues (liver, skeletal muscle, and kidney) Affymetrix time course data sets following corticosteroid (CS) drug administration. Both simulation and real data analysis results show that the genomic changes over time and gene-gene interaction in response to CS treatment can be well captured by the proposed models. The proposed dynamic Hierarchical Bayesian state space modeling approaches could be expanded and applied to other large scale genomic data, such as next generation sequence (NGS) combined with real time and time varying electronic health record (EHR) for more comprehensive and robust systematic and network based analysis in order to transform big biomedical data into predictions and diagnostics for precision medicine and personalized healthcare with better decision making and patient outcomes.
Preon representations and composite models
International Nuclear Information System (INIS)
Kang, Kyungsik
1982-01-01
This is a brief report on the preon models which are investigated by In-Gyu Koh, A. N. Schellekens and myself and based on complex, anomaly-free and asymptotically free representations of SU(3) to SU(8), SO(4N+2) and E 6 with no more than two different preons. Complete list of the representations that are complex anomaly-free and asymptotically free has been given by E. Eichten, I.-G. Koh and myself. The assumptions made about the ground state composites and the role of Fermi statistics to determine the metaflavor wave functions are discussed in some detail. We explain the method of decompositions of tensor products with definite permutation properties which has been developed for this purpose by I.-G. Koh, A.N. Schellekens and myself. An example based on an anomaly-free representation of the confining metacolor group SU(5) is discussed
The Representation of Female Characters by Women Directors in Surveillance Spaces in Turkish Cinema
Berceste Gülçin Özdemir
2017-01-01
The representation of women characters in cinema has been discussed for centuries. In cinema where dominant narrative codes prevail and scopophilic views exist over women characters, passive stereotypes of women are observed in the representation of women characters. In films shot from a woman’s point of view in Turkish Cinema and even in the films outside the main stream in which the stories of women characters are told, the fact that women characters are discussed on the basis of feminist f...
State-space dimensionality in short-memory hidden-variable theories
International Nuclear Information System (INIS)
Montina, Alberto
2011-01-01
Recently we have presented a hidden-variable model of measurements for a qubit where the hidden-variable state-space dimension is one-half the quantum-state manifold dimension. The absence of a short memory (Markov) dynamics is the price paid for this dimensional reduction. The conflict between having the Markov property and achieving the dimensional reduction was proved by Montina [A. Montina, Phys. Rev. A 77, 022104 (2008)] using an additional hypothesis of trajectory relaxation. Here we analyze in more detail this hypothesis introducing the concept of invertible process and report a proof that makes clearer the role played by the topology of the hidden-variable space. This is accomplished by requiring suitable properties of regularity of the conditional probability governing the dynamics. In the case of minimal dimension the set of continuous hidden variables is identified with an object living an N-dimensional Hilbert space whose dynamics is described by the Schroedinger equation. A method for generating the economical non-Markovian model for the qubit is also presented.
Rethinking democracy and representation: a proposal to extend the democratic canon
Directory of Open Access Journals (Sweden)
Alejandro Monsiváis Carrillo
2013-01-01
Full Text Available Rethinking political representation is necessary to understand many contemporary democratic challenges. However, a widely accepted view states that democracy and representation are two irreconcilable principles, thus hindering the theoretical assessment of political representation's democratic relevance. According to this view, what democracy needs is more popular participation; instead, representation involves elitism and political detachment. In this paper I will argue that such a view is inaccurate. Through the reconstruction of the democratic ideal, and the discussion of the concept of political representation, I intend to show that processes of political authorization, accountability and public justification are both elements of political representation and expression of democratic politics.
Guell, Xavier; Gabrieli, John D E; Schmahmann, Jeremy D
2018-05-15
Delineation of functional topography is critical to the evolving understanding of the cerebellum's role in a wide range of nervous system functions. We used data from the Human Connectome Project (n = 787) to analyze cerebellar fMRI task activation (motor, working memory, language, social and emotion processing) and resting-state functional connectivity calculated from cerebral cortical seeds corresponding to the peak Cohen's d of each task contrast. The combination of exceptional statistical power, activation from both motor and multiple non-motor tasks in the same participants, and convergent resting-state networks in the same participants revealed novel aspects of the functional topography of the human cerebellum. Consistent with prior studies there were two distinct representations of motor activation. Newly revealed were three distinct representations each for working memory, language, social, and emotional task processing that were largely separate for these four cognitive and affective domains. In most cases, the task-based activations and the corresponding resting-network correlations were congruent in identifying the two motor representations and the three non-motor representations that were unique to working memory, language, social cognition, and emotion. The definitive localization and characterization of distinct triple representations for cognition and emotion task processing in the cerebellum opens up new basic science questions as to why there are triple representations (what different functions are enabled by the different representations?) and new clinical questions (what are the differing consequences of lesions to the different representations?). Copyright © 2018 Elsevier Inc. All rights reserved.
Mixture estimation with state-space components and Markov model of switching
Czech Academy of Sciences Publication Activity Database
Nagy, Ivan; Suzdaleva, Evgenia
2013-01-01
Roč. 37, č. 24 (2013), s. 9970-9984 ISSN 0307-904X R&D Projects: GA TA ČR TA01030123 Institutional support: RVO:67985556 Keywords : probabilistic dynamic mixtures, * probability density function * state-space models * recursive mixture estimation * Bayesian dynamic decision making under uncertainty * Kerridge inaccuracy Subject RIV: BC - Control Systems Theory Impact factor: 2.158, year: 2013 http://library.utia.cas.cz/separaty/2013/AS/nagy-mixture estimation with state-space components and markov model of switching.pdf
On the Riesz representation theorem and integral operators ...
African Journals Online (AJOL)
We present a Riesz representation theorem in the setting of extended integration theory as introduced in [6]. The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces of vector valued extended integrable functions. Keywords: Vector integral, integral operators, operator ...