WorldWideScience

Sample records for tensor product states

  1. The tensor rank of tensor product of two three-qubit W states is eight

    OpenAIRE

    Chen, Lin; Friedland, Shmuel

    2017-01-01

    We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states.

  2. A practical introduction to tensor networks: Matrix product states and projected entangled pair states

    Energy Technology Data Exchange (ETDEWEB)

    Orús, Román, E-mail: roman.orus@uni-mainz.de

    2014-10-15

    This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of tensor network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d and 2d quantum lattice systems are also discussed. - Highlights: • A practical introduction to selected aspects of tensor network methods is presented. • We provide analytical examples of MPS and 2d PEPS. • We provide basic aspects on several numerical methods for MPS and 2d PEPS. • We discuss a number of applications of tensor network methods from a broad perspective.

  3. Unifying neural-network quantum states and correlator product states via tensor networks

    Science.gov (United States)

    Clark, Stephen R.

    2018-04-01

    Correlator product states (CPS) are a powerful and very broad class of states for quantum lattice systems whose (unnormalised) amplitudes in a fixed basis can be sampled exactly and efficiently. They work by gluing together states of overlapping clusters of sites on the lattice, called correlators. Recently Carleo and Troyer (2017 Science 355 602) introduced a new type sampleable ansatz called neural-network quantum states (NQS) that are inspired by the restricted Boltzmann model used in machine learning. By employing the formalism of tensor networks we show that NQS are a special form of CPS with novel properties. Diagramatically a number of simple observations become transparent. Namely, that NQS are CPS built from extensively sized GHZ-form correlators making them uniquely unbiased geometrically. The appearance of GHZ correlators also relates NQS to canonical polyadic decompositions of tensors. Another immediate implication of the NQS equivalence to CPS is that we are able to formulate exact NQS representations for a wide range of paradigmatic states, including superpositions of weighed-graph states, the Laughlin state, toric code states, and the resonating valence bond state. These examples reveal the potential of using higher dimensional hidden units and a second hidden layer in NQS. The major outlook of this study is the elevation of NQS to correlator operators allowing them to enhance conventional well-established variational Monte Carlo approaches for strongly correlated fermions.

  4. Categorical Tensor Network States

    Directory of Open Access Journals (Sweden)

    Jacob D. Biamonte

    2011-12-01

    Full Text Available We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not previously appeared in either side of the literature. Our approach enabled the development of a tensor network framework allowing a solution to the quantum decomposition problem which has several appealing features. Specifically, given an n-body quantum state |ψ〉, we present a new and general method to factor |ψ〉 into a tensor network of clearly defined building blocks. We use the solution to expose a previously unknown and large class of quantum states which we prove can be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states.

  5. Tensor rank is not multiplicative under the tensor product

    DEFF Research Database (Denmark)

    Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen

    2018-01-01

    The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection b...

  6. Tensor rank is not multiplicative under the tensor product

    NARCIS (Netherlands)

    M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)

    2018-01-01

    textabstractThe tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the

  7. Tensor rank is not multiplicative under the tensor product

    NARCIS (Netherlands)

    M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)

    2017-01-01

    textabstractThe tensor rank of a tensor is the smallest number r such that the tensor can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor (not to be confused with the "tensor Kronecker product" used in

  8. Tensor product of quantum logics

    Science.gov (United States)

    Pulmannová, Sylvia

    1985-01-01

    A quantum logic is the couple (L,M) where L is an orthomodular σ-lattice and M is a strong set of states on L. The Jauch-Piron property in the σ-form is also supposed for any state of M. A ``tensor product'' of quantum logics is defined. This definition is compared with the definition of a free orthodistributive product of orthomodular σ-lattices. The existence and uniqueness of the tensor product in special cases of Hilbert space quantum logics and one quantum and one classical logic are studied.

  9. Tensor rank is not multiplicative under the tensor product

    OpenAIRE

    Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen

    2017-01-01

    The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specif...

  10. Tensor Product of Polygonal Cell Complexes

    OpenAIRE

    Chien, Yu-Yen

    2017-01-01

    We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the tensor product, and study the symmetries of tensor products of polygonal cell complexes.

  11. Fermionic topological quantum states as tensor networks

    Science.gov (United States)

    Wille, C.; Buerschaper, O.; Eisert, J.

    2017-06-01

    Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.

  12. Tensor product varieties and crystals. GL case

    OpenAIRE

    Malkin, Anton

    2001-01-01

    The role of Spaltenstein varieties in the tensor product for GL is explained. In particular a direct (non-combinatorial) proof of the fact that the number of irreducible components of a Spaltenstein variety is equal to a Littlewood-Richardson coefficient (i.e. certain tensor product multiplicity) is obtained.

  13. Tensor products of higher almost split sequences

    OpenAIRE

    Pasquali, Andrea

    2015-01-01

    We investigate how the higher almost split sequences over a tensor product of algebras are related to those over each factor. Herschend and Iyama gave a precise criterion for when the tensor product of an $n$-representation finite algebra and an $m$-representation finite algebra is $(n+m)$-representation finite. In this case we give a complete description of the higher almost split sequences over the tensor product by expressing every higher almost split sequence as the mapping cone of a suit...

  14. Tensor network state correspondence and holography

    Science.gov (United States)

    Singh, Sukhwinder

    2018-01-01

    In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"—a correspondence between quantum many-body states mediated by tensor networks as we describe—to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.

  15. Vector and tensor meson production in quasi-two-body final states using the dual fermion model

    International Nuclear Information System (INIS)

    Becker, L.; Matthaeus, E.; Weigt, G.

    1976-01-01

    Phenomenological dual fermion amplitudes are obtained by using Neveu-Schwarz-Ramond model as a guide to incorporate half-integer spin. The model relates the production mechanism of different resonances lying on the same degenerate Regge trajectory, thus allowing a simultaneous description of vector and tensor meson production. A characteristic feature of the amplitudes is their non-evasive coupling structure. Predictions of the model for rho 0 -f-g 0 , ω-A 2 - and anti K*(890)-anti K*(1420) production in quasi-two-body reactions are compared with experimental data. The differential cross sections for natural and unnatural spin-parity t-channel exchanges as well as their contributions to different helicities of the produced resonances are given. In particular, new properties arise from the non-evasive pion exchange. Reasonable agreement with the data is found. (Auth.)

  16. Vector and tensor meson production in quasi-two-body final states using the dual fermion model

    International Nuclear Information System (INIS)

    Becker, L.; Matthaeus, E.; Weigt, G.

    1975-01-01

    Phenomenological dual fermion amplitudes are obtained by using the Neveu-Schwarz-Ramond model as a guide to incorporate half-integer spin. The model relates the production mechanism of different resonances lying on the same degenerated Regge trajectory, thus allowing a simultaneous description of vector and tensor meson production. A characteristic feature of the amplitudes is their non-evasive coupling structure. Predictions of the model for rho 0 - f - g 0 , ω - A 2 - and anti K-890 and anti K-1420 resonances production in quasi-two-body reactions are compared with experimental data. The differential cross sections for natural and unnatural spin-parity t-channel exchanges as well as their contributions to different helicities of the produced resonances are given. In particular, new properties arise from the non-evasive pion exchange. Reasonable agreement with the data is found. (author)

  17. Entanglement and tensor product decomposition for two fermions

    International Nuclear Information System (INIS)

    Caban, P; Podlaski, K; Rembielinski, J; Smolinski, K A; Walczak, Z

    2005-01-01

    The problem of the choice of tensor product decomposition in a system of two fermions with the help of Bogoliubov transformations of creation and annihilation operators is discussed. The set of physical states of the composite system is restricted by the superselection rule forbidding the superposition of fermions and bosons. It is shown that the Wootters concurrence is not the proper entanglement measure in this case. The explicit formula for the entanglement of formation is found. This formula shows that the entanglement of a given state depends on the tensor product decomposition of a Hilbert space. It is shown that the set of separable states is narrower than in the two-qubit case. Moreover, there exist states which are separable with respect to all tensor product decompositions of the Hilbert space. (letter to the editor)

  18. Tensor rank of the tripartite state |W>xn

    International Nuclear Information System (INIS)

    Yu Nengkun; Guo Cheng; Duan Runyao; Chitambar, Eric

    2010-01-01

    Tensor rank refers to the number of product states needed to express a given multipartite quantum state. Its nonadditivity as an entanglement measure has recently been observed. In this Brief Report, we estimate the tensor rank of multiple copies of the tripartite state |W>=(1/√(3))(|100>+|010>+|001>). Both an upper bound and a lower bound of this rank are derived. In particular, it is proven that the rank of |W> x 2 is 7, thus resolving a previously open problem. Some implications of this result are discussed in terms of transformation rates between |W> xn and multiple copies of the state |GHZ>=(1/√(2))(|000>+|111>).

  19. Product numerical range in a space with tensor product structure

    OpenAIRE

    Puchała, Zbigniew; Gawron, Piotr; Miszczak, Jarosław Adam; Skowronek, Łukasz; Choi, Man-Duen; Życzkowski, Karol

    2010-01-01

    We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are derived. Product numerical range of a non-Hermitian operator forms a subset of the standard numerical range containing the barycenter of the spectrum. While the latter set is convex, the product range needs not to be convex nor simply connected. The product ...

  20. Holographic spin networks from tensor network states

    Science.gov (United States)

    Singh, Sukhwinder; McMahon, Nathan A.; Brennen, Gavin K.

    2018-01-01

    In the holographic correspondence of quantum gravity, a global on-site symmetry at the boundary generally translates to a local gauge symmetry in the bulk. We describe one way how the global boundary on-site symmetries can be gauged within the formalism of the multiscale renormalization ansatz (MERA), in light of the ongoing discussion between tensor networks and holography. We describe how to "lift" the MERA representation of the ground state of a generic one dimensional (1D) local Hamiltonian, which has a global on-site symmetry, to a dual quantum state of a 2D "bulk" lattice on which the symmetry appears gauged. The 2D bulk state decomposes in terms of spin network states, which label a basis in the gauge-invariant sector of the bulk lattice. This decomposition is instrumental to obtain expectation values of gauge-invariant observables in the bulk, and also reveals that the bulk state is generally entangled between the gauge and the remaining ("gravitational") bulk degrees of freedom that are not fixed by the symmetry. We present numerical results for ground states of several 1D critical spin chains to illustrate that the bulk entanglement potentially depends on the central charge of the underlying conformal field theory. We also discuss the possibility of emergent topological order in the bulk using a simple example, and also of emergent symmetries in the nongauge (gravitational) sector in the bulk. More broadly, our holographic model translates the MERA, a tensor network state, to a superposition of spin network states, as they appear in lattice gauge theories in one higher dimension.

  1. Tensor products of quantized tilting modules

    International Nuclear Information System (INIS)

    Andersen, H.H.

    1992-01-01

    Let U k denote the quantized enveloping algebra corresponding to a finite dimensional simple complex Lie algebra L. Assume that the quantum parameter is a root of unity in k of order at least the Coxeter number for pound. Also assume that this order is odd and not divisible by 3 if type G 2 occurs. We demonstrate how one can define a reduced tensor product on the family F consisting of those finite dimensional simple U k -modules which are deformations of simple L-modules and which have non-zero quantum dimension. This together with the work of Reshetikhin-Turaev and Turaev-Wenzl prove that (U k , F) is a modular Hopf algebra and hence produces invariants of 3-manifolds. Also by recent work of Duurhus, Jakobsen and Nest it leads to a general topological quantum field theory. The method of proof explores quantized analogues of tilting modules for algebraic groups. (orig.)

  2. Fast evaluation of nonlinear functionals of tensor product wavelet expansions

    NARCIS (Netherlands)

    Schwab, C.; Stevenson, R.

    2011-01-01

    Abstract For a nonlinear functional f, and a function u from the span of a set of tensor product interpolets, it is shown how to compute the interpolant of f (u) from the span of this set of tensor product interpolets in linear complexity, assuming that the index set has a certain multiple tree

  3. TensorLy: Tensor Learning in Python

    NARCIS (Netherlands)

    Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja

    2016-01-01

    Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.

  4. Time integration of tensor trains

    OpenAIRE

    Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart

    2014-01-01

    A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The algorithm can be used for updating time-dependent tensors in the given data-sparse tensor train / matrix product state format and for computing an approximate solution to high-dimensional tensor differential equations within this data-sparse format. The formul...

  5. Tensor products of process matrices with indefinite causal structure

    Science.gov (United States)

    Jia, Ding; Sakharwade, Nitica

    2018-03-01

    Theories with indefinite causal structure have been studied from both the fundamental perspective of quantum gravity and the practical perspective of information processing. In this paper we point out a restriction in forming tensor products of objects with indefinite causal structure in certain models: there exist both classical and quantum objects the tensor products of which violate the normalization condition of probabilities, if all local operations are allowed. We obtain a necessary and sufficient condition for when such unrestricted tensor products of multipartite objects are (in)valid. This poses a challenge to extending communication theory to indefinite causal structures, as the tensor product is the fundamental ingredient in the asymptotic setting of communication theory. We discuss a few options to evade this issue. In particular, we show that the sequential asymptotic setting does not suffer the violation of normalization.

  6. Simulated annealing for tensor network states

    International Nuclear Information System (INIS)

    Iblisdir, S

    2014-01-01

    Markov chains for probability distributions related to matrix product states and one-dimensional Hamiltonians are introduced. With appropriate ‘inverse temperature’ schedules, these chains can be combined into a simulated annealing scheme for ground states of such Hamiltonians. Numerical experiments suggest that a linear, i.e., fast, schedule is possible in non-trivial cases. A natural extension of these chains to two-dimensional settings is next presented and tested. The obtained results compare well with Euclidean evolution. The proposed Markov chains are easy to implement and are inherently sign problem free (even for fermionic degrees of freedom). (paper)

  7. Symmetric Topological Phases and Tensor Network States

    Science.gov (United States)

    Jiang, Shenghan

    Classification and simulation of quantum phases are one of main themes in condensed matter physics. Quantum phases can be distinguished by their symmetrical and topological properties. The interplay between symmetry and topology in condensed matter physics often leads to exotic quantum phases and rich phase diagrams. Famous examples include quantum Hall phases, spin liquids and topological insulators. In this thesis, I present our works toward a more systematically understanding of symmetric topological quantum phases in bosonic systems. In the absence of global symmetries, gapped quantum phases are characterized by topological orders. Topological orders in 2+1D are well studied, while a systematically understanding of topological orders in 3+1D is still lacking. By studying a family of exact solvable models, we find at least some topological orders in 3+1D can be distinguished by braiding phases of loop excitations. In the presence of both global symmetries and topological orders, the interplay between them leads to new phases termed as symmetry enriched topological (SET) phases. We develop a framework to classify a large class of SET phases using tensor networks. For each tensor class, we can write down generic variational wavefunctions. We apply our method to study gapped spin liquids on the kagome lattice, which can be viewed as SET phases of on-site symmetries as well as lattice symmetries. In the absence of topological order, symmetry could protect different topological phases, which are often referred to as symmetry protected topological (SPT) phases. We present systematic constructions of tensor network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries.

  8. 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.)

  9. 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.)

  10. Physical states in the canonical tensor model from the perspective of random tensor networks

    Energy Technology Data Exchange (ETDEWEB)

    Narain, Gaurav [The Institute for Fundamental Study “The Tah Poe Academia Institute”,Naresuan University, Phitsanulok 65000 (Thailand); Sasakura, Naoki [Yukawa Institute for Theoretical Physics,Kyoto University, Kyoto 606-8502 (Japan); Sato, Yuki [National Institute for Theoretical Physics,School of Physics and Centre for Theoretical Physics,University of the Witwartersrand, WITS 2050 (South Africa)

    2015-01-07

    Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the algebra of which resembles the Dirac algebra of general relativity. When quantized, the physical states are defined to be vanished by the quantized constraints. In explicit representations, the constraint equations are a set of partial differential equations for the physical wave-functions, which do not seem straightforward to be solved due to their non-linear character. In this paper, after providing some explicit solutions for N=2,3, we show that certain scale-free integration of partition functions of statistical systems on random networks (or random tensor networks more generally) provides a series of solutions for general N. Then, by generalizing this form, we also obtain various solutions for general N. Moreover, we show that the solutions for the cases with a cosmological constant can be obtained from those with no cosmological constant for increased N. This would imply the interesting possibility that a cosmological constant can always be absorbed into the dynamics and is not an input parameter in the canonical tensor model. We also observe the possibility of symmetry enhancement in N=3, and comment on an extension of Airy function related to the solutions.

  11. The tensor product in Wadler's analysis of lists

    DEFF Research Database (Denmark)

    Nielson, Flemming; Nielson, Hanne Riis

    1992-01-01

    We consider abstract interpretation (in particular strictness analysis) for pairs and lists. We begin by reviewing the well-known fact that the best known description of a pair of elements is obtained using the tensor product rather than the cartesian product. We next present a generalisation...... of Wadler's strictness analysis for lists using the notion of open set. Finally, we illustrate the intimate connection between the case analysis implicit in Wadler's strictness analysis and the precision that the tensor product allows for modelling the inverse cons operation....

  12. The tensor product in Wadler's analysis of lists

    DEFF Research Database (Denmark)

    Nielson, Flemming; Nielson, Hanne Riis

    1994-01-01

    We consider abstract interpretation (in particular strictness analysis) for pairs and lists. We begin by reviewing the well-known fact that the best known description of a pair of elements is obtained using the tensor product rather than the cartesian product. We next present a generalisation...... of Wadler's strictness analysis for lists (1987) using the notion of open set. Finally, we illustrate the intimate connection between the case analysis implicit in Wadler's strictness analysis and the precision that the tensor product allows for modelling the inverse cons operation...

  13. Tables of Products of Tensor Operators and Stevens Operators

    DEFF Research Database (Denmark)

    Lindgård, Per-Anker

    1975-01-01

    Numerical tables of products of tensor (Racah) operators, Rl,m(J), and Stevens operators Olm(J), working within a J-multiplet are given as a function of X=J(J+1). Examples of the use of the tables, such as the calculation of commutation relations and thermal averages are given.......Numerical tables of products of tensor (Racah) operators, Rl,m(J), and Stevens operators Olm(J), working within a J-multiplet are given as a function of X=J(J+1). Examples of the use of the tables, such as the calculation of commutation relations and thermal averages are given....

  14. The metric theory of tensor products Grothendieck's resume revisited

    CERN Document Server

    Diestel, Joe; Swart, Johan; Swarte, Johannes Laurentius; Diestel, Joseph

    2008-01-01

    Grothendieck's Resumé is a landmark in functional analysis. Despite having appeared more than a half century ago, its techniques and results are still not widely known nor appreciated. This is due, no doubt, to the fact that Grothendieck included practically no proofs, and the presentation is based on the theory of the very abstract notion of tensor products. This book aims at providing the details of Grothendieck's constructions and laying bare how the important classes of operators are a consequence of the abstract operations on tensor norms. Particular attention is paid to how the classical

  15. Fermionic Orbital Optimization in Tensor Network States

    Czech Academy of Sciences Publication Activity Database

    Krumnow, C.; Veis, Libor; Legeza, Ö.; Eisert, J.

    2016-01-01

    Roč. 117, č. 21 (2016), s. 210402 ISSN 0031-9007 R&D Projects: GA ČR GA16-12052S Institutional support: RVO:61388955 Keywords : Ground state * Linear transformations * quantum chemistry Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 8.462, year: 2016

  16. C7-Decompositions of the Tensor Product of Complete Graphs

    Directory of Open Access Journals (Sweden)

    Manikandan R.S.

    2017-08-01

    Full Text Available In this paper we consider a decomposition of Km × Kn, where × denotes the tensor product of graphs, into cycles of length seven. We prove that for m, n ≥ 3, cycles of length seven decompose the graph Km × Kn if and only if (1 either m or n is odd and (2 14 | m(m − 1n(n − 1. The results of this paper together with the results of [Cp-Decompositions of some regular graphs, Discrete Math. 306 (2006 429–451] and [C5-Decompositions of the tensor product of complete graphs, Australasian J. Combinatorics 37 (2007 285–293], give necessary and sufficient conditions for the existence of a p-cycle decomposition, where p ≥ 5 is a prime number, of the graph Km × Kn.

  17. Filtering overpopulated isoscalar tensor states with mass relations

    International Nuclear Information System (INIS)

    Burakovsky, Leonid; Page, Philip R.

    2000-01-01

    Schwinger-type mass formulas are used to analyze glueball-meson mixing for isoscalar tensor mesons. In one solution, the f J (2220) is the physical glueball, and in the other the glueball is distributed over various states, with f 2 (1810) having the largest glueball component. Neither the f 2 (1565) nor the f J (1710) are among the physical states without assuming significant coupling to decay channels. The decay f 2 (1525)→ππ is consistent with experiment, and f J (2220) is neither narrow nor decays flavor democratically. (c) 2000 The American Physical Society

  18. Tensor network states in time-bin quantum optics

    Science.gov (United States)

    Lubasch, Michael; Valido, Antonio A.; Renema, Jelmer J.; Kolthammer, W. Steven; Jaksch, Dieter; Kim, M. S.; Walmsley, Ian; García-Patrón, Raúl

    2018-06-01

    The current shift in the quantum optics community towards experiments with many modes and photons necessitates new classical simulation techniques that efficiently encode many-body quantum correlations and go beyond the usual phase-space formulation. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. We extensively analyze the quantum and classical correlations of time-bin interference in a single fiber loop. We then generalize our results to more complex time-bin quantum setups and identify different classes of architectures for high-complexity and low-overhead boson sampling experiments.

  19. Entanglement entropy from tensor network states for stabilizer codes

    Science.gov (United States)

    He, Huan; Zheng, Yunqin; Bernevig, B. Andrei; Regnault, Nicolas

    2018-03-01

    In this paper, we present the construction of tensor network states (TNS) for some of the degenerate ground states of three-dimensional (3D) stabilizer codes. We then use the TNS formalism to obtain the entanglement spectrum and entropy of these ground states for some special cuts. In particular, we work out examples of the 3D toric code, the X-cube model, and the Haah code. The latter two models belong to the category of "fracton" models proposed recently, while the first one belongs to the conventional topological phases. We mention the cases for which the entanglement entropy and spectrum can be calculated exactly: For these, the constructed TNS is a singular value decomposition (SVD) of the ground states with respect to particular entanglement cuts. Apart from the area law, the entanglement entropies also have constant and linear corrections for the fracton models, while the entanglement entropies for the toric code models only have constant corrections. For the cuts we consider, the entanglement spectra of these three models are completely flat. We also conjecture that the negative linear correction to the area law is a signature of extensive ground-state degeneracy. Moreover, the transfer matrices of these TNSs can be constructed. We show that the transfer matrices are projectors whose eigenvalues are either 1 or 0. The number of nonzero eigenvalues is tightly related to the ground-state degeneracy.

  20. Analysis of the scalar, axialvector, vector, tensor doubly charmed tetraquark states with QCD sum rules

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Zhi-Gang; Yan, Ze-Hui [North China Electric Power University, Department of Physics, Baoding (China)

    2018-01-15

    In this article, we construct the axialvector-diquark-axialvector-antidiquark type currents to interpolate the scalar, axialvector, vector, tensor doubly charmed tetraquark states, and study them with QCD sum rules systematically by carrying out the operator product expansion up to the vacuum condensates of dimension 10 in a consistent way, the predicted masses can be confronted with the experimental data in the future. We can search for those doubly charmed tetraquark states in the Okubo-Zweig-Iizuka super-allowed strong decays to the charmed-meson pairs. (orig.)

  1. A Tensor-Product-Kernel Framework for Multiscale Neural Activity Decoding and Control

    Science.gov (United States)

    Li, Lin; Brockmeier, Austin J.; Choi, John S.; Francis, Joseph T.; Sanchez, Justin C.; Príncipe, José C.

    2014-01-01

    Brain machine interfaces (BMIs) have attracted intense attention as a promising technology for directly interfacing computers or prostheses with the brain's motor and sensory areas, thereby bypassing the body. The availability of multiscale neural recordings including spike trains and local field potentials (LFPs) brings potential opportunities to enhance computational modeling by enriching the characterization of the neural system state. However, heterogeneity on data type (spike timing versus continuous amplitude signals) and spatiotemporal scale complicates the model integration of multiscale neural activity. In this paper, we propose a tensor-product-kernel-based framework to integrate the multiscale activity and exploit the complementary information available in multiscale neural activity. This provides a common mathematical framework for incorporating signals from different domains. The approach is applied to the problem of neural decoding and control. For neural decoding, the framework is able to identify the nonlinear functional relationship between the multiscale neural responses and the stimuli using general purpose kernel adaptive filtering. In a sensory stimulation experiment, the tensor-product-kernel decoder outperforms decoders that use only a single neural data type. In addition, an adaptive inverse controller for delivering electrical microstimulation patterns that utilizes the tensor-product kernel achieves promising results in emulating the responses to natural stimulation. PMID:24829569

  2. Coupling coefficients for tensor product representations of quantum SU(2)

    International Nuclear Information System (INIS)

    Groenevelt, Wolter

    2014-01-01

    We study tensor products of infinite dimensional irreducible * -representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometric orthogonal polynomials and q-Bessel-type functions

  3. Coupling coefficients for tensor product representations of quantum SU(2)

    Science.gov (United States)

    Groenevelt, Wolter

    2014-10-01

    We study tensor products of infinite dimensional irreducible *-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometric orthogonal polynomials and q-Bessel-type functions.

  4. Generalization of binary tensor product schemes depends upon four parameters

    International Nuclear Information System (INIS)

    Bashir, R.; Bari, M.; Mustafa, G.

    2018-01-01

    This article deals with general formulae of parametric and non parametric bivariate subdivision scheme with four parameters. By assigning specific values to those parameters we get some special cases of existing tensor product schemes as well as a new proposed scheme. The behavior of schemes produced by the general formulae is interpolating, approximating and relaxed. Approximating bivariate subdivision schemes produce some other surfaces as compared to interpolating bivariate subdivision schemes. Polynomial reproduction and polynomial generation are desirable properties of subdivision schemes. Capability of polynomial reproduction and polynomial generation is strongly connected with smoothness, sum rules, convergence and approximation order. We also calculate the polynomial generation and polynomial reproduction of 9-point bivariate approximating subdivision scheme. Comparison of polynomial reproduction, polynomial generation and continuity of existing and proposed schemes has also been established. Some numerical examples are also presented to show the behavior of bivariate schemes. (author)

  5. Frames and bases in tensor products of Hilbert spaces and Hilbert C ...

    Indian Academy of Sciences (India)

    In this article, we study tensor product of Hilbert *-modules and Hilbert spaces. We show that if is a Hilbert -module and is a Hilbert -module, then tensor product of frames (orthonormal bases) for and produce frames (orthonormal bases) for Hilbert A ⊗ B -module E ⊗ F , and we get more results. For Hilbert ...

  6. Tensor representation techniques for full configuration interaction: A Fock space approach using the canonical product format.

    Science.gov (United States)

    Böhm, Karl-Heinz; Auer, Alexander A; Espig, Mike

    2016-06-28

    In this proof-of-principle study, we apply tensor decomposition techniques to the Full Configuration Interaction (FCI) wavefunction in order to approximate the wavefunction parameters efficiently and to reduce the overall computational effort. For this purpose, the wavefunction ansatz is formulated in an occupation number vector representation that ensures antisymmetry. If the canonical product format tensor decomposition is then applied, the Hamiltonian and the wavefunction can be cast into a multilinear product form. As a consequence, the number of wavefunction parameters does not scale to the power of the number of particles (or orbitals) but depends on the rank of the approximation and linearly on the number of particles. The degree of approximation can be controlled by a single threshold for the rank reduction procedure required in the algorithm. We demonstrate that using this approximation, the FCI Hamiltonian matrix can be stored with N(5) scaling. The error of the approximation that is introduced is below Millihartree for a threshold of ϵ = 10(-4) and no convergence problems are observed solving the FCI equations iteratively in the new format. While promising conceptually, all effort of the algorithm is shifted to the required rank reduction procedure after the contraction of the Hamiltonian with the coefficient tensor. At the current state, this crucial step is the bottleneck of our approach and even for an optimistic estimate, the algorithm scales beyond N(10) and future work has to be directed towards reduction-free algorithms.

  7. Equivalence of restricted Boltzmann machines and tensor network states

    Science.gov (United States)

    Chen, Jing; Cheng, Song; Xie, Haidong; Wang, Lei; Xiang, Tao

    2018-02-01

    The restricted Boltzmann machine (RBM) is one of the fundamental building blocks of deep learning. RBM finds wide applications in dimensional reduction, feature extraction, and recommender systems via modeling the probability distributions of a variety of input data including natural images, speech signals, and customer ratings, etc. We build a bridge between RBM and tensor network states (TNS) widely used in quantum many-body physics research. We devise efficient algorithms to translate an RBM into the commonly used TNS. Conversely, we give sufficient and necessary conditions to determine whether a TNS can be transformed into an RBM of given architectures. Revealing these general and constructive connections can cross fertilize both deep learning and quantum many-body physics. Notably, by exploiting the entanglement entropy bound of TNS, we can rigorously quantify the expressive power of RBM on complex data sets. Insights into TNS and its entanglement capacity can guide the design of more powerful deep learning architectures. On the other hand, RBM can represent quantum many-body states with fewer parameters compared to TNS, which may allow more efficient classical simulations.

  8. Flavour fields in steady state: stress tensor and free energy

    International Nuclear Information System (INIS)

    Banerjee, Avik; Kundu, Arnab; Kundu, Sandipan

    2016-01-01

    The dynamics of a probe brane in a given gravitational background is governed by the Dirac-Born-Infeld action. The corresponding open string metric arises naturally in studying the fluctuations on the probe. In Gauge-String duality, it is known that in the presence of a constant electric field on the worldvolume of the probe, the open string metric acquires an event horizon and therefore the fluctuation modes on the probe experience an effective temperature. In this article, we bring together various properties of such a system to a formal definition and a subsequent narration of the effective thermodynamics and the stress tensor of the corresponding flavour fields, also including a non-vanishing chemical potential. In doing so, we point out a potentially infinitely-degenerate scheme-dependence of regularizing the free energy, which nevertheless yields a universal contribution in certain cases. This universal piece appears as the coefficient of a log-divergence in free energy when a space-filling probe brane is embedded in AdS d+1 -background, for d=2,4, and is related to conformal anomaly. For the special case of d=2, the universal factor has a striking resemblance to the well-known heat current formula in (1+1)-dimensional conformal field theory in steady-state, which endows a plausible physical interpretation to it. Interestingly, we observe a vanishing conformal anomaly in d=6.

  9. The metric theory of tensor products (grthendieck's résumé revisited ...

    African Journals Online (AJOL)

    This paper presents the first of a multi-part series of papers on the metric theory of tensor products according to Grothendieck's “Résumé de la theorie metrique des produits tensoriels topologiques” It contains the basics on tensor norms: a discussion of the special character of the injective and the projective norms, ...

  10. Tensor products and regularity properties of Cuntz semigroups

    CERN Document Server

    Antoine, Ramon; Thiel, Hannes

    2018-01-01

    The Cuntz semigroup of a C^*-algebra is an important invariant in the structure and classification theory of C^*-algebras. It captures more information than K-theory but is often more delicate to handle. The authors systematically study the lattice and category theoretic aspects of Cuntz semigroups. Given a C^*-algebra A, its (concrete) Cuntz semigroup \\mathrm{Cu}(A) is an object in the category \\mathrm{Cu} of (abstract) Cuntz semigroups, as introduced by Coward, Elliott and Ivanescu. To clarify the distinction between concrete and abstract Cuntz semigroups, the authors call the latter \\mathrm{Cu}-semigroups. The authors establish the existence of tensor products in the category \\mathrm{Cu} and study the basic properties of this construction. They show that \\mathrm{Cu} is a symmetric, monoidal category and relate \\mathrm{Cu}(A\\otimes B) with \\mathrm{Cu}(A)\\otimes_{\\mathrm{Cu}}\\mathrm{Cu}(B) for certain classes of C^*-algebras. As a main tool for their approach the authors introduce the category \\mathrm{W} of ...

  11. Energy-momentum tensor and definition of particle states for Robertson-Walker space-time

    International Nuclear Information System (INIS)

    Brown, M.R.; Dutton, C.R.

    1978-01-01

    A new regularization scheme is developed for calculating expectation values of the energy-momentum tensor of a quantized scalar field in Robertson-Walker space-times. Using this regularized stress tensor we consider a definition for the vacuum state of the scalar field on any initial hypersurface. Asymptotic methods are developed to investigate the structure of both the divergent and finite terms of the stress tensor when evaluated in this state. The conformal anomaly is discussed in the context of this model. It does not naturally enter into the analysis and we argue that its inclusion is unnecessary

  12. The deuteron bound state wave function with tensor forces

    International Nuclear Information System (INIS)

    Takemasa, Tadashi

    1991-01-01

    A FORTRAN program named DEUTERON is developed to calculate the binding energy and wave function of a deuteron, when the interaction between two nucleons is described in terms of central, tensor, spin-orbit, and quadratic LS potentials with or without a hard core. An important use of the program is to provide the deuteron wave function required in nuclear reaction calculations involving a deuteron. Also, this program may be employed in nuclear Hartree-Fock calculations using an effective nucleon-nucleon interaction with a tensor component. (author)

  13. Tensor product of no-signaling boxes in the framework of quantum logics

    International Nuclear Information System (INIS)

    Tylec, T I; Kuś, M

    2017-01-01

    In the quantum logic framework we show that the no-signaling box model is a particular type of tensor product with single box logics. Such notion of a tensor product is too strong to apply in the category of logics of quantum mechanical systems. In the light of the obtained results, the statement that no-signaling box models are generalizations of quantum models is questionable. (letter)

  14. Entanglement beyond tensor product structure: algebraic aspects of quantum non-separability

    International Nuclear Information System (INIS)

    Derkacz, Łukasz; Gwóźdź, Marek; Jakóbczyk, Lech

    2012-01-01

    An algebraic approach to quantum non-separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not exploited. Even in this simple case, such a general formulation has some advantages. Using algebraic formalism, we can explicitly show the relativity of the notion of entanglement to the observables measured in the system and characterize separable and non-separable pure states. As a universal measure of non-separability of pure states, we propose to take the so-called total correlation. This quantity depends on the state as well as on the algebraic partition. Its numerical value is given by the norm of the corresponding correlation matrix. (paper)

  15. Tensor structure for Nori motives

    OpenAIRE

    Barbieri-Viale, Luca; Huber, Annette; Prest, Mike

    2018-01-01

    We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.

  16. Scale transformations, the energy-momentum tensor, and the equation of state

    International Nuclear Information System (INIS)

    Carruthers, P.

    1989-01-01

    The Equation of State (EOS) relates diagonal elements of the energy-momentum tensor θ μν . The first moment of the energy-momentum tensor generates scale transformations. The virial theorem, a consequence of the behavior of the energy density under scale transformations, allows one to eliminate the kinetic energy in terms of the potential terms. The trace theorem for the energy-momentum tensor expresses ε-3p in terms of ensemble averages of scale-breaking operators, allowing a new approach to the EOS. 10 refs

  17. Some duality relations in the theory of tensor products

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr Pavel; Smith, R. J.

    2012-01-01

    Roč. 30, č. 3 (2012), s. 239-249 ISSN 0723-0869 R&D Projects: GA ČR(CZ) GAP201/11/0345 Institutional support: RVO:67985840 Keywords : tensor * projective * injective Subject RIV: BA - General Mathematics Impact factor: 0.780, year: 2012 http://www.sciencedirect.com/science/article/pii/S072308691200045X

  18. Detecting brain dynamics during resting state: a tensor based evolutionary clustering approach

    Science.gov (United States)

    Al-sharoa, Esraa; Al-khassaweneh, Mahmood; Aviyente, Selin

    2017-08-01

    Human brain is a complex network with connections across different regions. Understanding the functional connectivity (FC) of the brain is important both during resting state and task; as disruptions in connectivity patterns are indicators of different psychopathological and neurological diseases. In this work, we study the resting state functional connectivity networks (FCNs) of the brain from fMRI BOLD signals. Recent studies have shown that FCNs are dynamic even during resting state and understanding the temporal dynamics of FCNs is important for differentiating between different conditions. Therefore, it is important to develop algorithms to track the dynamic formation and dissociation of FCNs of the brain during resting state. In this paper, we propose a two step tensor based community detection algorithm to identify and track the brain network community structure across time. First, we introduce an information-theoretic function to reduce the dynamic FCN and identify the time points that are similar topologically to combine them into a tensor. These time points will be used to identify the different FC states. Second, a tensor based spectral clustering approach is developed to identify the community structure of the constructed tensors. The proposed algorithm applies Tucker decomposition to the constructed tensors and extract the orthogonal factor matrices along the connectivity mode to determine the common subspace within each FC state. The detected community structure is summarized and described as FC states. The results illustrate the dynamic structure of resting state networks (RSNs), including the default mode network, somatomotor network, subcortical network and visual network.

  19. Application of modern tensor calculus to engineered domain structures. 2. Tensor distinction of domain states

    Czech Academy of Sciences Publication Activity Database

    Kopský, Vojtěch

    2006-01-01

    Roč. 62, - (2006), s. 65-76 ISSN 0108-7673 R&D Projects: GA ČR GA202/04/0992 Institutional research plan: CEZ:AV0Z10100520 Keywords : tensorial covariants * domain states * stability spaces Subject RIV: BE - Theoretical Physics Impact factor: 1.676, year: 2006

  20. Energy momentum tensor and operator product expansion in local causal perturbation theory

    International Nuclear Information System (INIS)

    Prange, D.

    2000-09-01

    We derive new examples for algebraic relations of interacting fields in local perturbative quantum field theory. The fundamental building blocks in this approach are time ordered products of free (composed) fields. We give explicit formulas for the construction of Poincare covariant ones, which were already known to exist through cohomological arguments. For a large class of theories the canonical energy momentum tensor is shown to be conserved. Classical theories without dimensionful couplings admit an improved tensor that is additionally traceless. On the example of φ 4 -theory we discuss the improved tensor in the quantum theory. Its trace receives an anomalous contribution due to its conservation. Moreover, we define an interacting bilocal normal product for scalar theories. This leads to an operator product expansion of two time ordered fields. (orig.) [de

  1. Tensor Factorization for Low-Rank Tensor Completion.

    Science.gov (United States)

    Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao

    2018-03-01

    Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.

  2. Tensor Renormalization of Quantum Many-Body Systems Using Projected Entangled Simplex States

    Directory of Open Access Journals (Sweden)

    Z. Y. Xie

    2014-02-01

    Full Text Available We propose a new class of tensor-network states, which we name projected entangled simplex states (PESS, for studying the ground-state properties of quantum lattice models. These states extend the pair-correlation basis of projected entangled pair states to a simplex. PESS are exact representations of the simplex solid states, and they provide an efficient trial wave function that satisfies the area law of entanglement entropy. We introduce a simple update method for evaluating the PESS wave function based on imaginary-time evolution and the higher-order singular-value decomposition of tensors. By applying this method to the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice, we obtain accurate and systematic results for the ground-state energy, which approach the lowest upper bounds yet estimated for this quantity.

  3. A Tensor Decomposition-Based Approach for Detecting Dynamic Network States From EEG.

    Science.gov (United States)

    Mahyari, Arash Golibagh; Zoltowski, David M; Bernat, Edward M; Aviyente, Selin

    2017-01-01

    Functional connectivity (FC), defined as the statistical dependency between distinct brain regions, has been an important tool in understanding cognitive brain processes. Most of the current works in FC have focused on the assumption of temporally stationary networks. However, recent empirical work indicates that FC is dynamic due to cognitive functions. The purpose of this paper is to understand the dynamics of FC for understanding the formation and dissolution of networks of the brain. In this paper, we introduce a two-step approach to characterize the dynamics of functional connectivity networks (FCNs) by first identifying change points at which the network connectivity across subjects shows significant changes and then summarizing the FCNs between consecutive change points. The proposed approach is based on a tensor representation of FCNs across time and subjects yielding a four-mode tensor. The change points are identified using a subspace distance measure on low-rank approximations to the tensor at each time point. The network summarization is then obtained through tensor-matrix projections across the subject and time modes. The proposed framework is applied to electroencephalogram (EEG) data collected during a cognitive control task. The detected change-points are consistent with a priori known ERN interval. The results show significant connectivities in medial-frontal regions which are consistent with widely observed ERN amplitude measures. The tensor-based method outperforms conventional matrix-based methods such as singular value decomposition in terms of both change-point detection and state summarization. The proposed tensor-based method captures the topological structure of FCNs which provides more accurate change-point-detection and state summarization.

  4. Adaptive estimation of multivariate functions using conditionally Gaussian tensor-product spline priors

    NARCIS (Netherlands)

    Jonge, de R.; Zanten, van J.H.

    2012-01-01

    We investigate posterior contraction rates for priors on multivariate functions that are constructed using tensor-product B-spline expansions. We prove that using a hierarchical prior with an appropriate prior distribution on the partition size and Gaussian prior weights on the B-spline

  5. Analysis and control of Boolean networks a semi-tensor product approach

    CERN Document Server

    Cheng, Daizhan; Li, Zhiqiang

    2010-01-01

    This book presents a new approach to the investigation of Boolean control networks, using the semi-tensor product (STP), which can express a logical function as a conventional discrete-time linear system. This makes it possible to analyze basic control problems.

  6. Frames and bases in tensor products of Hilbert spaces and Hilbert C ...

    Indian Academy of Sciences (India)

    [14] Heil C E and Walnut D F, Continuous and discrete wavelet transforms, SIAM Review 31. (1989) 628–666. [15] Khosravi A and Asgari M S, Frames and bases in tensor product of Hilbert spaces, Int. J. Math. 4(6) (2003) 527–538. [16] Lance E C, Hilbert C. ∗. -modules – a toolkit for operator algebraists, London Math. Soc.

  7. Self-adaptive tensor network states with multi-site correlators

    Science.gov (United States)

    Kovyrshin, Arseny; Reiher, Markus

    2017-12-01

    We introduce the concept of self-adaptive tensor network states (SATNSs) based on multi-site correlators. The SATNS ansatz gradually extends its variational space incorporating the most important next-order correlators into the ansatz for the wave function. The selection of these correlators is guided by entanglement-entropy measures from quantum information theory. By sequentially introducing variational parameters and adjusting them to the system under study, the SATNS ansatz achieves keeping their number significantly smaller than the total number of full-configuration interaction parameters. The SATNS ansatz is studied for manganocene in its lowest-energy sextet and doublet states; the latter of which is known to be difficult to describe. It is shown that the SATNS parametrization solves the convergence issues found for previous correlator-based tensor network states.

  8. Efficient Low Rank Tensor Ring Completion

    OpenAIRE

    Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

    2017-01-01

    Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors in the MPS representation. This development is motivated in part by the success of matrix completion algorithms that alternate over the (low-rank) factors. In this paper, we propose a spectral initialization for the tensor ring completion algorithm and ana...

  9. Random SU(2) invariant tensors

    Science.gov (United States)

    Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei

    2018-04-01

    SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n  =  4. In this paper, we show that for n  >  4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.

  10. Irreducible integrable theories form tensor products of conformal models

    International Nuclear Information System (INIS)

    Mathur, S.D.; Warner, N.P.

    1991-01-01

    By using Toda field theories we show that there are perturbations of direct products of conformal theories that lead to irreducible integrable field theories. The same affine Toda theory can be truncated to different quantum integrable models for different choices of the charge at infinity and the coupling. The classification of integrable models that can be obtained in this fashion follows the classification of symmetric spaces of type G/H with rank H = rank G. (orig.)

  11. Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods

    Science.gov (United States)

    Diosady, Laslo T.; Murman, Scott M.

    2017-02-01

    A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

  12. Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods

    Science.gov (United States)

    Diosady, Laslo T.; Murman, Scott M.

    2016-01-01

    space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

  13. Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

    Science.gov (United States)

    Chou, Chia-Chun; Kouri, Donald J

    2013-04-25

    We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.

  14. A remark on the unitary group of a tensor product of n finite ...

    Indian Academy of Sciences (India)

    By using the method of quantum circuits in the theory of quantum computing as outlined in Nielsen and Chuang [2] and using a key lemma of Jaikumar [1] we show that every unitary operator on the tensor product H = H 1 ⊗ H 2 ⊗ … ⊗ H n can be expressed as a composition of a finite number of unitary operators living on ...

  15. Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group

    Science.gov (United States)

    Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic

    2018-05-01

    We present a state interaction spin-orbit coupling method to calculate electron paramagnetic resonance g-tensors from density matrix renormalization group wavefunctions. We apply the technique to compute g-tensors for the TiF3 and CuCl42 - complexes, a [2Fe-2S] model of the active center of ferredoxins, and a Mn4CaO5 model of the S2 state of the oxygen evolving complex. These calculations raise the prospects of determining g-tensors in multireference calculations with a large number of open shells.

  16. Tensor Force and D-state Effects Upon (d,x) Cross Sections

    Science.gov (United States)

    Hawk, Eric; McNeil, James; Cecil, F. Edward; Hofstee, Mariet; Greife, Uwe; Pallone, Arthur

    2000-09-01

    The effects of the inclusion of the tensor force and the internal deuteron D-state upon low-energy deuteron-stripping reactions (d,x) are examined within the context of the distorted-wave Born approximation (DWBA). Inclusion of these effects requires a relaxation of the commonly employed zero-range approximation. This relaxation is treated via a derivative expansion. Comparisons with the differential cross sections found using zero-range, S-state calculations are made for several low-Z nuclei.

  17. ψ(2S) Hadronic Decays to Vector-Tensor Final States

    International Nuclear Information System (INIS)

    Bai, J.Z.; Bian, J.G.; Chai, Z.W.; Chen, G.P.; Chen, J.C.; Chen, Y.; Chen, Y.B.; Chen, Y.Q.; Cheng, B.S.; Cui, X.Z.; Ding, H.L.; Ding, L.Y.; Dong, L.Y.; Du, Z.Z.; Feng, S.; Gao, C.S.; Gao, M.L.; Gao, S.Q.; Gu, J.H.; Gu, S.D.; Gu, W.X.; Gu, Y.F.; Guo, Y.N.; Han, S.W.; Han, Y.; He, J.; He, J.T.; Hu, G.Y.; Hu, H.M.; Hu, J.L.; Hu, Q.H.; Hu, T.; Hu, X.Q.; Huang, J.D.; Huang, Y.Z.; Jiang, C.H.; Jin, Y.; Ke, Z.J.; Lai, Y.F.; Lang, P.F.; Li, C.G.; Li, D.; Li, H.B.; Li, J.; Li, P.Q.; Li, R.B.; Li, W.; Li, W.D.; Li, W.G.; Li, X.H.; Li, X.N.; Liu, H.M.; Liu, J.; Liu, J.H.; Liu, R.G.; Liu, Y.; Lu, F.; Lu, J.G.; Lu, J.Y.; Lu, L.C.; Luo, C.H.; Ma, A.M.; Ma, E.C.; Ma, J.M.; Mao, H.S.; Mao, Z.P.; Meng, X.C.; Nie, J.; Qi, N.D.; Qi, X.R.; Qiu, J.F.; Qu, Y.H.; Que, Y.K.; Rong, G.; Shao, Y.Y.; Shen, B.W.; Shen, D.L.; Shen, H.; Shen, X.Y.; Sheng, H.Y.; Shi, H.Z.; Song, X.F.; Sun, F.; Sun, H.S.; Tang, S.Q.; Tong, G.L.; Wang, F.; Wang, L.S.; Wang, L.Z.; Wang, M.; Wang, M.; Wang, P.; Wang, P.L.; Wang, S.M.; Wang, T.J.; Wang, Y.Y.; Wei, C.L.; Wu, Y.G.; Xi, D.M.; Xia, X.M.; Xie, P.P.; Xie, Y.; Xie, Y.H.; Xiong, W.J.; Xu, C.C.; Xu, G.F.; Xue, S.T.; Yan, J.; Yan, W.G.; Yang, C.M.; Yang, C.Y.; Yang, J.; Yang, X.F.; Ye, M.H.; Yi, K.; Yu, C.S.; Yu, C.X.; Yu, Z.Q.; Yu, Z.T.; Yuan, C.Z.; Yuan, Y.; Zhang, B.Y.; Zhang, C.C.; Zhang, D.H.; Zhang, D.; Zhang, H.L.; Zhang, J.; Zhang, J.L.; Zhang, J.W.; Zhang, L.S.; Zhang, Q.J.; Zhang, S.Q.; Zhang, Y.; Zhang, Y.Y.; Zhao, D.X.; Zhao, H.W.; Zhao, J.W.; Zhao, M.; Zhao, W.R.; Zhao, Z.G.; Zheng, J.P.; Zheng, L.S.; Zheng, Z.P.; Zhou, G.P.; Zhou, H.S.; Zhou, L.; Zhu, Q.M.; Zhu, Y.C.; Zhu, Y.S.; Zhuang, B.A.; Hitlin, D.G.; Kelsey, M.H.; Oyang, J.; Panetta, J.; Porter, F.; Weaver, M.; Chen, J.; Malchow, R.; Toki, W.; Yang, W.

    1998-01-01

    The decays of the ψ(2S) into vector plus tensor meson final states have been studied for the first time using the BES detector. We determine upper limits on branching fractions for ψ(2S) decays into ωf 2 , ρa 2 , K *0 K *0 2 +c.c. , and φf ' 2 (1525) that are, in each case, significantly smaller than the corresponding branching fractions for the J/ψ meson, scaled according to the expectations of perturbative QCD. copyright 1998 The American Physical Society

  18. Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem

    Directory of Open Access Journals (Sweden)

    Xuqing Zhang

    2013-01-01

    Full Text Available This paper discusses spectral method with the tensor-product nodal basis at the Legendre-Gauss-Lobatto points for solving the Steklov eigenvalue problem. A priori error estimates of spectral method are discussed, and based on the work of Melenk and Wohlmuth (2001, a posterior error estimator of the residual type is given and analyzed. In addition, this paper combines the shifted-inverse iterative method and spectral method to establish an efficient scheme. Finally, numerical experiments with MATLAB program are reported.

  19. Tensor Product Model Transformation Based Adaptive Integral-Sliding Mode Controller: Equivalent Control Method

    Directory of Open Access Journals (Sweden)

    Guoliang Zhao

    2013-01-01

    Full Text Available This paper proposes new methodologies for the design of adaptive integral-sliding mode control. A tensor product model transformation based adaptive integral-sliding mode control law with respect to uncertainties and perturbations is studied, while upper bounds on the perturbations and uncertainties are assumed to be unknown. The advantage of proposed controllers consists in having a dynamical adaptive control gain to establish a sliding mode right at the beginning of the process. Gain dynamics ensure a reasonable adaptive gain with respect to the uncertainties. Finally, efficacy of the proposed controller is verified by simulations on an uncertain nonlinear system model.

  20. Using Tensor Completion Method to Achieving Better Coverage of Traffic State Estimation from Sparse Floating Car Data.

    Science.gov (United States)

    Ran, Bin; Song, Li; Zhang, Jian; Cheng, Yang; Tan, Huachun

    2016-01-01

    Traffic state estimation from the floating car system is a challenging problem. The low penetration rate and random distribution make available floating car samples usually cover part space and time points of the road networks. To obtain a wide range of traffic state from the floating car system, many methods have been proposed to estimate the traffic state for the uncovered links. However, these methods cannot provide traffic state of the entire road networks. In this paper, the traffic state estimation is transformed to solve a missing data imputation problem, and the tensor completion framework is proposed to estimate missing traffic state. A tensor is constructed to model traffic state in which observed entries are directly derived from floating car system and unobserved traffic states are modeled as missing entries of constructed tensor. The constructed traffic state tensor can represent spatial and temporal correlations of traffic data and encode the multi-way properties of traffic state. The advantage of the proposed approach is that it can fully mine and utilize the multi-dimensional inherent correlations of traffic state. We tested the proposed approach on a well calibrated simulation network. Experimental results demonstrated that the proposed approach yield reliable traffic state estimation from very sparse floating car data, particularly when dealing with the floating car penetration rate is below 1%.

  1. Using Tensor Completion Method to Achieving Better Coverage of Traffic State Estimation from Sparse Floating Car Data.

    Directory of Open Access Journals (Sweden)

    Bin Ran

    Full Text Available Traffic state estimation from the floating car system is a challenging problem. The low penetration rate and random distribution make available floating car samples usually cover part space and time points of the road networks. To obtain a wide range of traffic state from the floating car system, many methods have been proposed to estimate the traffic state for the uncovered links. However, these methods cannot provide traffic state of the entire road networks. In this paper, the traffic state estimation is transformed to solve a missing data imputation problem, and the tensor completion framework is proposed to estimate missing traffic state. A tensor is constructed to model traffic state in which observed entries are directly derived from floating car system and unobserved traffic states are modeled as missing entries of constructed tensor. The constructed traffic state tensor can represent spatial and temporal correlations of traffic data and encode the multi-way properties of traffic state. The advantage of the proposed approach is that it can fully mine and utilize the multi-dimensional inherent correlations of traffic state. We tested the proposed approach on a well calibrated simulation network. Experimental results demonstrated that the proposed approach yield reliable traffic state estimation from very sparse floating car data, particularly when dealing with the floating car penetration rate is below 1%.

  2. TensorLy: Tensor Learning in Python

    OpenAIRE

    Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja

    2016-01-01

    Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not on the same footing. In order to bridge this gap, we have developed \\emph{TensorLy}, a high-level API for tensor methods and deep tensorized neural networks in Python. TensorLy aims to follow the same standards adopted by the main projects of the Python scie...

  3. Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods

    Science.gov (United States)

    Pazner, Will; Persson, Per-Olof

    2018-02-01

    In this paper, we develop a new tensor-product based preconditioner for discontinuous Galerkin methods with polynomial degrees higher than those typically employed. This preconditioner uses an automatic, purely algebraic method to approximate the exact block Jacobi preconditioner by Kronecker products of several small, one-dimensional matrices. Traditional matrix-based preconditioners require O (p2d) storage and O (p3d) computational work, where p is the degree of basis polynomials used, and d is the spatial dimension. Our SVD-based tensor-product preconditioner requires O (p d + 1) storage, O (p d + 1) work in two spatial dimensions, and O (p d + 2) work in three spatial dimensions. Combined with a matrix-free Newton-Krylov solver, these preconditioners allow for the solution of DG systems in linear time in p per degree of freedom in 2D, and reduce the computational complexity from O (p9) to O (p5) in 3D. Numerical results are shown in 2D and 3D for the advection, Euler, and Navier-Stokes equations, using polynomials of degree up to p = 30. For many test cases, the preconditioner results in similar iteration counts when compared with the exact block Jacobi preconditioner, and performance is significantly improved for high polynomial degrees p.

  4. Matrix product states for lattice field theories

    Energy Technology Data Exchange (ETDEWEB)

    Banuls, M.C.; Cirac, J.I. [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Saito, H. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Tsukuba Univ., Ibaraki (Japan). Graduate School of Pure and Applied Sciences

    2013-10-15

    The term Tensor Network States (TNS) refers to a number of families of states that represent different ansaetze for the efficient description of the state of a quantum many-body system. Matrix Product States (MPS) are one particular case of TNS, and have become the most precise tool for the numerical study of one dimensional quantum many-body systems, as the basis of the Density Matrix Renormalization Group method. Lattice Gauge Theories (LGT), in their Hamiltonian version, offer a challenging scenario for these techniques. While the dimensions and sizes of the systems amenable to TNS studies are still far from those achievable by 4-dimensional LGT tools, Tensor Networks can be readily used for problems which more standard techniques, such as Markov chain Monte Carlo simulations, cannot easily tackle. Examples of such problems are the presence of a chemical potential or out-of-equilibrium dynamics. We have explored the performance of Matrix Product States in the case of the Schwinger model, as a widely used testbench for lattice techniques. Using finite-size, open boundary MPS, we are able to determine the low energy states of the model in a fully non-perturbativemanner. The precision achieved by the method allows for accurate finite size and continuum limit extrapolations of the ground state energy, but also of the chiral condensate and the mass gaps, thus showing the feasibility of these techniques for gauge theory problems.

  5. Priors on the effective dark energy equation of state in scalar-tensor theories

    Science.gov (United States)

    Raveri, Marco; Bull, Philip; Silvestri, Alessandra; Pogosian, Levon

    2017-10-01

    Constraining the dark energy (DE) equation of state, wDE, is one of the primary science goals of ongoing and future cosmological surveys. In practice, with imperfect data and incomplete redshift coverage, this requires making assumptions about the evolution of wDE with redshift z . These assumptions can be manifested in a choice of a specific parametric form, which can potentially bias the outcome, or else one can reconstruct wDE(z ) nonparametrically, by specifying a prior covariance matrix that correlates values of wDE at different redshifts. In this work, we derive the theoretical prior covariance for the effective DE equation of state predicted by general scalar-tensor theories with second order equations of motion (Horndeski theories). This is achieved by generating a large ensemble of possible scalar-tensor theories using a Monte Carlo methodology, including the application of physical viability conditions. We also separately consider the special subcase of the minimally coupled scalar field, or quintessence. The prior shows a preference for tracking behaviors in the most general case. Given the covariance matrix, theoretical priors on parameters of any specific parametrization of wDE(z ) can also be readily derived by projection.

  6. The Computation of Nash Equilibrium in Fashion Games via Semi-Tensor Product Method

    Institute of Scientific and Technical Information of China (English)

    GUO Peilian; WANG Yuzhen

    2016-01-01

    Using the semi-tensor product of matrices,this paper investigates the computation of pure-strategy Nash equilibrium (PNE) for fashion games,and presents several new results.First,a formal fashion game model on a social network is given.Second,the utility function of each player is converted into an algebraic form via the semi-tensor product of matrices,based on which the case of two-strategy fashion game is studied and two methods are obtained for the case to verify the existence of PNE.Third,the multi-strategy fashion game model is investigated and an algorithm is established to find all the PNEs for the general case.Finally,two kinds of optimization problems,that is,the so-called social welfare and normalized satisfaction degree optimization problems are investigated and two useful results are given.The study of several illustrative examples shows that the new results obtained in this paper are effective.

  7. On the geometry of mixed states and the Fisher information tensor

    Energy Technology Data Exchange (ETDEWEB)

    Contreras, I., E-mail: icontrer@illinois.edu [Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801 (United States); Ercolessi, E., E-mail: ercolessi@bo.infn.it [Dipartimento di Fisica e Astronomia, Università di Bologna and INFN, V. Irnerio 46, 40127 Bologna (Italy); Schiavina, M., E-mail: michele.schiavina@math.uzh.ch [Institut für Mathematik, Winterthurerstrasse 190, 8057 Zürich (Switzerland)

    2016-06-15

    In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant–Kirillov–Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjoint orbits, seen as spaces of mixed states, is also discussed.

  8. Effect on Tensor Correlations on Gamow- Teller States in 90Zr and 208Pb

    International Nuclear Information System (INIS)

    Bai, C. L.; Sagawa, H.; Zhang, H. Q.

    2009-01-01

    The tensor terms of the Skyrme effective interaction are included in the self-consistent Hartree-Fock plus Random Phase Approximation (HF-RPA) model. The Gamow-Teller (GT) strength function of 9 0Z r and 2 08P b are calculated with and without the tensor terms. The main peaks are moved downwards by about 2 MeV when including the tensor contribution. About 10% of the non-energy weighted sum rule is shifted to the excitation energy region above 30 MeV by the RPA tensor correlations. The contribution of the tensor terms to the energy weighted sum rule is given analytically, and compared to the outcome of RPA. A microscopic origin of the quenching of GT sum rule is discussed in relation with the coupling to giant spin-quadrupole excitations by the tensor interactions.(author)

  9. Effect of Tensor Correlations on Gamow-Teller States in 90Zr and 208Pb

    International Nuclear Information System (INIS)

    Bai, C. L.; Zhang, H. Q.; Zhang, X. Z.

    2009-01-01

    The tensor terms of the Skyrme effective interaction are included in the self-consistent Hartree-Fock plus Random Phase Approximation (HF-RPA) model. The Gamow-Teller (GT) strength functions of 9 0Z r and 2 08P b is calculated with and without the tensor terms. The main peaks are moved downwards by about 2 MeV when including the tensor contribution. About 10% of the non-energy weighted sum rule is shifted to the excitation energy region above 30 MeV by the RPA tensor correlations. The contribution of the tensor terms to the energy weighted sum rule is given analytically, and compared to the outcome of RPA. A microscopic origin of the quenching of GT sum rule due to the tensor force is discussed.(author)

  10. Stress-free states of continuum dislocation fields : Rotations, grain boundaries, and the Nye dislocation density tensor

    NARCIS (Netherlands)

    Limkumnerd, Surachate; Sethna, James P.

    We derive general relations between grain boundaries, rotational deformations, and stress-free states for the mesoscale continuum Nye dislocation density tensor. Dislocations generally are associated with long-range stress fields. We provide the general form for dislocation density fields whose

  11. Tensor Permutation Matrices in Finite Dimensions

    OpenAIRE

    Christian, Rakotonirina

    2005-01-01

    We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...

  12. Vanishing of the vacuum amplitude of heterotic string compactified on a tensor product of N=2 superconformal models

    International Nuclear Information System (INIS)

    Kei Ito.

    1988-07-01

    The vacuum amplitude of heterotic string compactified on a tensor product of nine copies of c=1, N=2 superconformal models is shown to vanish due to a generalized Riemann's theta identity associated with the 12x12 matrix identity t BB=6 2 I 12 , identity B ij =-5(i=j), 1(i≠j). (author). 4 refs

  13. Tensor products of Uq′sl-caret(2)-modules and the big q2-Jacobi function transform

    International Nuclear Information System (INIS)

    Gade, R. M.

    2013-01-01

    Four tensor products of evaluation modules of the quantum affine algebra U q ′ sl-caret(2) obtained from the negative and positive series, the complementary and the strange series representations are investigated. Linear operators R(z) satisfying the intertwining property on finite linear combinations of the canonical basis elements of the tensor products are described in terms of two sets of infinite sums {τ (r,t) } r,t∈Z ≥0 and {τ (r,t) } r,t∈Z ≥0 involving big q 2 -Jacobi functions or related nonterminating basic hypergeometric series. Inhomogeneous recurrence relations can be derived for both sets. Evaluations of the simplest sums provide the corresponding initial conditions. For the first set of sums the relations entail a big q 2 -Jacobi function transform pair. An integral decomposition is obtained for the sum τ (r,t) . A partial description of the relation between the decompositions of the tensor products with respect to U q sl(2) or with respect to its complement in U q ′ sl-caret(2) can be formulated in terms of Askey-Wilson function transforms. For a particular combination of two tensor products, the occurrence of proper U q ′ sl-caret(2)-submodules is discussed.

  14. On the simplest scale invariant tree-tensor-states preserving the quantum symmetries of the antiferromagnetic XXZ chain

    Science.gov (United States)

    Monthus, Cécile

    2018-03-01

    For the line of critical antiferromagnetic XXZ chains with coupling J  >  0 and anisotropy 0<Δ ≤slant 1 , we describe how the block-spin renormalization procedure preserving the SU q (2) symmetry introduced by Martin-Delgado and Sierra (1996 Phys. Rev. Lett. 76 1146) can be reformulated as the translation-invariant scale-invariant tree-tensor-state of the smallest dimension that is compatible with the quantum symmetries of the model. The properties of this tree-tensor-state are studied in detail via the ground-state energy, the magnetizations and the staggered magnetizations, as well as the Shannon-Renyi entropies characterizing the multifractality of the components of the wave function.

  15. Towards an improved duality between tensor network states and AdS spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Papadopoulos, Charalampos; Orus, Roman [Institute of Physics, Johannes Gutenberg University, 55099 Mainz (Germany)

    2016-07-01

    The conjectured AdS/CFT Correspondence, which states that a Conformal Field Theory (CFT) in Minkowski spacetime has a gravity dual in an asymptotically Anti-de Sitter space (AdS), is one of the best understood examples of the holographic principle, and has important applications in condensed matter physics. Tensor Networks (TNs) are a efficient way to calculate low-energy properties for strongly-correlated quantum many-body systems. The Multi-scale Entanglement Renormalization Ansatz (MERA) is a specific TN for a efficient description of critical quantum systems (CFTs). It was recently suggested that the MERA provides naturally a discretization of AdS spacetime on a lattice. It is however known that a conventional MERA can not reproduce the so-called ''Bousso Bound'', also called holographic entropy bound, which is a bound on the bulk entropy in spacetime. In this context, our aim is to generalize the proposed AdS/MERA correspondence to a more general AdS/TN duality, where the Bousso bound is satisfied. Progress in this direction as well as connections to strongly correlated systems will be discussed.

  16. Interplay of tensor correlations and vibrational coupling for single-particle states in atomic nuclei

    International Nuclear Information System (INIS)

    Colo, G.; SAgawa, H.; Bortignon, P. F.

    2009-01-01

    To study the structure of atomic nuclei, the ab-initio methods can nowadays be applied only for mass number A smaller than ∼ 10-15. For heavier systems, the self-consistent mean-field (SCMF) approach is probably the most microscopic approach which can be systematically applied to stable and exotic nuclei. In practice, the SCMF is mostly based on parametrizations of an effective interaction. However, the are groups who are intensively working on the development of a general density functional (DF) which is not necessarily extracted from an Hamiltonian. The basic question is to what extent this allows improving on the existing functionals. In this contribution we analyze the performance of existing functionals as far as the reproduction of single-particle states is concerned. We start by analyzing the effect of the tensor terms, on which the attention of several groups have recently focused. Then we discuss the impact of the particle-vibration coupling (PVC). Although the basic idea of this approach dates back to long time ago, we present here for the first time calculations which are entirely based on microscopic interactions without dropping any term or introducing ad hoc parameters. We show results both for well-known, benchmark nuclei like 4 0C a and 2 08P b as well as unstable nuclei like 1 32S n. Both single-particle energies and spectroscopic factors are discussed.(author)

  17. Tensor spaces and exterior algebra

    CERN Document Server

    Yokonuma, Takeo

    1992-01-01

    This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.

  18. From Product Models to Product State Models

    DEFF Research Database (Denmark)

    Larsen, Michael Holm

    1999-01-01

    A well-known technology designed to handle product data is Product Models. Product Models are in their current form not able to handle all types of product state information. Hence, the concept of a Product State Model (PSM) is proposed. The PSM and in particular how to model a PSM is the Research...

  19. C1 finite elements on non-tensor-product 2d and 3d manifolds

    Science.gov (United States)

    Nguyen, Thien; Karčiauskas, Kęstutis; Peters, Jörg

    2015-01-01

    Geometrically continuous (Gk) constructions naturally yield families of finite elements for isogeometric analysis (IGA) that are Ck also for non-tensor-product layout. This paper describes and analyzes one such concrete C1 geometrically generalized IGA element (short: gIGA element) that generalizes bi-quadratic splines to quad meshes with irregularities. The new gIGA element is based on a recently-developed G1 surface construction that recommends itself by its a B-spline-like control net, low (least) polynomial degree, good shape properties and reproduction of quadratics at irregular (extraordinary) points. Remarkably, for Poisson’s equation on the disk using interior vertices of valence 3 and symmetric layout, we observe O(h3) convergence in the L∞ norm for this family of elements. Numerical experiments confirm the elements to be effective for solving the trivariate Poisson equation on the solid cylinder, deformations thereof (a turbine blade), modeling and computing geodesics on smooth free-form surfaces via the heat equation, for solving the biharmonic equation on the disk and for Koiter-type thin-shell analysis. PMID:26594070

  20. Charmless Hadronic B Decays into Vector, Axial Vector and Tensor Final States at BaBar

    International Nuclear Information System (INIS)

    Gandini, Paolo

    2012-01-01

    We present experimental measurements of branching fraction and longitudinal polarization fraction in charmless hadronic B decays into vector, axial vector and tensor final states with the final dataset of BABAR. Measurements of such kind of decays are a powerful tool both to test the Standard Model and search possible sources of new physics. In this document we present a short review of the last experimental results at BABAR concerning charmless quasi two-body decays in final states containing particles with spin 1 or spin 2 and different parities. This kind of decays has received considerable theoretical interest in the last few years and this particular attention has led to interesting experimental results at the current b-factories. In fact, the study of longitudinal polarization fraction f L in charmless B decays to vector vector (VV), vector axial-vector (VA) and axial-vector axial-vector (AA) mesons provides information on the underlying helicity structure of the decay mechanism. Naive helicity conservation arguments predict a dominant longitudinal polarization fraction f L ∼ 1 for both tree and penguin dominated decays and this pattern seems to be confirmed by tree-dominated B → ρρ and B + → (Omega)ρ + decays. Other penguin dominated decays, instead, show a different behavior: the measured value of f L ∼ 0.5 in B → φK* decays is in contrast with naive Standard Model (SM) calculations. Several solutions have been proposed such as the introduction of non-factorizable terms and penguin-annihilation amplitudes, while other explanations invoke new physics. New modes have been investigated to shed more light on the problem.

  1. Combination of diffusion tensor and functional magnetic resonance imaging during recovery from the vegetative state

    Directory of Open Access Journals (Sweden)

    Fernández-Espejo Davinia

    2010-09-01

    Full Text Available Abstract Background The rate of recovery from the vegetative state (VS is low. Currently, little is known of the mechanisms and cerebral changes that accompany those relatively rare cases of good recovery. Here, we combined functional magnetic resonance imaging (fMRI and diffusion tensor imaging (DTI to study the evolution of one VS patient at one month post-ictus and again twelve months later when he had recovered consciousness. Methods fMRI was used to investigate cortical responses to passive language stimulation as well as task-induced deactivations related to the default-mode network. DTI was used to assess the integrity of the global white matter and the arcuate fasciculus. We also performed a neuropsychological assessment at the time of the second MRI examination in order to characterize the profile of cognitive deficits. Results fMRI analysis revealed anatomically appropriate activation to speech in both the first and the second scans but a reduced pattern of task-induced deactivations in the first scan. In the second scan, following the recovery of consciousness, this pattern became more similar to that classically described for the default-mode network. DTI analysis revealed relative preservation of the arcuate fasciculus and of the global normal-appearing white matter at both time points. The neuropsychological assessment revealed recovery of receptive linguistic functioning by 12-months post-ictus. Conclusions These results suggest that the combination of different structural and functional imaging modalities may provide a powerful means for assessing the mechanisms involved in the recovery from the VS.

  2. Tensor surgery and tensor rank

    NARCIS (Netherlands)

    M. Christandl (Matthias); J. Zuiddam (Jeroen)

    2018-01-01

    textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new vertices

  3. Tensor surgery and tensor rank

    NARCIS (Netherlands)

    M. Christandl (Matthias); J. Zuiddam (Jeroen)

    2016-01-01

    textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new

  4. Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states

    Science.gov (United States)

    Kohn, Lucas; Tschirsich, Ferdinand; Keck, Maximilian; Plenio, Martin B.; Tamascelli, Dario; Montangero, Simone

    2018-01-01

    We provide evidence that randomized low-rank factorization is a powerful tool for the determination of the ground-state properties of low-dimensional lattice Hamiltonians through tensor network techniques. In particular, we show that randomized matrix factorization outperforms truncated singular value decomposition based on state-of-the-art deterministic routines in time-evolving block decimation (TEBD)- and density matrix renormalization group (DMRG)-style simulations, even when the system under study gets close to a phase transition: We report linear speedups in the bond or local dimension of up to 24 times in quasi-two-dimensional cylindrical systems.

  5. Multivariate Hermite interpolation on scattered point sets using tensor-product expo-rational B-splines

    Science.gov (United States)

    Dechevsky, Lubomir T.; Bang, Børre; Laksa˚, Arne; Zanaty, Peter

    2011-12-01

    At the Seventh International Conference on Mathematical Methods for Curves and Surfaces, To/nsberg, Norway, in 2008, several new constructions for Hermite interpolation on scattered point sets in domains in Rn,n∈N, combined with smooth convex partition of unity for several general types of partitions of these domains were proposed in [1]. All of these constructions were based on a new type of B-splines, proposed by some of the authors several years earlier: expo-rational B-splines (ERBS) [3]. In the present communication we shall provide more details about one of these constructions: the one for the most general class of domain partitions considered. This construction is based on the use of two separate families of basis functions: one which has all the necessary Hermite interpolation properties, and another which has the necessary properties of a smooth convex partition of unity. The constructions of both of these two bases are well-known; the new part of the construction is the combined use of these bases for the derivation of a new basis which enjoys having all above-said interpolation and unity partition properties simultaneously. In [1] the emphasis was put on the use of radial basis functions in the definitions of the two initial bases in the construction; now we shall put the main emphasis on the case when these bases consist of tensor-product B-splines. This selection provides two useful advantages: (A) it is easier to compute higher-order derivatives while working in Cartesian coordinates; (B) it becomes clear that this construction becomes a far-going extension of tensor-product constructions. We shall provide 3-dimensional visualization of the resulting bivariate bases, using tensor-product ERBS. In the main tensor-product variant, we shall consider also replacement of ERBS with simpler generalized ERBS (GERBS) [2], namely, their simplified polynomial modifications: the Euler Beta-function B-splines (BFBS). One advantage of using BFBS instead of ERBS

  6. Bivariate tensor product ( p , q $(p, q$ -analogue of Kantorovich-type Bernstein-Stancu-Schurer operators

    Directory of Open Access Journals (Sweden)

    Qing-Bo Cai

    2017-11-01

    Full Text Available Abstract In this paper, we construct a bivariate tensor product generalization of Kantorovich-type Bernstein-Stancu-Schurer operators based on the concept of ( p , q $(p, q$ -integers. We obtain moments and central moments of these operators, give the rate of convergence by using the complete modulus of continuity for the bivariate case and estimate a convergence theorem for the Lipschitz continuous functions. We also give some graphs and numerical examples to illustrate the convergence properties of these operators to certain functions.

  7. The Boolean Algebra of Cubical Areas as a Tensor Product in the Category of Semilattices with Zero

    Directory of Open Access Journals (Sweden)

    Nicolas Ninin

    2014-10-01

    Full Text Available In this paper we describe a model of concurrency together with an algebraic structure reflecting the parallel composition. For the sake of simplicity we restrict to linear concurrent programs i.e. the ones with no loops nor branching. Such programs are given a semantics using cubical areas. Such a semantics is said to be geometric. The collection of all these cubical areas enjoys a structure of tensor product in the category of semi-lattice with zero. These results naturally extend to fully fledged concurrent programs up to some technical tricks.

  8. Graded tensor calculus

    International Nuclear Information System (INIS)

    Scheunert, M.

    1982-10-01

    We develop a graded tensor calculus corresponding to arbitrary Abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the transpose, adjoint, and trace of a linear mapping, are generalized to the graded case and a multitude of canonical isomorphisms is presented. Moreover, the graded versions of the classical Lie algebras are introduced and some of their basic properties are described. (orig.)

  9. Can we see scalar, pseudoscalar or tensor interactions in coherent pion production?

    International Nuclear Information System (INIS)

    Rein, D.

    1988-01-01

    The possibility to detect nonconventional scalar, pseudoscalar or tensor interactions (SPT) in the angular distribution of pions produced coherently in neutrino nucleus reactions is reexamined. It is found that the angular distribution does not differ qualitatively from a corresponding distribution arising from conventional vector-axial vector (VA) interactions unless the energy of the outgoing pion is restricted. Even then SPT interactions are likely to be overshadowed by transverse VA interactions which can mimic the former at finite although small momentum transfer Q 2 . (author)

  10. A non-statistical regularization approach and a tensor product decomposition method applied to complex flow data

    Science.gov (United States)

    von Larcher, Thomas; Blome, Therese; Klein, Rupert; Schneider, Reinhold; Wolf, Sebastian; Huber, Benjamin

    2016-04-01

    Handling high-dimensional data sets like they occur e.g. in turbulent flows or in multiscale behaviour of certain types in Geosciences are one of the big challenges in numerical analysis and scientific computing. A suitable solution is to represent those large data sets in an appropriate compact form. In this context, tensor product decomposition methods currently emerge as an important tool. One reason is that these methods often enable one to attack high-dimensional problems successfully, another that they allow for very compact representations of large data sets. We follow the novel Tensor-Train (TT) decomposition method to support the development of improved understanding of the multiscale behavior and the development of compact storage schemes for solutions of such problems. One long-term goal of the project is the construction of a self-consistent closure for Large Eddy Simulations (LES) of turbulent flows that explicitly exploits the tensor product approach's capability of capturing self-similar structures. Secondly, we focus on a mixed deterministic-stochastic subgrid scale modelling strategy currently under development for application in Finite Volume Large Eddy Simulation (LES) codes. Advanced methods of time series analysis for the databased construction of stochastic models with inherently non-stationary statistical properties and concepts of information theory based on a modified Akaike information criterion and on the Bayesian information criterion for the model discrimination are used to construct surrogate models for the non-resolved flux fluctuations. Vector-valued auto-regressive models with external influences form the basis for the modelling approach [1], [2], [4]. Here, we present the reconstruction capabilities of the two modeling approaches tested against 3D turbulent channel flow data computed by direct numerical simulation (DNS) for an incompressible, isothermal fluid at Reynolds number Reτ = 590 (computed by [3]). References [1] I

  11. Tensor Train Neighborhood Preserving Embedding

    Science.gov (United States)

    Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

    2018-05-01

    In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.

  12. Tensors, relativity, and cosmology

    CERN Document Server

    Dalarsson, Mirjana

    2015-01-01

    Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in m...

  13. Tensor-based spatiotemporal saliency detection

    Science.gov (United States)

    Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen

    2018-03-01

    This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.

  14. Matrix product state description of Halperin states

    Science.gov (United States)

    Crépel, V.; Estienne, B.; Bernevig, B. A.; Lecheminant, P.; Regnault, N.

    2018-04-01

    Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact matrix product state (MPS) that was extensively studied for the systems without any spin or any other internal degrees of freedom. In that case, the correlators are built from a single electronic operator, which is primary with respect to the underlying conformal field theory. We generalize this construction to the archetype of Abelian multicomponent fractional quantum Hall wave functions, the Halperin states. These can be written as conformal blocks involving multiple electronic operators and we explicitly derive their exact MPS representation. In particular, we deal with the caveat of the full wave-function symmetry and show that any additional SU(2) symmetry is preserved by the natural MPS truncation scheme provided by the conformal dimension. We use our method to characterize the topological order of the Halperin states by extracting the topological entanglement entropy. We also evaluate their bulk correlation lengths, which are compared to plasma analogy arguments.

  15. Multiscale entropy analysis of resting-state magnetoencephalogram with tensor factorisations in Alzheimer's disease

    DEFF Research Database (Denmark)

    Escudero, Javier; Evrim, Acar Ataman; Fernández, Alberto

    2015-01-01

    dynamics. We consider the "refined composite multiscale entropy" (rcMSE), which computes entropy "profiles" showing levels of physiological complexity over temporal scales for individual signals. We compute the rcMSE of resting-state magnetoencephalogram (MEG) recordings from 36 patients with Alzheimer...

  16. Measurements of relative chemical shift tensor orientations in solid-state NMR: new slow magic angle spinning dipolar recoupling experiments.

    Science.gov (United States)

    Jurd, Andrew P S; Titman, Jeremy J

    2009-08-28

    Solid-state NMR experiments can be used to determine conformational parameters, such as interatomic distances and torsion angles. The latter can be obtained from measurements of the relative orientation of two chemical shift tensors, if the orientation of these with respect to the surrounding bonds is known. In this paper, a new rotor-synchronized magic angle spinning (MAS) dipolar correlation experiment is described which can be used in this way. Because the experiment requires slow MAS rates, a novel recoupling sequence, designed using symmetry principles, is incorporated into the mixing period. This recoupling sequence is based in turn on a new composite cyclic pulse referred to as COAST (for combined offset and anisotropy stabilization). The new COAST-C7(2)(1) sequence is shown to give good theoretical and experimental recoupling efficiency, even when the CSA far exceeds the MAS rate. In this regime, previous recoupling sequences, such as POST-C7(2)(1), exhibit poor recoupling performance. The effectiveness of the new method has been explored by a study of the dipeptide L-phenylalanyl-L-phenylalanine.

  17. The temperature dependence of the chiral condensate in the Schwinger model with Matrix Product States

    International Nuclear Information System (INIS)

    Saito, H; Jansen, K.; Cichy, K.; Frankfurt Univ.; Poznan Univ.

    2014-12-01

    We present our recent results for the tensor network (TN) approach to lattice gauge theories. TN methods provide an efficient approximation for quantum many-body states. We employ TN for one dimensional systems, Matrix Product States, to investigate the 1-flavour Schwinger model. In this study, we compute the chiral condensate at finite temperature. From the continuum extrapolation, we obtain the chiral condensate in the high temperature region consistent with the analytical calculation by Sachs and Wipf.

  18. Real-time image-based B-mode ultrasound image simulation of needles using tensor-product interpolation.

    Science.gov (United States)

    Zhu, Mengchen; Salcudean, Septimiu E

    2011-07-01

    In this paper, we propose an interpolation-based method for simulating rigid needles in B-mode ultrasound images in real time. We parameterize the needle B-mode image as a function of needle position and orientation. We collect needle images under various spatial configurations in a water-tank using a needle guidance robot. Then we use multidimensional tensor-product interpolation to simulate images of needles with arbitrary poses and positions using collected images. After further processing, the interpolated needle and seed images are superimposed on top of phantom or tissue image backgrounds. The similarity between the simulated and the real images is measured using a correlation metric. A comparison is also performed with in vivo images obtained during prostate brachytherapy. Our results, carried out for both the convex (transverse plane) and linear (sagittal/para-sagittal plane) arrays of a trans-rectal transducer indicate that our interpolation method produces good results while requiring modest computing resources. The needle simulation method we present can be extended to the simulation of ultrasound images of other wire-like objects. In particular, we have shown that the proposed approach can be used to simulate brachytherapy seeds.

  19. State Support of Domestic Production

    Energy Technology Data Exchange (ETDEWEB)

    Amy Wright

    2007-12-30

    This project was developed in response to a cooperative agreement offering by the U.S. Department of Energy (DOE) and the National Energy Technology Laboratory (NETL) under the State Support of Domestic Production DE-FC26-04NT15456. The Interstate Oil and Gas Compact Commission (IOGCC) performed efforts in support of State programs related to the security, reliability and growth if our nation's domestic production of oil and natural gas. The project objectives were to improve the States ability to monitor the security of oil and gas operations; to maximize the production of domestic oil and natural gas thereby minimizing the threat to national security posed by interruptions in energy imports; to assist States in developing and maintaining high standards of environmental protection; to assist in addressing issues that limit the capacity of the industry; to promote the deployment of the appropriate application of technology for regulatory efficiency; and to inform the public about emerging energy issues.

  20. Tensor Transpose and Its Properties

    OpenAIRE

    Pan, Ran

    2014-01-01

    Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are studied in relation to tensor multiplication, tensor eigenvalues, tensor decompositions and tensor rank.

  1. Tensor decomposition-based unsupervised feature extraction applied to matrix products for multi-view data processing

    Science.gov (United States)

    2017-01-01

    In the current era of big data, the amount of data available is continuously increasing. Both the number and types of samples, or features, are on the rise. The mixing of distinct features often makes interpretation more difficult. However, separate analysis of individual types requires subsequent integration. A tensor is a useful framework to deal with distinct types of features in an integrated manner without mixing them. On the other hand, tensor data is not easy to obtain since it requires the measurements of huge numbers of combinations of distinct features; if there are m kinds of features, each of which has N dimensions, the number of measurements needed are as many as Nm, which is often too large to measure. In this paper, I propose a new method where a tensor is generated from individual features without combinatorial measurements, and the generated tensor was decomposed back to matrices, by which unsupervised feature extraction was performed. In order to demonstrate the usefulness of the proposed strategy, it was applied to synthetic data, as well as three omics datasets. It outperformed other matrix-based methodologies. PMID:28841719

  2. Singular Poisson tensors

    International Nuclear Information System (INIS)

    Littlejohn, R.G.

    1982-01-01

    The Hamiltonian structures discovered by Morrison and Greene for various fluid equations were obtained by guessing a Hamiltonian and a suitable Poisson bracket formula, expressed in terms of noncanonical (but physical) coordinates. In general, such a procedure for obtaining a Hamiltonian system does not produce a Hamiltonian phase space in the usual sense (a symplectic manifold), but rather a family of symplectic manifolds. To state the matter in terms of a system with a finite number of degrees of freedom, the family of symplectic manifolds is parametrized by a set of Casimir functions, which are characterized by having vanishing Poisson brackets with all other functions. The number of independent Casimir functions is the corank of the Poisson tensor J/sup ij/, the components of which are the Poisson brackets of the coordinates among themselves. Thus, these Casimir functions exist only when the Poisson tensor is singular

  3. On the SU2 unit tensor

    International Nuclear Information System (INIS)

    Kibler, M.; Grenet, G.

    1979-07-01

    The SU 2 unit tensor operators tsub(k,α) are studied. In the case where the spinor point group G* coincides with U 1 , then tsub(k α) reduces up to a constant to the Wigner-Racah-Schwinger tensor operator tsub(kqα), an operator which produces an angular momentum state. One first investigates those general properties of tsub(kα) which are independent of their realization. The tsub(kα) in terms of two pairs of boson creation and annihilation operators are realized. This leads to look at the Schwinger calculus relative to one angular momentum of two coupled angular momenta. As a by-product, a procedure is given for producing recursion relationships between SU 2 Wigner coefficients. Finally, some of the properties of the Wigner and Racah operators for an arbitrary compact group and the SU 2 coupling coefficients are studied

  4. A new derivation of the plasma susceptibility tensor for a hot magnetized plasma without infinite sums of products of Bessel functions

    International Nuclear Information System (INIS)

    Qin Hong; Phillips, Cynthia K.; Davidson, Ronald C.

    2007-01-01

    The susceptibility tensor of a hot, magnetized plasma is conventionally expressed in terms of infinite sums of products of Bessel functions. For applications where the particle's gyroradius is larger than the wavelength, such as alpha particle dynamics interacting with lower-hybrid waves, and the focusing of charged particle beams using a solenoidal field, the infinite sums converge slowly. In this paper, a new derivation of the plasma susceptibility tensor is presented which exploits a symmetry in the particle's orbit to simplify the integration along the unperturbed trajectories. As a consequence, the infinite sums appearing in the conventional expression are replaced by definite double integrals over one gyroperiod, and the cyclotron resonances of all orders are captured by a single term. Furthermore, the double integrals can be carried out and expressed in terms of Bessel functions of complex order, in agreement with expressions deduced previously using the Newburger sum rule. From this new formulation, it is straightforward to derive the asymptotic form of the full hot plasma susceptibility tensor for a gyrotropic but otherwise arbitrary plasma distribution in the large gyroradius limit. These results are of more general importance in the numerical evaluation of the plasma susceptibility tensor. Instead of using the infinite sums occurring in the conventional expression, it is only necessary to evaluate the Bessel functions once according to the new expression, which has significant advantages, especially when the particle's gyroradius is large and the conventional infinite sums converge slowly. Depending on the size of the gyroradius, the computational saving enabled by this representation can be several orders-of-magnitude

  5. Shape anisotropy: tensor distance to anisotropy measure

    Science.gov (United States)

    Weldeselassie, Yonas T.; El-Hilo, Saba; Atkins, M. S.

    2011-03-01

    Fractional anisotropy, defined as the distance of a diffusion tensor from its closest isotropic tensor, has been extensively studied as quantitative anisotropy measure for diffusion tensor magnetic resonance images (DT-MRI). It has been used to reveal the white matter profile of brain images, as guiding feature for seeding and stopping in fiber tractography and for the diagnosis and assessment of degenerative brain diseases. Despite its extensive use in DT-MRI community, however, not much attention has been given to the mathematical correctness of its derivation from diffusion tensors which is achieved using Euclidean dot product in 9D space. But, recent progress in DT-MRI has shown that the space of diffusion tensors does not form a Euclidean vector space and thus Euclidean dot product is not appropriate for tensors. In this paper, we propose a novel and robust rotationally invariant diffusion anisotropy measure derived using the recently proposed Log-Euclidean and J-divergence tensor distance measures. An interesting finding of our work is that given a diffusion tensor, its closest isotropic tensor is different for different tensor distance metrics used. We demonstrate qualitatively that our new anisotropy measure reveals superior white matter profile of DT-MR brain images and analytically show that it has a higher signal to noise ratio than fractional anisotropy.

  6. Tensors for physics

    CERN Document Server

    Hess, Siegfried

    2015-01-01

    This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics,  at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to  tensors of any rank, at graduate level.  Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-...

  7. Random tensors

    CERN Document Server

    Gurau, Razvan

    2017-01-01

    Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another....

  8. Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor

    International Nuclear Information System (INIS)

    Senovilla, Jose M M

    2010-01-01

    The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved. (fast track communication)

  9. Should I use TensorFlow

    OpenAIRE

    Schrimpf, Martin

    2016-01-01

    Google's Machine Learning framework TensorFlow was open-sourced in November 2015 [1] and has since built a growing community around it. TensorFlow is supposed to be flexible for research purposes while also allowing its models to be deployed productively. This work is aimed towards people with experience in Machine Learning considering whether they should use TensorFlow in their environment. Several aspects of the framework important for such a decision are examined, such as the heterogenity,...

  10. The mass spectrum of the Schwinger model with matrix product states

    Energy Technology Data Exchange (ETDEWEB)

    Banuls, M.C.; Cirac, J.I. [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Poznan Univ. (Poland). Faculty of Physics; Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Cyprus Univ., Nicosia (Cyprus). Dept. of Physics

    2013-07-15

    We show the feasibility of tensor network solutions for lattice gauge theories in Hamiltonian formulation by applying matrix product states algorithms to the Schwinger model with zero and non-vanishing fermion mass. We introduce new techniques to compute excitations in a system with open boundary conditions, and to identify the states corresponding to low momentum and different quantum numbers in the continuum. For the ground state and both the vector and scalar mass gaps in the massive case, the MPS technique attains precisions comparable to the best results available from other techniques.

  11. Mississippi State Biodiesel Production Project

    Energy Technology Data Exchange (ETDEWEB)

    Rafael Hernandez; Todd French; Sandun Fernando; Tingyu Li; Dwane Braasch; Juan Silva; Brian Baldwin

    2008-03-20

    Biodiesel is a renewable fuel conventionally generated from vegetable oils and animal fats that conforms to ASTM D6751. Depending on the free fatty acid content of the feedstock, biodiesel is produced via transesterification, esterification, or a combination of these processes. Currently the cost of the feedstock accounts for more than 80% of biodiesel production cost. The main goal of this project was to evaluate and develop non-conventional feedstocks and novel processes for producing biodiesel. One of the most novel and promising feedstocks evaluated involves the use of readily available microorganisms as a lipid source. Municipal wastewater treatment facilities (MWWTF) in the USA produce (dry basis) of microbial sludge annually. This sludge is composed of a variety of organisms, which consume organic matter in wastewater. The content of phospholipids in these cells have been estimated at 24% to 25% of dry mass. Since phospholipids can be transesterified they could serve as a ready source of biodiesel. Examination of the various transesterification methods shows that in situ conversion of lipids to FAMEs provides the highest overall yield of biodiesel. If one assumes a 7.0% overall yield of FAMEs from dry sewage sludge on a weight basis, the cost per gallon of extracted lipid would be $3.11. Since the lipid is converted to FAMEs, also known as biodiesel, in the in Situ extraction process, the product can be used as is for renewable fuel. As transesterification efficiency increases the cost per gallon drops quickly, hitting $2.01 at 15.0% overall yield. An overall yield of 10.0% is required to obtain biodiesel at $2.50 per gallon, allowing it to compete with soybean oil in the marketplace. Twelve plant species with potential for oil production were tested at Mississippi State, MS. Of the species tested, canola, rapeseed and birdseed rape appear to have potential in Mississippi as winter annual crops because of yield. Two perennial crops were investigated, Chinese

  12. Tensor Network Quantum Virtual Machine (TNQVM)

    Energy Technology Data Exchange (ETDEWEB)

    2016-11-18

    There is a lack of state-of-the-art quantum computing simulation software that scales on heterogeneous systems like Titan. Tensor Network Quantum Virtual Machine (TNQVM) provides a quantum simulator that leverages a distributed network of GPUs to simulate quantum circuits in a manner that leverages recent results from tensor network theory.

  13. Tensor gauge condition and tensor field decomposition

    Science.gov (United States)

    Zhu, Ben-Chao; Chen, Xiang-Song

    2015-10-01

    We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.

  14. Tensor eigenvalues and their applications

    CERN Document Server

    Qi, Liqun; Chen, Yannan

    2018-01-01

    This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.

  15. Harmonic d-tensors

    Energy Technology Data Exchange (ETDEWEB)

    Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)

    2016-07-01

    Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.

  16. Transfer matrices and excitations with matrix product states

    International Nuclear Information System (INIS)

    Zauner, V; Rams, M M; Verstraete, F; Draxler, D; Vanderstraeten, L; Degroote, M; Haegeman, J; Stojevic, V; Schuch, N

    2015-01-01

    We use the formalism of tensor network states to investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low-energy excitations. In particular, we show that the matrix product state transfer matrix (MPS-TM)—a central object in the computation of static correlation functions—provides important information about the location and magnitude of the minima of the low-energy dispersion relation(s), and we present supporting numerical data for one-dimensional lattice and continuum models as well as two-dimensional lattice models on a cylinder. We elaborate on the peculiar structure of the MPS-TM’s eigenspectrum and give several arguments for the close relation between the structure of the low-energy spectrum of the system and the form of the static correlation functions. Finally, we discuss how the MPS-TM connects to the exact quantum transfer matrix of the model at zero temperature. We present a renormalization group argument for obtaining finite bond dimension approximations of the MPS, which allows one to reinterpret variational MPS techniques (such as the density matrix renormalization group) as an application of Wilson’s numerical renormalization group along the virtual (imaginary time) dimension of the system. (paper)

  17. Monograph On Tensor Notations

    Science.gov (United States)

    Sirlin, Samuel W.

    1993-01-01

    Eight-page report describes systems of notation used most commonly to represent tensors of various ranks, with emphasis on tensors in Cartesian coordinate systems. Serves as introductory or refresher text for scientists, engineers, and others familiar with basic concepts of coordinate systems, vectors, and partial derivatives. Indicial tensor, vector, dyadic, and matrix notations, and relationships among them described.

  18. Pulpwood Production in the Lake States

    Science.gov (United States)

    James E. Blyth; Jerold T. Hahn

    1977-01-01

    This 31st annual report shows 1976 pulpwood production by county and species group in Michigan, Minnesota, and Wisconsin. Production in these three Lake States climbed to 4.7 million cords from 4.1 million cords in 1975

  19. Confinement through tensor gauge fields

    International Nuclear Information System (INIS)

    Salam, A.; Strathdee, J.

    1977-12-01

    Using the 0(3,2)-symmetric de Sitter solution of Einstein's equation describing a strongly interacting tensor field it is shown that hadronic bags confining quarks can be represented as de Sitter ''micro-universes'' with radii given 1/R 2 =lambdak 2 /6. Here k 2 and lambda are the strong coupling and the ''cosmological'' constant which apear in the Einstein equation used. Surprisingly the energy spectrum for the two-body hadronic states is the same as that for a harmonic oscillator potential, though the wave functions are completely different. The Einstein equation can be extended to include colour for the tensor fields

  20. Extremum uncertainty product and sum states

    Energy Technology Data Exchange (ETDEWEB)

    Mehta, C L; Kumar, S [Indian Inst. of Tech., New Delhi. Dept. of Physics

    1978-01-01

    The extremum product states and sum states of the uncertainties in non-commuting observables have been examined. These are illustrated by two specific examples of harmonic oscillator and the angular momentum states. It shows that the coherent states of the harmonic oscillator are characterized by the minimum uncertainty sum <(..delta..q)/sup 2/>+<(..delta..p)/sup 2/>. The extremum values of the sums and products of the uncertainties of the components of the angular momentum are also obtained.

  1. Bowen-York tensors

    International Nuclear Information System (INIS)

    Beig, Robert; Krammer, Werner

    2004-01-01

    For a conformally flat 3-space, we derive a family of linear second-order partial differential operators which sends vectors into trace-free, symmetric 2-tensors. These maps, which are parametrized by conformal Killing vectors on the 3-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular, these maps send source-free electric fields into TT tensors. Moreover, if the original vector field is the Coulomb field on R 3 {0}, the resulting tensor fields on R 3 {0} are nothing but the family of TT tensors originally written by Bowen and York

  2. Ab initio potential energy surface, electric-dipole moment, polarizability tensor, and theoretical rovibrational spectra in the electronic ground state of {sup 14}NH{sub 3}{sup +}

    Energy Technology Data Exchange (ETDEWEB)

    Yurchenko, Sergei N. [Technische Universitaet Dresden, Institut fuer Physikalische Chemie und Elektrochemie, D-01062 Dresden (Germany); Thiel, Walter [Max-Planck-Institut fuer Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Muelheim an der Ruhr (Germany); Carvajal, Miguel [Departamento de Fisica Aplicada, Facultad de Ciencias Experimentales, Avenida de las Fuerzas Armadas s/n, Universidad de Huelva, E-21071 Huelva (Spain); Jensen, Per [Theoretische Chemie, Bergische Universitaet, D-42097 Wuppertal (Germany)], E-mail: jensen@uni-wuppertal.de

    2008-05-04

    We report the calculation of a six-dimensional CCSD(T)/aug-cc-pVQZ potential energy surface for the electronic ground state of NH{sub 3}{sup +} together with the corresponding CCSD(T)/aug-cc-pVTZ dipole moment and polarizability surface of {sup 14}NH{sub 3}{sup +}. These electronic properties have been computed on a large grid of molecular geometries. A number of newly calculated band centers are presented along with the associated electric-dipole transition moments. We further report the first calculation of vibrational matrix elements of the polarizability tensor components for {sup 14}NH{sub 3}{sup +}; these matrix elements determine the intensities of Raman transitions. In addition, the rovibrational absorption spectra of the {nu}{sub 2}, {nu}{sub 3}, {nu}{sub 4}, 2{nu}{sub 2}-{nu}{sub 2}, and {nu}{sub 2}+{nu}{sub 3}-{nu}{sub 2} bands have been simulated.

  3. Estimating state-contingent production functions

    DEFF Research Database (Denmark)

    Rasmussen, Svend; Karantininis, Kostas

    The paper reviews the empirical problem of estimating state-contingent production functions. The major problem is that states of nature may not be registered and/or that the number of observation per state is low. Monte Carlo simulation is used to generate an artificial, uncertain production...... environment based on Cobb Douglas production functions with state-contingent parameters. The pa-rameters are subsequently estimated based on different sizes of samples using Generalized Least Squares and Generalized Maximum Entropy and the results are compared. It is concluded that Maximum Entropy may...

  4. Local cloning of two product states

    International Nuclear Information System (INIS)

    Ji Zhengfeng; Feng Yuan; Ying Mingsheng

    2005-01-01

    Local quantum operations and classical communication (LOCC) put considerable constraints on many quantum information processing tasks such as cloning and discrimination. Surprisingly, however, discrimination of any two pure states survives such constraints in some sense. We show that cloning is not that lucky; namely, probabilistic LOCC cloning of two product states is strictly less efficient than global cloning. We prove our result by giving explicitly the efficiency formula of local cloning of any two product states

  5. Estimating GSP and labor productivity by state

    OpenAIRE

    Paul W. Bauer; Yoonsoo Lee

    2006-01-01

    In gauging the health of state economies, arguably the two most important series to track are employment and output. While employment by state is available about three weeks after the end of a month, data on output, as measured by Gross State Product (GSP), are only available annually and with a significant lag. This Policy Discussion Paper details how more current estimates of GSP can be generated using U.S. Gross Domestic Product and personal income along with individual states’ personal in...

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

    International Nuclear Information System (INIS)

    Adler, Stephen L

    2007-01-01

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

  7. A recursive reduction of tensor Feynman integrals

    International Nuclear Information System (INIS)

    Diakonidis, T.; Riemann, T.; Tausk, J.B.; Fleischer, J.

    2009-07-01

    We perform a recursive reduction of one-loop n-point rank R tensor Feynman integrals [in short: (n,R)-integrals] for n≤6 with R≤n by representing (n,R)-integrals in terms of (n,R-1)- and (n-1,R-1)-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, we find the recursive reduction for the tensors. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories. (orig.)

  8. Entanglement in Gaussian matrix-product states

    International Nuclear Information System (INIS)

    Adesso, Gerardo; Ericsson, Marie

    2006-01-01

    Gaussian matrix-product states are obtained as the outputs of projection operations from an ancillary space of M infinitely entangled bonds connecting neighboring sites, applied at each of N sites of a harmonic chain. Replacing the projections by associated Gaussian states, the building blocks, we show that the entanglement range in translationally invariant Gaussian matrix-product states depends on how entangled the building blocks are. In particular, infinite entanglement in the building blocks produces fully symmetric Gaussian states with maximum entanglement range. From their peculiar properties of entanglement sharing, a basic difference with spin chains is revealed: Gaussian matrix-product states can possess unlimited, long-range entanglement even with minimum number of ancillary bonds (M=1). Finally we discuss how these states can be experimentally engineered from N copies of a three-mode building block and N two-mode finitely squeezed states

  9. Density induced phase transitions in the Schwinger model. A study with matrix product states

    Energy Technology Data Exchange (ETDEWEB)

    Banuls, Mari Carmen; Cirac, J. Ignacio; Kuehn, Stefan [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

    2017-02-15

    We numerically study the zero temperature phase structure of the multiflavor Schwinger model at nonzero chemical potential. Using matrix product states, we reproduce analytical results for the phase structure for two flavors in the massless case and extend the computation to the massive case, where no analytical predictions are available. Our calculations allow us to locate phase transitions in the mass-chemical potential plane with great precision and provide a concrete example of tensor networks overcoming the sign problem in a lattice gauge theory calculation.

  10. Cartesian tensors an introduction

    CERN Document Server

    Temple, G

    2004-01-01

    This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t

  11. Efficient MATLAB computations with sparse and factored tensors.

    Energy Technology Data Exchange (ETDEWEB)

    Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)

    2006-12-01

    In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.

  12. Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI

    Science.gov (United States)

    Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.

    2015-01-01

    Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085

  13. Productivity growth in food crop production in Imo State, Nigeria ...

    African Journals Online (AJOL)

    Agriculture plays pivotal roles in Nigeria including food security, employment, foreign exchange earnings and poverty reduction. This study examined the growth in food crop productivity in Imo State in Nigeria with emphasis on the decomposition of total factor productivity (TFP) into technical progress, changes in technical ...

  14. Characterizing locally distinguishable orthogonal product states

    OpenAIRE

    Feng, Yuan; Shi, Yaoyun

    2007-01-01

    Bennett et al. \\cite{BDF+99} identified a set of orthogonal {\\em product} states in the $3\\otimes 3$ Hilbert space such that reliably distinguishing those states requires non-local quantum operations. While more examples have been found for this counter-intuitive ``nonlocality without entanglement'' phenomenon, a complete and computationally verifiable characterization for all such sets of states remains unknown. In this Letter, we give such a characterization for the $3\\otimes 3$ space.

  15. Improved tensor multiplets

    International Nuclear Information System (INIS)

    Wit, B. de; Rocek, M.

    1982-01-01

    We construct a conformally invariant theory of the N = 1 supersymmetric tensor gauge multiplet and discuss the situation in N = 2. We show that our results give rise to the recently proposed variant of Poincare supergravity, and provide the complete tensor calculus for the theory. Finally, we argue that this theory cannot be quantized sensibly. (orig.)

  16. A Tour of TensorFlow

    OpenAIRE

    Goldsborough, Peter

    2016-01-01

    Deep learning is a branch of artificial intelligence employing deep neural network architectures that has significantly advanced the state-of-the-art in computer vision, speech recognition, natural language processing and other domains. In November 2015, Google released $\\textit{TensorFlow}$, an open source deep learning software library for defining, training and deploying machine learning models. In this paper, we review TensorFlow and put it in context of modern deep learning concepts and ...

  17. Quantum mechanics of Yano tensors: Dirac equation in curved spacetime

    International Nuclear Information System (INIS)

    Cariglia, Marco

    2004-01-01

    In spacetimes admitting Yano tensors, the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank 2, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors

  18. Tensor-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics.

    Science.gov (United States)

    Greene, Samuel M; Batista, Victor S

    2017-09-12

    We introduce the "tensor-train split-operator Fourier transform" (TT-SOFT) method for simulations of multidimensional nonadiabatic quantum dynamics. TT-SOFT is essentially the grid-based SOFT method implemented in dynamically adaptive tensor-train representations. In the same spirit of all matrix product states, the tensor-train format enables the representation, propagation, and computation of observables of multidimensional wave functions in terms of the grid-based wavepacket tensor components, bypassing the need of actually computing the wave function in its full-rank tensor product grid space. We demonstrate the accuracy and efficiency of the TT-SOFT method as applied to propagation of 24-dimensional wave packets, describing the S 1 /S 2 interconversion dynamics of pyrazine after UV photoexcitation to the S 2 state. Our results show that the TT-SOFT method is a powerful computational approach for simulations of quantum dynamics of polyatomic systems since it avoids the exponential scaling problem of full-rank grid-based representations.

  19. Product quality of parenteral vancomycin products in the United States.

    Science.gov (United States)

    Nambiar, S; Madurawe, R D; Zuk, S M; Khan, S R; Ellison, C D; Faustino, P J; Mans, D J; Trehy, M L; Hadwiger, M E; Boyne, M T; Biswas, K; Cox, E M

    2012-06-01

    In response to concerns raised about the quality of parenteral vancomycin products, the U.S. Food and Drug Administration (FDA) is investigating the product quality of all FDA-approved parenteral vancomycin products available in the United States. Product quality was evaluated independently at two FDA Office of Testing and Research (FDA-OTR) sites. In the next phase of the investigation, being done in collaboration with the National Institute of Allergy and Infectious Diseases, the in vivo activity of these products will be evaluated in an appropriate animal model. This paper summarizes results of the FDA investigation completed thus far. One site used a validated ultrahigh-pressure liquid chromatography method (OTR-UPLC), and the second site used the high-performance liquid chromatography (HPLC) method for related substances provided in the British Pharmacopeia (BP) monograph for vancomycin intravenous infusion. Similar results were obtained by the two FDA-OTR laboratories using two different analytical methods. The products tested had 90 to 95% vancomycin B (active component of vancomycin) by the BP-HPLC method and 89 to 94% vancomycin by OTR-UPLC methods. Total impurities were 5 to 10% by BP-HPLC and 6 to 11% by OTR-UPLC methods. No single impurity was >2.0%, and the CDP-1 level was ≤ 2.0% across all products. Some variability in impurity profiles of the various products was observed. No adverse product quality issues were identified with the six U.S. vancomycin parenteral products. The quality parameters of all parenteral vancomycin products tested surpassed the United States Pharmacopeia acceptance criteria. Additional testing will characterize in vivo performance characteristics of these products.

  20. Calculus of tensors and differential forms

    CERN Document Server

    Sinha, Rajnikant

    2014-01-01

    Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.

  1. Tensor spherical harmonics and tensor multipoles. II. Minkowski space

    International Nuclear Information System (INIS)

    Daumens, M.; Minnaert, P.

    1976-01-01

    The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation

  2. Classification of the Ricci and Plebanski tensors in general relativity using Newman--Penrose formalism

    International Nuclear Information System (INIS)

    McIntosh, C.B.G.; Foyster, J.M.; Lun, A.W.h.

    1981-01-01

    A list is given of a canonical set of the Newman--Penrose quantities Phi/sub A/B, the tetrad components of the trace-free Ricci tensor, for each Plebanski class according to Plebanski's classification of this tensor. This comparative list can easily be extended to cover the classification in tetrad language of any second-order, trace-free, symmetric tensor in a space-time. A fourth-order tensor which is the product of two such tensors was defined by Plebanski and used in his classification. This has the same symmetries as the Weyl tensor. The Petrov classification of this tensor, here called the Plebanski tensor, is discussed along with the classification of the Ricci tensor. The use of the Plebanski tensor in a couple of areas of general relativity is also briefly discussed

  3. Complex Kohn variational principle for two-nucleon bound-state and scattering with the tensor potential

    International Nuclear Information System (INIS)

    Araujo Junior, C.F. de; Adhikari, S.K.; Tomio, L.

    1993-10-01

    Complex Kohn variational principle is applied to the numerical solution of the fully off-shell Lippmann-Schwinger equation for nucleon-nucleon scattering for various partial waves including the coupled 3 S 1 - 3 D 1 channel. Analytic expressions are obtained for all the integrals in the method for a suitable choice of expansion functions. Calculations with the partial waves 1 S 0 , 1 P 1 , 1 D 2 , and 3 S 1 - 3 D 1 of the Reid soft core potential show that the method converges faster than other solution schemes not only for the phase shift but also for the off-shell t matrix elements. It is also shown that its is trivial to modify this variational principle in order to make it suitable for bound-stage calculations. The bound-state approach is illustrated for the 3 S 1 - 3 D 1 channel of the Reid soft-core potential for calculating the deuteron binding, wave function and the D state asymptotic parameters. (author)

  4. Tensor network decompositions in the presence of a global symmetry

    International Nuclear Information System (INIS)

    Singh, Sukhwinder; Pfeifer, Robert N. C.; Vidal, Guifre

    2010-01-01

    Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group G, in tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group G. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance in the context of tensor network algorithms as well, thus setting the stage for cross-fertilization between these two areas of research.

  5. Tensors and their applications

    CERN Document Server

    Islam, Nazrul

    2006-01-01

    About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel`s Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci`s Coefficients of Rotation and Congruence Hyper Surfaces

  6. Symmetric Tensor Decomposition

    DEFF Research Database (Denmark)

    Brachat, Jerome; Comon, Pierre; Mourrain, Bernard

    2010-01-01

    We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....

  7. Reconstruction from scalar-tensor theory and the inhomogeneous equation of state in f(T) gravity

    Energy Technology Data Exchange (ETDEWEB)

    Said, Jackson Levi [University of Malta, Institute of Space Sciences and Astronomy, Msida (Malta); University of Malta, Department of Physics, Msida (Malta)

    2017-12-15

    General relativity (GR) characterizes gravity as a geometric properly exhibited as curvature on spacetime. Teleparallelism describes gravity through torsional properties, and can reproduce GR at the level of equations. Similar to f(R) gravity, on taking a generalization, f(T) gravity can produce various modifications its gravitational mechanism. The resulting field equations are inherently distinct to f(R) gravity in that they are second order. In the present work, f(T) gravity is examined in the cosmological context with a number of solutions reconstructed by means of an auxiliary scalar field. To do this, various forms of the Hubble parameter are considered with an f(T) Lagrangian emerging for each instance. In addition, the inhomogeneous equation of state (EoS) is investigated with a particular Hubble parameter model used to show how this can be used to reconstruct the f(T) Lagrangian. Observationally, the auxiliary scalar field and the exotic terms in the FRW field equations give the same results, meaning that the variation in the Hubble parameter may be interpreted as the need to reformulate gravity in some way, as in f(T) gravity. (orig.)

  8. Reconstruction from scalar-tensor theory and the inhomogeneous equation of state in f(T) gravity

    International Nuclear Information System (INIS)

    Said, Jackson Levi

    2017-01-01

    General relativity (GR) characterizes gravity as a geometric properly exhibited as curvature on spacetime. Teleparallelism describes gravity through torsional properties, and can reproduce GR at the level of equations. Similar to f(R) gravity, on taking a generalization, f(T) gravity can produce various modifications its gravitational mechanism. The resulting field equations are inherently distinct to f(R) gravity in that they are second order. In the present work, f(T) gravity is examined in the cosmological context with a number of solutions reconstructed by means of an auxiliary scalar field. To do this, various forms of the Hubble parameter are considered with an f(T) Lagrangian emerging for each instance. In addition, the inhomogeneous equation of state (EoS) is investigated with a particular Hubble parameter model used to show how this can be used to reconstruct the f(T) Lagrangian. Observationally, the auxiliary scalar field and the exotic terms in the FRW field equations give the same results, meaning that the variation in the Hubble parameter may be interpreted as the need to reformulate gravity in some way, as in f(T) gravity. (orig.)

  9. Current density tensors

    Science.gov (United States)

    Lazzeretti, Paolo

    2018-04-01

    It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.

  10. Properties of the tensor correlation in He isotopes

    International Nuclear Information System (INIS)

    Myo, Takayuki; Sugimoto, Satoru; Kato, Kiyoshi; Toki, Hiroshi; Ikeda, Kiyomi

    2006-01-01

    We investigate the roles of the tensor correlation on the structures of 4,5 He. For 4 He, we take the high angular momentum states as much as possible with the 2p2h excitations of the shell model type method to describe the tensor correlation. Three specific configurations are found to be favored for the tensor correlation. This correlation is also important to describe the scattering phenomena of the 4 He+nsystem including the higher partial waves consistently

  11. Sparse tensor spherical harmonics approximation in radiative transfer

    International Nuclear Information System (INIS)

    Grella, K.; Schwab, Ch.

    2011-01-01

    The stationary monochromatic radiative transfer equation is a partial differential transport equation stated on a five-dimensional phase space. To obtain a well-posed problem, boundary conditions have to be prescribed on the inflow part of the domain boundary. We solve the equation with a multi-level Galerkin FEM in physical space and a spectral discretization with harmonics in solid angle and show that the benefits of the concept of sparse tensor products, known from the context of sparse grids, can also be leveraged in combination with a spectral discretization. Our method allows us to include high spectral orders without incurring the 'curse of dimension' of a five-dimensional computational domain. Neglecting boundary conditions, we find analytically that for smooth solutions, the convergence rate of the full tensor product method is retained in our method up to a logarithmic factor, while the number of degrees of freedom grows essentially only as fast as for the purely spatial problem. For the case with boundary conditions, we propose a splitting of the physical function space and a conforming tensorization. Numerical experiments in two physical and one angular dimension show evidence for the theoretical convergence rates to hold in the latter case as well.

  12. A Review of Tensors and Tensor Signal Processing

    Science.gov (United States)

    Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.

    Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.

  13. Quantum Phase Transitions in Matrix Product States

    International Nuclear Information System (INIS)

    Jing-Min, Zhu

    2008-01-01

    We present a new general and much simpler scheme to construct various quantum phase transitions (QPTs) in spin chain systems with matrix product ground states. By use of the scheme we take into account one kind of matrix product state (MPS) QPT and provide a concrete model. We also study the properties of the concrete example and show that a kind of QPT appears, accompanied by the appearance of the discontinuity of the parity absent block physical observable, diverging correlation length only for the parity absent block operator, and other properties which are that the fixed point of the transition point is an isolated intermediate-coupling fixed point of renormalization flow and the entanglement entropy of a half-infinite chain is discontinuous

  14. Quantum phase transitions in matrix product states

    International Nuclear Information System (INIS)

    Zhu Jingmin

    2008-01-01

    We present a new general and much simpler scheme to construct various quantum phase transitions (QPTs) in spin chain systems with matrix product ground states. By use of the scheme we take into account one kind of matrix product state (MPS) QPT and provide a concrete model. We also study the properties of the concrete example and show that a kind of QPT appears, accompanied by the appearance of the discontinuity of the parity absent block physical observable, diverging correlation length only for the parity absent block operator, and other properties which are that the fixed point of the transition point is an isolated intermediate-coupling fixed point of renormalization flow and the entanglement entropy of a half-infinite chain is discontinuous. (authors)

  15. Q-creation and annihilation tensors for the two parameters deformation of U(SU(2))

    International Nuclear Information System (INIS)

    Wehrhahn, R.F.; Vraceanu, D.

    1993-03-01

    The Jordan-Schwinger construction for the Hopf algebra U qp (su(2)) is realized. The creation and annihilation tensor operators together with their tensor products including the Casimir operators are calculated. (orig.)

  16. Decomposition of a symmetric second-order tensor

    Science.gov (United States)

    Heras, José A.

    2018-05-01

    In the three-dimensional space there are different definitions for the dot and cross products of a vector with a second-order tensor. In this paper we show how these products can uniquely be defined for the case of symmetric tensors. We then decompose a symmetric second-order tensor into its ‘dot’ part, which involves the dot product, and the ‘cross’ part, which involves the cross product. For some physical applications, this decomposition can be interpreted as one in which the dot part identifies with the ‘parallel’ part of the tensor and the cross part identifies with the ‘perpendicular’ part. This decomposition of a symmetric second-order tensor may be suitable for undergraduate courses of vector calculus, mechanics and electrodynamics.

  17. Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.

    Science.gov (United States)

    Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben

    2017-08-02

    It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.

  18. An introduction to tensors and group theory for physicists

    CERN Document Server

    Jeevanjee, Nadir

    2011-01-01

    An Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory. Part I of the text begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to classical and quantum physics through the use of tensor products. Part II introduces abstract groups along with matrix Lie groups and Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Exercises and examples are provided throughout for go...

  19. Tensor analysis for physicists

    CERN Document Server

    Schouten, J A

    1989-01-01

    This brilliant study by a famed mathematical scholar and former professor of mathematics at the University of Amsterdam integrates a concise exposition of the mathematical basis of tensor analysis with admirably chosen physical examples of the theory. The first five chapters incisively set out the mathematical theory underlying the use of tensors. The tensor algebra in EN and RN is developed in Chapters I and II. Chapter II introduces a sub-group of the affine group, then deals with the identification of quantities in EN. The tensor analysis in XN is developed in Chapter IV. In chapters VI through IX, Professor Schouten presents applications of the theory that are both intrinsically interesting and good examples of the use and advantages of the calculus. Chapter VI, intimately connected with Chapter III, shows that the dimensions of physical quantities depend upon the choice of the underlying group, and that tensor calculus is the best instrument for dealing with the properties of anisotropic media. In Chapte...

  20. Generalized dielectric permittivity tensor

    International Nuclear Information System (INIS)

    Borzdov, G.N.; Barkovskii, L.M.; Fedorov, F.I.

    1986-01-01

    The authors deal with the question of what is to be done with the formalism of the electrodynamics of dispersive media based on the introduction of dielectric-permittivity tensors for purely harmonic fields when Voigt waves and waves of more general form exist. An attempt is made to broaden and generalize the formalism to take into account dispersion of waves of the given type. In dispersive media, the polarization, magnetization, and conduction current-density vectors of point and time are determined by the values of the electromagnetic field vectors in the vicinity of this point (spatial dispersion) in the preceding instants of time (time dispersion). The dielectric-permittivity tensor and other tensors of electrodynamic parameters of the medium are introduced in terms of a set of evolution operators and not the set of harmonic function. It is noted that a magnetic-permeability tensor and an elastic-modulus tensor may be introduced for an acoustic field in dispersive anisotropic media with coupling equations of general form

  1. The tensor network theory library

    Science.gov (United States)

    Al-Assam, S.; Clark, S. R.; Jaksch, D.

    2017-09-01

    In this technical paper we introduce the tensor network theory (TNT) library—an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The objectives of this paper are (i) to give an overview of the structure of TNT library, and (ii) to help scientists decide whether to use the TNT library in their research. We show how to employ the TNT routines by giving examples of ground-state and dynamical calculations of one-dimensional bosonic lattice system. We also discuss different options for gaining access to the software available at www.tensornetworktheory.org.

  2. Killing tensors and conformal Killing tensors from conformal Killing vectors

    International Nuclear Information System (INIS)

    Rani, Raffaele; Edgar, S Brian; Barnes, Alan

    2003-01-01

    Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors

  3. Tensor Galileons and gravity

    Energy Technology Data Exchange (ETDEWEB)

    Chatzistavrakidis, Athanasios [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Khoo, Fech Scen [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany); Roest, Diederik [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Schupp, Peter [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany)

    2017-03-13

    The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian p-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to p-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.

  4. Empirical logic and tensor products

    International Nuclear Information System (INIS)

    Foulis, D.J.; Randall, C.H.

    1981-01-01

    In our work we are developing a formalism called empirical logic to support a generalization of conventional statistics; the resulting generalization is called operational statistics. We are not attempting to develop or advocate any particular physical theory; rather we are formulating a precision 'language' in which such theories can be expressed, compared, evaluated, and related to laboratory experiments. We believe that only in such a language can the connections between real physical procedures (operations) and physical theories be made explicit and perspicuous. (orig./HSI)

  5. State of the art on bioethanol production

    International Nuclear Information System (INIS)

    Barisano, D.; De Bari, I.; Viola, E.; Zimbardi, F.; Braccio, G.; Cantarella, M.; Gallifuoco, A.

    2001-01-01

    The state of the art, deals with the ethanol production from current processes based on the use of sugar and starch as feedstock and those under development based on lignocellulosic biomass. In the first section are reported the commercially available processes together with hints to the newest technologies. As regard the ethanol production from lignocellulosics, it has been collected data on the biomass availability in Europe as energy crops, industrial crops, agricultural residues and domestic waste. It is provided a bibliographic study on the technologies and processes under development worldwide for the conversion of lignocellulosics into ethanol. Finally, a brief discussion on the economics highlights the near term viability of producing ethanol by this way [it

  6. How Glassy States Affect Brown Carbon Production?

    Science.gov (United States)

    Liu, P.; Li, Y.; Wang, Y.; Bateman, A. P.; Zhang, Y.; Gong, Z.; Gilles, M. K.; Martin, S. T.

    2015-12-01

    Secondary organic material (SOM) can become light-absorbing (i.e. brown carbon) via multiphase reactions with nitrogen-containing species such as ammonia and amines. The physical states of SOM, however, potentially slow the diffusion of reactant molecules in organic matrix under conditions that semisolids or solids prevail, thus inhibiting the browning reaction pathways. In this study, the physical states and the in-particle diffusivity were investigated by measuring the evaporation kinetics of both water and organics from aromatic-derived SOMs using a quartz-crystal-microbalance (QCM). The results indicate that the SOMs derived from aromatic precursors toluene and m-xylene became solid (glassy) and the in particle diffusion was significantly impeded for sufficiently low relative humidity ( toluene-derived SOM after ammonia exposure at varied RHs. The results suggest that the production of light-absorbing nitrogen-containing compounds from multiphase reactions with ammonia was kinetically limited in the glassy organic matrix, which otherwise produce brown carbon. The results of this study have significant implications for production and optical properties of brown carbon in urban atmospheres that ultimately influence the climate and tropospheric photochemistry.

  7. The simplicial Ricci tensor

    International Nuclear Information System (INIS)

    Alsing, Paul M; McDonald, Jonathan R; Miller, Warner A

    2011-01-01

    The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area-an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.

  8. The simplicial Ricci tensor

    Science.gov (United States)

    Alsing, Paul M.; McDonald, Jonathan R.; Miller, Warner A.

    2011-08-01

    The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincarè conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area—an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.

  9. Applied tensor stereology

    DEFF Research Database (Denmark)

    Ziegel, Johanna; Nyengaard, Jens Randel; Jensen, Eva B. Vedel

    In the present paper, statistical procedures for estimating shape and orientation of arbitrary three-dimensional particles are developed. The focus of this work is on the case where the particles cannot be observed directly, but only via sections. Volume tensors are used for describing particle s...

  10. The evolution of tensor polarization

    International Nuclear Information System (INIS)

    Huang, H.; Lee, S.Y.; Ratner, L.

    1993-01-01

    By using the equation of motion for the vector polarization, the spin transfer matrix for spin tensor polarization, the spin transfer matrix for spin tensor polarization is derived. The evolution equation for the tensor polarization is studied in the presence of an isolate spin resonance and in the presence of a spin rotor, or snake

  11. Tensor Calculus: Unlearning Vector Calculus

    Science.gov (United States)

    Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

    2018-01-01

    Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

  12. On the energy-momentum tensor in Moyal space

    International Nuclear Information System (INIS)

    Balasin, Herbert; Schweda, Manfred; Blaschke, Daniel N.; Gieres, Francois

    2015-01-01

    We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is well known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another star-product. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the last two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line. (orig.)

  13. Introduction to vector and tensor analysis

    CERN Document Server

    Wrede, Robert C

    1972-01-01

    A broad introductory treatment, this volume examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, fundamental notions in n-space, Riemannian geometry, algebraic properties of the curvature tensor, and more. 1963 edition.

  14. Diffusion tensor image registration using hybrid connectivity and tensor features.

    Science.gov (United States)

    Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang

    2014-07-01

    Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. Copyright © 2013 Wiley Periodicals, Inc.

  15. A Closed-Form Solution to Tensor Voting: Theory and Applications

    OpenAIRE

    Wu, Tai-Pang; Yeung, Sai-Kit; Jia, Jiaya; Tang, Chi-Keung; Medioni, Gerard

    2016-01-01

    We prove a closed-form solution to tensor voting (CFTV): given a point set in any dimensions, our closed-form solution provides an exact, continuous and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence...

  16. Gogny interactions with tensor terms

    Energy Technology Data Exchange (ETDEWEB)

    Anguiano, M.; Lallena, A.M.; Bernard, R.N. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain); Co' , G. [INFN, Lecce (Italy); De Donno, V. [Universita del Salento, Dipartimento di Matematica e Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Grasso, M. [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France)

    2016-07-15

    We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations. (orig.)

  17. The geomagnetic field gradient tensor

    DEFF Research Database (Denmark)

    Kotsiaros, Stavros; Olsen, Nils

    2012-01-01

    We develop the general mathematical basis for space magnetic gradiometry in spherical coordinates. The magnetic gradient tensor is a second rank tensor consisting of 3 × 3 = 9 spatial derivatives. Since the geomagnetic field vector B is always solenoidal (∇ · B = 0) there are only eight independent...... tensor elements. Furthermore, in current free regions the magnetic gradient tensor becomes symmetric, further reducing the number of independent elements to five. In that case B is a Laplacian potential field and the gradient tensor can be expressed in series of spherical harmonics. We present properties...... of the magnetic gradient tensor and provide explicit expressions of its elements in terms of spherical harmonics. Finally we discuss the benefit of using gradient measurements for exploring the Earth’s magnetic field from space, in particular the advantage of the various tensor elements for a better determination...

  18. Interplay between tensor force and deformation in even–even nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Bernard, Rémi N., E-mail: rbernard@ugr.es; Anguiano, Marta

    2016-09-15

    In this work we study the effect of the nuclear tensor force on properties related with deformation. We focus on isotopes in the Mg, Si, S, Ar, Sr and Zr chains within the Hartree–Fock–Bogoliubov theory using the D1ST2a Gogny interaction. Contributions to the tensor energy in terms of saturated and unsaturated subshells are analyzed. Like–particle and proton–neutron parts of the tensor term are independently examinated. We found that the tensor term may considerably modify the potential energy landscapes and change the ground state shape. We analyze too how the pairing characteristics of the ground state change when the tensor force is included.

  19. Inclusive strange particle production and vector and tensor meson production in $K^{+}p$ interactions at 70 GeV/c

    CERN Document Server

    Ross, R T

    1982-01-01

    Results on K^{0}, K^{0} Lambda ^{0}, Lambda , K* and rho ^{0} production from an exposure of BEBC filled with hydrogen to a 70 Ge V/c K^{+} beam are presented. Inclusive channel and differential cross sections are presented. Inclusive channel and differential cross sections are presented. Scaling of the structure functions with data at 32 GeV/c is observed in the dominant X-region for each reaction and in some cases over the full X-region. Polarisation and spin density matrix measurements are given where obtainable. In particular a significant polarisation for forward produced Lambda s is observed.

  20. TensorFlow Distributions

    OpenAIRE

    Dillon, Joshua V.; Langmore, Ian; Tran, Dustin; Brevdo, Eugene; Vasudevan, Srinivas; Moore, Dave; Patton, Brian; Alemi, Alex; Hoffman, Matt; Saurous, Rif A.

    2017-01-01

    The TensorFlow Distributions library implements a vision of probability theory adapted to the modern deep-learning paradigm of end-to-end differentiable computation. Building on two basic abstractions, it offers flexible building blocks for probabilistic computation. Distributions provide fast, numerically stable methods for generating samples and computing statistics, e.g., log density. Bijectors provide composable volume-tracking transformations with automatic caching. Together these enable...

  1. One-loop tensor Feynman integral reduction with signed minors

    DEFF Research Database (Denmark)

    Fleischer, Jochem; Riemann, Tord; Yundin, Valery

    2012-01-01

    of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically......We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms...

  2. Tensor hypercontraction. II. Least-squares renormalization

    Science.gov (United States)

    Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David

    2012-12-01

    The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

  3. The tensor distribution function.

    Science.gov (United States)

    Leow, A D; Zhu, S; Zhan, L; McMahon, K; de Zubicaray, G I; Meredith, M; Wright, M J; Toga, A W; Thompson, P M

    2009-01-01

    Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.

  4. On energy-momentum tensors of gravitational field

    International Nuclear Information System (INIS)

    Nikishov, A.I.

    2001-01-01

    The phenomenological approach to gravitation is discussed in which the 3-graviton interaction is reduced to the interaction of each graviton with the energy-momentum tensor of two others. If this is so, (and in general relativity this is not so), then the problem of choosing the correct energy-momentum tensor comes to finding the right 3-graviton vertex. Several energy-momentum tensors od gravitational field are considered and compared in the lowest approximation. Each of them together with the energy-momentum tensor of point-like particles satisfies the conservation laws when equations of motion of particles are the same as in general relativity. It is shown that in Newtonian approximation the considered tensors differ one from other in the way their energy density is distributed between energy density of interaction (nonzero only at locations of particles) and energy density of gravitational field. Stating from Lorentz invariance, the Lagrangians for spin-2, mass-0 field are considered [ru

  5. Dark energy in scalar-tensor theories

    Energy Technology Data Exchange (ETDEWEB)

    Moeller, J.

    2007-12-15

    We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of {sigma}-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)

  6. Dark energy in scalar-tensor theories

    International Nuclear Information System (INIS)

    Moeller, J.

    2007-12-01

    We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of σ-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)

  7. The Twist Tensor Nuclear Norm for Video Completion.

    Science.gov (United States)

    Hu, Wenrui; Tao, Dacheng; Zhang, Wensheng; Xie, Yuan; Yang, Yehui

    2017-12-01

    In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an efficient computation using fast Fourier transform. On the other, t-TNN is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain, which extends the traditional matrix nuclear norm in a block circulant way. We test the t-TNN model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness, especially when dealing with video recorded by a nonstationary panning camera. The block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance. This representation, after transformation, exploits the horizontal translation relationship between the frames in a video, and endows the t-TNN model with a more powerful ability to reconstruct panning videos than the existing state-of-the-art low-rank models.

  8. Experimental status of scalar and tensor mesons

    International Nuclear Information System (INIS)

    Von Dombrowski, S.

    1997-01-01

    The recent discoveries of a 0 (1450) and f 0 (1370)/f 0 (1500) in antiproton-proton annihilation at rest shed new light on the interpretation of light scalar mesons. The properties of f 0 (1500) match the expectations of a scalar glueball mixed with nearby qq states. New decay modes of the ξ(2230) are reported in radiative J/Ψ decays, pointing also towards a (tensor) glueball nature of this state. Results from different experiments are discussed and compared. (orig.)

  9. Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format

    KAUST Repository

    Dolgov, Sergey; Khoromskij, Boris N.; Litvinenko, Alexander; Matthies, Hermann G.

    2015-01-01

    We apply the tensor train (TT) decomposition to construct the tensor product polynomial chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization, and to compute some

  10. Notes on super Killing tensors

    Energy Technology Data Exchange (ETDEWEB)

    Howe, P.S. [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Lindström, University [Department of Physics and Astronomy, Theoretical Physics, Uppsala University,SE-751 20 Uppsala (Sweden); Theoretical Physics, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom)

    2016-03-14

    The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.

  11. Tensor norms and operator ideals

    CERN Document Server

    Defant, A; Floret, K

    1992-01-01

    The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exer

  12. Exact tensor network ansatz for strongly interacting systems

    Science.gov (United States)

    Zaletel, Michael P.

    It appears that the tensor network ansatz, while not quite complete, is an efficient coordinate system for the tiny subset of a many-body Hilbert space which can be realized as a low energy state of a local Hamiltonian. However, we don't fully understand precisely which phases are captured by the tensor network ansatz, how to compute their physical observables (even numerically), or how to compute a tensor network representation for a ground state given a microscopic Hamiltonian. These questions are algorithmic in nature, but their resolution is intimately related to understanding the nature of quantum entanglement in many-body systems. For this reason it is useful to compute the tensor network representation of various `model' wavefunctions representative of different phases of matter; this allows us to understand how the entanglement properties of each phase are expressed in the tensor network ansatz, and can serve as test cases for algorithm development. Condensed matter physics has many illuminating model wavefunctions, such as Laughlin's celebrated wave function for the fractional quantum Hall effect, the Bardeen-Cooper-Schrieffer wave function for superconductivity, and Anderson's resonating valence bond ansatz for spin liquids. This thesis presents some results on exact tensor network representations of these model wavefunctions. In addition, a tensor network representation is given for the time evolution operator of a long-range one-dimensional Hamiltonian, which allows one to numerically simulate the time evolution of power-law interacting spin chains as well as two-dimensional strips and cylinders.

  13. E6 unification model building. III. Clebsch-Gordan coefficients in E6 tensor products of the 27 with higher dimensional representations

    International Nuclear Information System (INIS)

    Anderson, Gregory W.; Blazek, Tomas

    2005-01-01

    E 6 is an attractive group for unification model building. However, the complexity of a rank 6 group makes it nontrivial to write down the structure of higher dimensional operators in an E 6 theory in terms of the states labeled by quantum numbers of the standard model gauge group. In this paper, we show the results of our computation of the Clebsch-Gordan coefficients for the products of the 27 with irreducible representations of higher dimensionality: 78, 351, 351 ' , 351, and 351 ' . Application of these results to E 6 model building involving higher dimensional operators is straightforward

  14. Economic analysis of honey production in Edo State, Nigeria ...

    African Journals Online (AJOL)

    This research work was carried out to analyze the economics of honey production in Edo State. The objectives of the study were to examine the demographic characteristics of honey production, assess the profitability of honey bee and the problems facing honey production .The list of honey farmers in the state was ...

  15. Alignment of Product Models and Product State Models - Integration of the Product Lifecycle Phases

    DEFF Research Database (Denmark)

    Larsen, Michael Holm; Kirkby, Lars Phillip; Vesterager, Johan

    1999-01-01

    The purpose of this paper is to discuss the integration of the Product Model (PM) and the Product State Model (PCM). Focus is on information exchange from the PSM to the PM within the manufacturing of a single ship. The paper distinguishes between information and knowledge integration. The paper ...... provides some overall strategies for integrating PM and PSM. The context of this discussion is a development project at Odense Steel Shipyard....

  16. Tensor valuations and their applications in stochastic geometry and imaging

    CERN Document Server

    Kiderlen, Markus

    2017-01-01

    The purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the modern theory of tensor valuations. Product and Fourier-type transforms are introduced and various integral formulae are derived. New and well-known results are presented, together with generalizations in several directions, including extensions to the non-Euclidean setting and to non-convex sets. A variety of applications of tensor valuations to models in stochastic geometry, to local stereology and to imaging are also discussed.

  17. Measurement of the $pp\\to H\\to ZZ^* \\to 4 \\ell$ Production and $HZZ$ Tensor Coupling with the ATLAS Detector at 13 TeV Centre-of-Mass Energy

    CERN Document Server

    Walbrecht, Verena Maria; Kortner, Sandra

    In this master thesis the measurement of the Higgs boson production in the $H\\to~ZZ^*~\\to 4~\\ell$ decay channel ($\\ell=e,\\mu$) is performed together with the measurement of the tensor structure of the Higgs boson couplings to $Z$ bosons. The results are based on the Run~II dataset of LHC's proton-proton collisions at a centre-of-mass energy of 13~TeV, with the ATLAS detector and corresponding to a total integrated luminosity of $14.78$~fb$^{-1}$. Special emphasis is given to the estimation of the reducible background contribution. Based on the signal and background estimations, there are $32.0\\pm3.2$ Higgs boson candidates expected after the final event selection, while $44$ candidates are observed. The difference is compatible at the level of about $2$ standard derivations with the Standard Model predictions. All selected candidates are used in the study of the tensor structure of the $HZZ$ coupling between the Higgs boson and the two $Z$ bosons. For this study a dedicated signal model is introduced to desc...

  18. Uranium production, the United States perspective

    International Nuclear Information System (INIS)

    Glasier, G.E.

    1984-06-01

    U.S. uranium production appears to be headed for a level of approximately one quarter of the peak production of the early 1980's. In a free world market the majority of the U.S. production capability is noncompetitive and unnecessary to supply the free world's demand. Those world producers which can produce into the competitive uranium market of the present and the foreseeable future will be sufficient to supply the uranium needs of the world for the next ten to fifteen years. Thus, the U.S. production industry once the leading producer in the world will not regain nor approach that status in the foreseeable future

  19. Potential of solid state fermentation for production of ergot alkaloids

    OpenAIRE

    Trejo Hernandez, M.R.; Raimbault, Maurice; Roussos, Sevastianos; Lonsane, B.K.

    1992-01-01

    Production of total ergot alkaloids by #Claviceps fusiformis$ in solid state fermentation was 3.9 times higher compared to that in submerged fermentation. Production was equal in the case of #Claviceps purpurea$ but the spectra of alkaloids were advantageous with the use of solid state fermentation. The data establish potential of solid state fermentation which was not explored earlier for production of ergot alkaloids. (Résumé d'auteur)

  20. Factors affecting oil palm production in Ondo state of Nigeria

    African Journals Online (AJOL)

    sola

    ... affecting oil palm production in predominantly oil palm producing areas of Ondo state of Nigeria. ... This was because the mangrove swamp zone does not .... Research stations e.g. NIFOR. Radio .... palm production management practices.

  1. Architecture of the Product State Model Environment

    DEFF Research Database (Denmark)

    Holm Larsen, Michael; Lynggaard, Hans Jørgen B.

    2003-01-01

    on thedevelopment activities of the PSM architecture. An example discusses how to handle product relatedinformation on the shop floor in a manufacturing company and focuses on how dynamically updatedproduct data can improve control of production activities. This prototype example of welding a jointbetween two steel...... plates serves as proof of concept for the PSM architecture....

  2. Information Sharing In Shipbuilding based on the Product State Model

    DEFF Research Database (Denmark)

    Larsen, Michael Holm

    1999-01-01

    The paper provides a review of product modelling technologies and the overall architecture for the Product State Model (PSM) environment as a basis for how dynamically updated product data can improve control of production activities. Especially, the paper focuses on the circumstances prevailing...

  3. STATE TAXATION OF MINERAL DEPOSITS AND PRODUCTION

    Science.gov (United States)

    Development of energy resources in the more rural western states is likely to create severe financial problems for some state and local governments. This new economic activity, with population in-migration and greater demand for public services, will generate a need for more gove...

  4. Factors Affecting Productivity in the United States Naval Construction Force

    National Research Council Canada - National Science Library

    Morton, Darren

    1997-01-01

    By using a craftsman questionnaire, this thesis identifies and ranks the most important factors impairing Petty Officer productivity and morale in the United States Naval Construction Force (Seabees...

  5. Typesafe Abstractions for Tensor Operations

    OpenAIRE

    Chen, Tongfei

    2017-01-01

    We propose a typesafe abstraction to tensors (i.e. multidimensional arrays) exploiting the type-level programming capabilities of Scala through heterogeneous lists (HList), and showcase typesafe abstractions of common tensor operations and various neural layers such as convolution or recurrent neural networks. This abstraction could lay the foundation of future typesafe deep learning frameworks that runs on Scala/JVM.

  6. Indicial tensor manipulation on MACSYMA

    International Nuclear Information System (INIS)

    Bogen, R.A.; Pavelle, R.

    1977-01-01

    A new computational tool for physical calculations is described. It is the first computer system capable of performing indicial tensor calculus (as opposed to component tensor calculus). It is now operational on the symbolic manipulation system MACSYMA. The authors outline the capabilities of the system and describe some of the physical problems considered as well as others being examined at this time. (Auth.)

  7. 75 FR 13345 - Pricing for Certain United States Mint Products

    Science.gov (United States)

    2010-03-19

    ... DEPARTMENT OF THE TREASURY United States Mint Pricing for Certain United States Mint Products AGENCY: United States Mint, Department of the Treasury. ACTION: Notice. SUMMARY: The United States Mint is announcing the price of First Spouse Bronze Medals and 2010 First Spouse Bronze Medal Series: Four...

  8. Old tensor mesons in QCD sum rules

    International Nuclear Information System (INIS)

    Aliev, T.M.; Shifman, M.A.

    1981-01-01

    Tensor mesons f, A 2 and A 3 are analyzed within the framework of QCD sum rules. The effects of gluon and quark condensate is accounted for phenomenologically. Accurate estimates of meson masses and coupling constants of the lowest-lying states are obtained. It is shown that the masses are reproduced within theoretical uncertainty of about 80 MeV. The coupling of f meson to the corresponding quark current is determined. The results are in good aqreement with experimental data [ru

  9. productivity growth in food crop production in imo state, nigeria

    African Journals Online (AJOL)

    Prof. Adipala Ekwamu

    Agriculture plays pivotal roles in Nigeria including food security, employment, foreign exchange earnings and ... Key Words: Productivity decomposition, scale effect, allocative efficiency ... and subsidies in the form of cheap credit was.

  10. On deformed tensor potential for inelastic deuteron scattering

    International Nuclear Information System (INIS)

    Raynal, Jacques.

    1980-08-01

    Tensor analysing powers for inelastic deuteron scattering have been measured around 12 to 15 MeV. There is no problem to use such a tensor potential for the excited states in coupled channel calculations. However, for transition potentials, form factors are very different. A fit has been done with the first order vibrational model for 64 Ni(d,d') 64 Ni*, 2 + at 1,344 MeV

  11. The multi-flavor Schwinger model with chemical potential. Overcoming the sign problem with matrix product states

    International Nuclear Information System (INIS)

    Banuls, Mari Carmen; Cirac, J. Ignacio; Kuehn, Stefan; Cichy, Krzysztof

    2016-11-01

    During recent years there has been an increasing interest in the application of matrix product states, and more generally tensor networks, to lattice gauge theories. This non-perturbative method is sign problem free and has already been successfully used to compute mass spectra, thermal states and phase diagrams, as well as real-time dynamics for Abelian and non-Abelian gauge models. In previous work we showed the suitability of the method to explore the zero-temperature phase structure of the multi-flavor Schwinger model at non-zero chemical potential, a regime where the conventional Monte Carlo approach suffers from the sign problem. Here we extend our numerical study by looking at the spatially resolved chiral condensate in the massless case. We recover spatial oscillations, similar to the theoretical predictions for the single-flavor case, with a chemical potential dependent frequency and an amplitude approximately given by the homogeneous zero density condensate value.

  12. The multi-flavor Schwinger model with chemical potential. Overcoming the sign problem with matrix product states

    Energy Technology Data Exchange (ETDEWEB)

    Banuls, Mari Carmen; Cirac, J. Ignacio; Kuehn, Stefan [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Saito, Hana [AISIN AW Co., Ltd., Aichi (Japan)

    2016-11-15

    During recent years there has been an increasing interest in the application of matrix product states, and more generally tensor networks, to lattice gauge theories. This non-perturbative method is sign problem free and has already been successfully used to compute mass spectra, thermal states and phase diagrams, as well as real-time dynamics for Abelian and non-Abelian gauge models. In previous work we showed the suitability of the method to explore the zero-temperature phase structure of the multi-flavor Schwinger model at non-zero chemical potential, a regime where the conventional Monte Carlo approach suffers from the sign problem. Here we extend our numerical study by looking at the spatially resolved chiral condensate in the massless case. We recover spatial oscillations, similar to the theoretical predictions for the single-flavor case, with a chemical potential dependent frequency and an amplitude approximately given by the homogeneous zero density condensate value.

  13. Killing-Yano tensors and Nambu mechanics

    International Nuclear Information System (INIS)

    Baleanu, D.

    1998-01-01

    Killing-Yano tensors were introduced in 1952 by Kentaro-Yano from mathematical point of view. The physical interpretation of Killing-Yano tensors of rank higher than two was unclear. We found that all Killing-Yano tensors η i 1 i 2 . .. i n with covariant derivative zero are Nambu tensors. We found that in the case of flat space case all Killing-Yano tensors are Nambu tensors. In the case of Taub-NUT and Kerr-Newmann metric Killing-Yano tensors of order two generate Nambu tensors of rank 3

  14. Steady state compact toroidal plasma production

    Science.gov (United States)

    Turner, William C.

    1986-01-01

    Apparatus and method for maintaining steady state compact toroidal plasmas. A compact toroidal plasma is formed by a magnetized coaxial plasma gun and held in close proximity to the gun electrodes by applied magnetic fields or magnetic fields produced by image currents in conducting walls. Voltage supply means maintains a constant potential across the electrodes producing an increasing magnetic helicity which drives the plasma away from a minimum energy state. The plasma globally relaxes to a new minimum energy state, conserving helicity according to Taylor's relaxation hypothesis, and injecting net helicity into the core of the compact toroidal plasma. Controlling the voltage so as to inject net helicity at a predetermined rate based on dissipative processes maintains or increases the compact toroidal plasma in a time averaged steady state mode.

  15. BIOTECHNOLOGIES OF MEAT PRODUCTS MANUFACTURE. CURRENT STATE

    Directory of Open Access Journals (Sweden)

    Bal-Prilipko L. V.

    2014-10-01

    Full Text Available The analysis of literature and patents related to the possibilities of biotechnology for optimizing the domestic meat processing plants was the aim of the article. The analysis of the results of the use of biotechnological methods in the meat processing industry is given. The prospects for their implementation are evaluated. The main development strategy of technological meat processing to develop the methods of obtaining high quality and safe meat products is highlighted. Targeted use of special strains of microorganisms in production of functional meat products offers some opportunities. Thus, such action is associated with formation of the following specific dietary components: organic acids, bactericins, enzymes, vitamins and others. They promote to improve the sanitary microbiological, organoleptic, functional and technological parameters of meat products. Using of denitrifying microbial strains could reduce the residual content of sodium nitrite in the finished product, minimizing the possible carcinogenic and mutagenic impact of this compound on a human body, producing functional safe products while maintaining its high organoleptic characteristics.

  16. TensorFlow: A system for large-scale machine learning

    OpenAIRE

    Abadi, Martín; Barham, Paul; Chen, Jianmin; Chen, Zhifeng; Davis, Andy; Dean, Jeffrey; Devin, Matthieu; Ghemawat, Sanjay; Irving, Geoffrey; Isard, Michael; Kudlur, Manjunath; Levenberg, Josh; Monga, Rajat; Moore, Sherry; Murray, Derek G.

    2016-01-01

    TensorFlow is a machine learning system that operates at large scale and in heterogeneous environments. TensorFlow uses dataflow graphs to represent computation, shared state, and the operations that mutate that state. It maps the nodes of a dataflow graph across many machines in a cluster, and within a machine across multiple computational devices, including multicore CPUs, general-purpose GPUs, and custom designed ASICs known as Tensor Processing Units (TPUs). This architecture gives flexib...

  17. Diffusion tensor imaging tensor shape analysis for assessment of regional white matter differences.

    Science.gov (United States)

    Middleton, Dana M; Li, Jonathan Y; Lee, Hui J; Chen, Steven; Dickson, Patricia I; Ellinwood, N Matthew; White, Leonard E; Provenzale, James M

    2017-08-01

    Purpose The purpose of this study was to investigate a novel tensor shape plot analysis technique of diffusion tensor imaging data as a means to assess microstructural differences in brain tissue. We hypothesized that this technique could distinguish white matter regions with different microstructural compositions. Methods Three normal canines were euthanized at seven weeks old. Their brains were imaged using identical diffusion tensor imaging protocols on a 7T small-animal magnetic resonance imaging system. We examined two white matter regions, the internal capsule and the centrum semiovale, each subdivided into an anterior and posterior region. We placed 100 regions of interest in each of the four brain regions. Eigenvalues for each region of interest triangulated onto tensor shape plots as the weighted average of three shape metrics at the plot's vertices: CS, CL, and CP. Results The distribution of data on the plots for the internal capsule differed markedly from the centrum semiovale data, thus confirming our hypothesis. Furthermore, data for the internal capsule were distributed in a relatively tight cluster, possibly reflecting the compact and parallel nature of its fibers, while data for the centrum semiovale were more widely distributed, consistent with the less compact and often crossing pattern of its fibers. This indicates that the tensor shape plot technique can depict data in similar regions as being alike. Conclusion Tensor shape plots successfully depicted differences in tissue microstructure and reflected the microstructure of individual brain regions. This proof of principle study suggests that if our findings are reproduced in larger samples, including abnormal white matter states, the technique may be useful in assessment of white matter diseases.

  18. MATLAB tensor classes for fast algorithm prototyping.

    Energy Technology Data Exchange (ETDEWEB)

    Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)

    2004-10-01

    Tensors (also known as mutidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor as matrix class supports the 'matricization' of a tensor, i.e., the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp tensor and tucker tensor. We descibe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.

  19. Towards overcoming the Monte Carlo sign problem with tensor networks

    Directory of Open Access Journals (Sweden)

    Bañuls Mari Carmen

    2017-01-01

    Full Text Available The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density.

  20. Ethanol Demand in United States Gasoline Production

    Energy Technology Data Exchange (ETDEWEB)

    Hadder, G.R.

    1998-11-24

    The Oak Ridge National Laboratory (OWL) Refinery Yield Model (RYM) has been used to estimate the demand for ethanol in U.S. gasoline production in year 2010. Study cases examine ethanol demand with variations in world oil price, cost of competing oxygenate, ethanol value, and gasoline specifications. For combined-regions outside California summer ethanol demand is dominated by conventional gasoline (CG) because the premised share of reformulated gasoline (RFG) production is relatively low and because CG offers greater flexibility for blending high vapor pressure components like ethanol. Vapor pressure advantages disappear for winter CG, but total ethanol used in winter RFG remains low because of the low RFG production share. In California, relatively less ethanol is used in CG because the RFG production share is very high. During the winter in California, there is a significant increase in use of ethanol in RFG, as ethanol displaces lower-vapor-pressure ethers. Estimated U.S. ethanol demand is a function of the refiner value of ethanol. For example, ethanol demand for reference conditions in year 2010 is 2 billion gallons per year (BGY) at a refiner value of $1.00 per gallon (1996 dollars), and 9 BGY at a refiner value of $0.60 per gallon. Ethanol demand could be increased with higher oil prices, or by changes in gasoline specifications for oxygen content, sulfur content, emissions of volatile organic compounds (VOCS), and octane numbers.

  1. Efficient tensor completion for color image and video recovery: Low-rank tensor train

    OpenAIRE

    Bengua, Johann A.; Phien, Ho N.; Tuan, Hoang D.; Do, Minh N.

    2016-01-01

    This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor tra...

  2. An introduction to tensors and group theory for physicists

    CERN Document Server

    Jeevanjee, Nadir

    2015-01-01

    The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics.  Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations.  New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional “invitation” sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students.   Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part...

  3. Ryu-Takayanagi formula for symmetric random tensor networks

    Science.gov (United States)

    Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi

    2018-06-01

    We consider the special case of random tensor networks (RTNs) endowed with gauge symmetry constraints on each tensor. We compute the Rényi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large-bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background-independent quantum gravity, and for importing quantum gravity tools into tensor network research.

  4. A defect in holographic interpretations of tensor networks

    Energy Technology Data Exchange (ETDEWEB)

    Czech, Bartłomiej [Institute for Advanced Study,Princeton, NJ 08540 (United States); Nguyen, Phuc H.; Swaminathan, Sivaramakrishnan [Theory Group, Department of Physics and Texas Cosmology Center,The University of Texas at Austin,Austin, TX 78712 (United States)

    2017-03-16

    We initiate the study of how tensor networks reproduce properties of static holographic space-times, which are not locally pure anti-de Sitter. We consider geometries that are holographically dual to ground states of defect, interface and boundary CFTs and compare them to the structure of the requisite MERA networks predicted by the theory of minimal updates. When the CFT is deformed, certain tensors require updating. On the other hand, even identical tensors can contribute differently to estimates of entanglement entropies. We interpret these facts holographically by associating tensor updates to turning on non-normalizable modes in the bulk. In passing, we also clarify and complement existing arguments in support of the theory of minimal updates, propose a novel ansatz called rayed MERA that applies to a class of generalized interface CFTs, and analyze the kinematic spaces of the thin wall and AdS{sub 3}-Janus geometries.

  5. Traffic Speed Data Imputation Method Based on Tensor Completion

    Directory of Open Access Journals (Sweden)

    Bin Ran

    2015-01-01

    Full Text Available Traffic speed data plays a key role in Intelligent Transportation Systems (ITS; however, missing traffic data would affect the performance of ITS as well as Advanced Traveler Information Systems (ATIS. In this paper, we handle this issue by a novel tensor-based imputation approach. Specifically, tensor pattern is adopted for modeling traffic speed data and then High accurate Low Rank Tensor Completion (HaLRTC, an efficient tensor completion method, is employed to estimate the missing traffic speed data. This proposed method is able to recover missing entries from given entries, which may be noisy, considering severe fluctuation of traffic speed data compared with traffic volume. The proposed method is evaluated on Performance Measurement System (PeMS database, and the experimental results show the superiority of the proposed approach over state-of-the-art baseline approaches.

  6. Traffic speed data imputation method based on tensor completion.

    Science.gov (United States)

    Ran, Bin; Tan, Huachun; Feng, Jianshuai; Liu, Ying; Wang, Wuhong

    2015-01-01

    Traffic speed data plays a key role in Intelligent Transportation Systems (ITS); however, missing traffic data would affect the performance of ITS as well as Advanced Traveler Information Systems (ATIS). In this paper, we handle this issue by a novel tensor-based imputation approach. Specifically, tensor pattern is adopted for modeling traffic speed data and then High accurate Low Rank Tensor Completion (HaLRTC), an efficient tensor completion method, is employed to estimate the missing traffic speed data. This proposed method is able to recover missing entries from given entries, which may be noisy, considering severe fluctuation of traffic speed data compared with traffic volume. The proposed method is evaluated on Performance Measurement System (PeMS) database, and the experimental results show the superiority of the proposed approach over state-of-the-art baseline approaches.

  7. Open source Matrix Product States: Opening ways to simulate entangled many-body quantum systems in one dimension

    Science.gov (United States)

    Jaschke, Daniel; Wall, Michael L.; Carr, Lincoln D.

    2018-04-01

    Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States (MPSs), have attracted interest from different fields of quantum physics ranging from solid state systems to quantum simulators and quantum computing. Our open source MPS code provides the community with a toolset to analyze the statics and dynamics of one-dimensional quantum systems. Here, we present our open source library, Open Source Matrix Product States (OSMPS), of MPS methods implemented in Python and Fortran2003. The library includes tools for ground state calculation and excited states via the variational ansatz. We also support ground states for infinite systems with translational invariance. Dynamics are simulated with different algorithms, including three algorithms with support for long-range interactions. Convenient features include built-in support for fermionic systems and number conservation with rotational U(1) and discrete Z2 symmetries for finite systems, as well as data parallelism with MPI. We explain the principles and techniques used in this library along with examples of how to efficiently use the general interfaces to analyze the Ising and Bose-Hubbard models. This description includes the preparation of simulations as well as dispatching and post-processing of them.

  8. BIOTECHNOLOGIES OF MEAT PRODUCTS MANUFACTURE. CURRENT STATE

    OpenAIRE

    Bal-Prilipko L. V.; Leonova B. I.

    2014-01-01

    The analysis of literature and patents related to the possibilities of biotechnology for optimizing the domestic meat processing plants was the aim of the article. The analysis of the results of the use of biotechnological methods in the meat processing industry is given. The prospects for their implementation are evaluated. The main development strategy of technological meat processing to develop the methods of obtaining high quality and safe meat products is highlighted. Targeted use of spe...

  9. Factors Affecting Oil Palm Production in Ondo State of Nigeria ...

    African Journals Online (AJOL)

    The discovery of crude oil and the civil war adversely affected oil palm production in Nigeria. This has resulted in scarcity and high cost of palm products and palm oil. The study therefore investigated the factors influencing oil palm production in Ondo State, Nigeria. One hundred and fifty respondents were selected from ...

  10. Investigation of cognitive circuits using steady-state cerebral blood volume and diffusion tensor imaging in patients with mild cognitive impairment following electrical injury

    International Nuclear Information System (INIS)

    Park, Chang-hyun; Seo, Cheong Hoon; Joo, So Young; Jung, Myung Hun; Jang, Soyeon; Lee, Ho Young; Ohn, Suk Hoon

    2017-01-01

    We utilized cerebral blood volume (CBV) magnetic resonance imaging and diffusion tensor imaging (DTI) to investigate changes in cognitive networks in patients experiencing cognitive dysfunction following electrical injury. Cognitive function was assessed across various domains, including attention, verbal memory, executive function, and language. Depressive symptoms were also evaluated. CBV maps and DTI measures were obtained from 24 patients (age, 41.8 ± 5.8 years; education, 13.3 ± 1.9 years) and 24 healthy controls (age, 42.3 ± 2.7 years; education, 14.3 ± 1.9 years). CBV maps and DTI measures were compared between patients and controls, and correlations between these measures and each cognitive assessment score were examined. Patients exhibited lower attention, verbal memory, and executive function scores than controls (all p < 0.01). Patients also exhibited higher depression scores than controls (p < 0.01), as well as a predominant increase in CBV in the cerebellar vermis relative to that of controls (height p < uncorrected 0.001, extent p < corrected 0.05). Correlation analyses revealed a strong association between executive function scores and CBV in the bilateral posterior cingulate cortex and left mammillary body in patients (height p < uncorrected 0.001, extent p < corrected 0.05). There were no significant differences in DTI measures between patients and controls. The CBV maps showed hypermetabolism in the cerebello-limbic system; DTI did not find any microstructural changes. Our results suggest that patients experiencing cognitive dysfunction following electrical injury may possess a cognitive reserve that protects against deteriorating conditions such as dementia. (orig.)

  11. Structural characterization of MAO and related aluminum complexes. 1. Solid-state (27)Al NMR with comparison to EFG tensors from ab initio molecular orbital calculations.

    Science.gov (United States)

    Bryant, P L; Harwell, C R; Mrse, A A; Emery, E F; Gan, Z; Caldwell, T; Reyes, A P; Kuhns, P; Hoyt, D W; Simeral, L S; Hall, R W; Butler, L G

    2001-12-05

    Experimental and ab initio molecular orbital techniques are developed for study of aluminum species with large quadrupole coupling constants to test structural models for methylaluminoxanes (MAO). The techniques are applied to nitrogen- and oxygen-containing complexes of aluminum and to solid MAO isolated from active commercial MAO preparations. (Aminato)- and (propanolato)aluminum clusters with 3-, 4-, and 6-coordinate aluminum sites are studied with three (27)Al NMR techniques optimized for large (27)Al quadrupole coupling constants: field-swept, frequency-stepped, and high-field MAS NMR. Four-membered (aminato)aluminum complexes with AlN(4) coordination yield slightly smaller C(q) values than similar AlN(2)C(2) sites: 12.2 vs 15.8 MHz. Planar 3-coordinate AlN(2)C sites have the largest C(q) values, 37 MHz. In all cases, molecular orbital calculations of the electric field gradient tensors yields C(q) and eta values that match with experiment, even for a large hexameric (aminato)aluminum cage. A D(3d) symmetry hexaaluminum oxane cluster, postulated as a model for MAO, yields a calculated C(q) of -23.7 MHz, eta = 0.7474, and predicts a spectrum that is too broad to match the field-swept NMR of methylaluminoxane, which shows at least three sites, all with C(q) values greater than 15 MHz but less than 21 MHz. Thus, the proposed hexaaluminum cluster, with its strained four-membered rings, is not a major component of MAO. However, calculations for dimers of the cage complex, either edge-bridged or face-bridged, show a much closer match to experiment. Also, MAO preparations differ, with a gel form of MAO having significantly larger (27)Al C(q) values than a nongel form, a conclusion reached on the basis of (27)Al NMR line widths in field-swept NMR spectra acquired from 13 to 24 T.

  12. Investigation of cognitive circuits using steady-state cerebral blood volume and diffusion tensor imaging in patients with mild cognitive impairment following electrical injury

    Energy Technology Data Exchange (ETDEWEB)

    Park, Chang-hyun [Catholic University of Korea, Department of Psychiatry, College of Medicine, Seoul (Korea, Republic of); Seo, Cheong Hoon; Joo, So Young [Hallym University College of Medicine, Department of Physical Medicine and Rehabilitation, Hangang Sacred Heart Hospital, Seoul (Korea, Republic of); Jung, Myung Hun [Hallym University Sacred Heart Hospital, Hallym University College of Medicine, Department of Psychiatry, Dongan-gu Anyang, Gyeonggi-do (Korea, Republic of); Jang, Soyeon; Lee, Ho Young; Ohn, Suk Hoon [Hallym University Sacred Heart Hospital, Hallym University College of Medicine, Department of Physical Medicine and Rehabilitation, Dongan-gu Anyang, Gyeonggi-do (Korea, Republic of)

    2017-09-15

    We utilized cerebral blood volume (CBV) magnetic resonance imaging and diffusion tensor imaging (DTI) to investigate changes in cognitive networks in patients experiencing cognitive dysfunction following electrical injury. Cognitive function was assessed across various domains, including attention, verbal memory, executive function, and language. Depressive symptoms were also evaluated. CBV maps and DTI measures were obtained from 24 patients (age, 41.8 ± 5.8 years; education, 13.3 ± 1.9 years) and 24 healthy controls (age, 42.3 ± 2.7 years; education, 14.3 ± 1.9 years). CBV maps and DTI measures were compared between patients and controls, and correlations between these measures and each cognitive assessment score were examined. Patients exhibited lower attention, verbal memory, and executive function scores than controls (all p < 0.01). Patients also exhibited higher depression scores than controls (p < 0.01), as well as a predominant increase in CBV in the cerebellar vermis relative to that of controls (height p < uncorrected 0.001, extent p < corrected 0.05). Correlation analyses revealed a strong association between executive function scores and CBV in the bilateral posterior cingulate cortex and left mammillary body in patients (height p < uncorrected 0.001, extent p < corrected 0.05). There were no significant differences in DTI measures between patients and controls. The CBV maps showed hypermetabolism in the cerebello-limbic system; DTI did not find any microstructural changes. Our results suggest that patients experiencing cognitive dysfunction following electrical injury may possess a cognitive reserve that protects against deteriorating conditions such as dementia. (orig.)

  13. Bond dimension witnesses and the structure of homogeneous matrix product states

    Directory of Open Access Journals (Sweden)

    Miguel Navascues

    2018-01-01

    Full Text Available For the past twenty years, Matrix Product States (MPS have been widely used in solid state physics to approximate the ground state of one-dimensional spin chains. In this paper, we study homogeneous MPS (hMPS, or MPS constructed via site-independent tensors and a boundary condition. Exploiting a connection with the theory of matrix algebras, we derive two structural properties shared by all hMPS, namely: a there exist local operators which annihilate all hMPS of a given bond dimension; and b there exist local operators which, when applied over any hMPS of a given bond dimension, decouple (cut the particles where they act from the spin chain while at the same time join (glue the two loose ends back again into a hMPS. Armed with these tools, we show how to systematically derive `bond dimension witnesses', or 2-local operators whose expectation value allows us to lower bound the bond dimension of the underlying hMPS. We extend some of these results to the ansatz of Projected Entangled Pairs States (PEPS. As a bonus, we use our insight on the structure of hMPS to: a derive some theoretical limitations on the use of hMPS and hPEPS for ground state energy computations; b show how to decrease the complexity and boost the speed of convergence of the semidefinite programming hierarchies described in [Phys. Rev. Lett. 115, 020501 (2015] for the characterization of finite-dimensional quantum correlations.

  14. Tensor Network Wavefunctions for Topological Phases

    Science.gov (United States)

    Ware, Brayden Alexander

    The combination of quantum effects and interactions in quantum many-body systems can result in exotic phases with fundamentally entangled ground state wavefunctions--topological phases. Topological phases come in two types, both of which will be studied in this thesis. In topologically ordered phases, the pattern of entanglement in the ground state wavefunction encodes the statistics of exotic emergent excitations, a universal indicator of a phase that is robust to all types of perturbations. In symmetry protected topological phases, the entanglement instead encodes a universal response of the system to symmetry defects, an indicator that is robust only to perturbations respecting the protecting symmetry. Finding and creating these phases in physical systems is a motivating challenge that tests all aspects--analytical, numerical, and experimental--of our understanding of the quantum many-body problem. Nearly three decades ago, the creation of simple ansatz wavefunctions--such as the Laughlin fractional quantum hall state, the AKLT state, and the resonating valence bond state--spurred analytical understanding of both the role of entanglement in topological physics and physical mechanisms by which it can arise. However, quantitative understanding of the relevant phase diagrams is still challenging. For this purpose, tensor networks provide a toolbox for systematically improving wavefunction ansatz while still capturing the relevant entanglement properties. In this thesis, we use the tools of entanglement and tensor networks to analyze ansatz states for several proposed new phases. In the first part, we study a featureless phase of bosons on the honeycomb lattice and argue that this phase can be topologically protected under any one of several distinct subsets of the crystalline lattice symmetries. We discuss methods of detecting such phases with entanglement and without. In the second part, we consider the problem of constructing fixed-point wavefunctions for

  15. The Einstein tensor characterizing some Riemann spaces

    International Nuclear Information System (INIS)

    Rahman, M.S.

    1993-07-01

    A formal definition of the Einstein tensor is given. Mention is made of how this tensor plays a role of expressing certain conditions in a precise form. The cases of reducing the Einstein tensor to a zero tensor are studied on its merit. A lucid account of results, formulated as theorems, on Einstein symmetric and Einstein recurrent spaces is then presented. (author). 5 refs

  16. Group field theory and tensor networks: towards a Ryu–Takayanagi formula in full quantum gravity

    Science.gov (United States)

    Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi

    2018-06-01

    We establish a dictionary between group field theory (thus, spin networks and random tensors) states and generalized random tensor networks. Then, we use this dictionary to compute the Rényi entropy of such states and recover the Ryu–Takayanagi formula, in two different cases corresponding to two different truncations/approximations, suggested by the established correspondence.

  17. Colored Tensor Models - a Review

    Directory of Open Access Journals (Sweden)

    Razvan Gurau

    2012-04-01

    Full Text Available Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions, non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.

  18. Tensor Completion Algorithms in Big Data Analytics

    OpenAIRE

    Song, Qingquan; Ge, Hancheng; Caverlee, James; Hu, Xia

    2017-01-01

    Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data an...

  19. An Introduction to Tensors for Students of Physics and Engineering

    Science.gov (United States)

    Kolecki, Joseph C.

    2002-01-01

    Tensor analysis is the type of subject that can make even the best of students shudder. My own post-graduate instructor in the subject took away much of the fear by speaking of an implicit rhythm in the peculiar notation traditionally used, and helped us to see how this rhythm plays its way throughout the various formalisms. Prior to taking that class, I had spent many years "playing" on my own with tensors. I found the going to be tremendously difficult but was able, over time, to back out some physical and geometrical considerations that helped to make the subject a little more transparent. Today, it is sometimes hard not to think in terms of tensors and their associated concepts. This article, prompted and greatly enhanced by Marlos Jacob, whom I've met only by e-mail, is an attempt to record those early notions concerning tensors. It is intended to serve as a bridge from the point where most undergraduate students "leave off" in their studies of mathematics to the place where most texts on tensor analysis begin. A basic knowledge of vectors, matrices, and physics is assumed. A semi-intuitive approach to those notions underlying tensor analysis is given via scalars, vectors, dyads, triads, and higher vector products. The reader must be prepared to do some mathematics and to think. For those students who wish to go beyond this humble start, I can only recommend my professor's wisdom: find the rhythm in the mathematics and you will fare pretty well.

  20. Atomic-batched tensor decomposed two-electron repulsion integrals

    Science.gov (United States)

    Schmitz, Gunnar; Madsen, Niels Kristian; Christiansen, Ove

    2017-04-01

    We present a new integral format for 4-index electron repulsion integrals, in which several strategies like the Resolution-of-the-Identity (RI) approximation and other more general tensor-decomposition techniques are combined with an atomic batching scheme. The 3-index RI integral tensor is divided into sub-tensors defined by atom pairs on which we perform an accelerated decomposition to the canonical product (CP) format. In a first step, the RI integrals are decomposed to a high-rank CP-like format by repeated singular value decompositions followed by a rank reduction, which uses a Tucker decomposition as an intermediate step to lower the prefactor of the algorithm. After decomposing the RI sub-tensors (within the Coulomb metric), they can be reassembled to the full decomposed tensor (RC approach) or the atomic batched format can be maintained (ABC approach). In the first case, the integrals are very similar to the well-known tensor hypercontraction integral format, which gained some attraction in recent years since it allows for quartic scaling implementations of MP2 and some coupled cluster methods. On the MP2 level, the RC and ABC approaches are compared concerning efficiency and storage requirements. Furthermore, the overall accuracy of this approach is assessed. Initial test calculations show a good accuracy and that it is not limited to small systems.

  1. Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination.

    Science.gov (United States)

    Zhao, Qibin; Zhang, Liqing; Cichocki, Andrzej

    2015-09-01

    CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank . In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance.

  2. Development of the Tensoral Computer Language

    Science.gov (United States)

    Ferziger, Joel; Dresselhaus, Eliot

    1996-01-01

    The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.

  3. Donkey milk production: state of the art

    Directory of Open Access Journals (Sweden)

    Silvia Vincenzetti

    2010-01-01

    Full Text Available Milk is one of the most common causes of food allergies among children under one year of age. No specific therapy exists for this allergy, and thus the only feasible response is to avoid assumption of milk and derived products. Studies conducted on the serum of children with hypersensi- tivity to milk have shown that caseins are the proteins with the greater allergenic potential. However, in some cases, children have also shown hypersensitivity to the β-lactoglobulines and to the α-lactal- bumins. When food intolerance is diagnosed in an infant, it is often necessary to impose a period of total parenteral feeding, followed by breast feeding, considered the most correct method of re-feeding. When human milk can not be given, alternative food sources must be sought. Clinical studies have demonstrated that donkey milk could substitute breast feeding in infants affected by severe Ig-E me- diated milk allergies. In these subjects, donkey milk is not only useful, but also safer than other types of milk. In fact donkey milk composition in lipids (high levels of linoleic and linolenic acid and pro- teins (low caseins content is very close to human milk. Lysozyme content in donkey milk resulted to be very high (mean value 1.0 mg/ml if compared to bovine (traces, caprine (traces and human milk. The high lysozyme content of donkey milk may be responsible of the low bacterial count reported in literature and also makes this milk suitable to prevent intestine infections to infants. Among seropro- teins, β-lactoglobulin and α-lactalbumin content in donkey milk was respectively 3.75 and 1.80 mg/ml and remained substancially the same during the different stages of lactation.

  4. Economics of Local Cow Milk Products Marketing in Kwara State ...

    African Journals Online (AJOL)

    Economics of Local Cow Milk Products Marketing in Kwara State, Nigeria. ... The marketing chain for the commodity is simple and crude. It starts from the raw cow milk processors ... EMAIL FULL TEXT EMAIL FULL TEXT · DOWNLOAD FULL ...

  5. Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature

    OpenAIRE

    Loveridge, Lee C.

    2004-01-01

    Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.

  6. Piezoelectric and electrooptic ferroics - qualitative domain and tensor characteristics

    Czech Academy of Sciences Publication Activity Database

    Janovec, Václav; Čmelík, M.; Machonský, L.

    2010-01-01

    Roč. 83, č. 9 (2010), 670-681 ISSN 0141-1594 Institutional research plan: CEZ:AV0Z10100520 Keywords : ferroic crystals * piezoelectric materials * electrooptic materials * species * orientation states * tensor domain states Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.006, year: 2010

  7. Technical efficiency in pig production in Akwa Ibom State, Nigeria ...

    African Journals Online (AJOL)

    This study was designed to measure the level of technical efficiency and its determinants in pig production in Akwa Ibom State, Nigeria using a stochastic frontier production function. Multistage random sampling technique was used to select 60 pig farms from which input-output data were collected in 2004. The estimated ...

  8. Production of Citric Acid from Solid State Fermentation of Sugarcane ...

    African Journals Online (AJOL)

    Aspergillus niger is the leading microorganism of choice for citric acid production. Sugarcane waste was used as substrate under solid state fermentation to comparatively evaluate the citric acid production capacity of Aspergillus niger isolates and the indigenous microflora in the sugarcane waste. Known optimal cultural ...

  9. Lovastatin production by Aspergillus terreus in solid state and ...

    African Journals Online (AJOL)

    user

    Department of Biochemistry of Physiologically Active Compounds, Institute of ... Keywords: lovastatin, submerged fermentation, solid state fermentation, production ... water need in up-stream processing which minimizes production expense (Holker .... authors, a slowly utilizable carbon source is preferable for high lovastatin ...

  10. Lovastatin production by Aspergillus terreus in solid state and ...

    African Journals Online (AJOL)

    user

    Department of Biochemistry of Physiologically Active Compounds, Institute of ... Keywords: lovastatin, submerged fermentation, solid state fermentation, production ... water need in up-stream processing which minimizes production expense (Holker et .... Effect of carbon and nitrogen sources on lovastatin yield by Aspergillus ...

  11. Racial Diversity and Macroeconomic Productivity across US States and Cities

    OpenAIRE

    Sparber, Chad

    2007-01-01

    The United States is growing increasingly diverse, so it is important that economists understand the macroeconomic consequences of diversity within the US economy. International analyses often argue that heterogeneity reduces macroeconomic productivity by engendering corruption, political instability, and social turmoil. However, other studies claim that diversity improves creative decision making and augments productivity. This paper exploits differences in diversity across regions of the Un...

  12. Solid state fermentation studies of citric acid production

    African Journals Online (AJOL)

    SERVER

    2008-03-04

    Mar 4, 2008 ... solid waste management, biomass energy conservation, production of high value products and little risk ... The carrier, sugarcane bagasse for solid state fermentation was procured from National Sugar Institute ... constant weight and designated as dry solid residue (DSR). The filtrate (consisting of biomass, ...

  13. The Economic Importance of Forest Products in Enugu State, Nigeria

    African Journals Online (AJOL)

    The Economic Importance of Forest Products in Enugu State, Nigeria. ... International Journal of Tropical Agriculture and Food Systems ... The regression results, showed that access to modern forest products harvesting/processing technology (Te) and relative contribution of forest output in total household economy (Ro) ...

  14. Characteristics of Free-Range Chicken Production in Ogun State ...

    African Journals Online (AJOL)

    landlord

    The poultry sub-sector is the most commercialized in the livestock sector of ... often have an important role in the development of family poultry production ... extension in providing linkage services to farmers in Ogun state, Nigeria. ... knowledge of its value and production efficiency. ..... Guide to the sourcing of viable chicks.

  15. Profitability analysis of catfish production in Kaduna state, Nigeria ...

    African Journals Online (AJOL)

    This study examined the profitability of catfish production in Kaduna State, Nigeria. The objective was to determine the costs and returns in catfish production and thus the profit. Data for the study were collected through the use of well-structured questionnaire. A total of 60 catfish farmers were randomly selected from four ...

  16. STATE INVESTMENT IN SCIENCE AND SCIENTIFIC PRODUCTIVITY OF UNIVERSITIES

    OpenAIRE

    Domagoj Karacic; Ivan Miskulin; Hrvoje Serdarusic

    2016-01-01

    State investment in service activities of the public sector, as well as the financial returns analyzed from the aspect of service effectiveness and utilization of public goods, can be considered as one of the most significant dilemmas, especially in the field of education. When analyzing state investments, through investment in education and development of the university, we can conclude that state investments in scientific productivity of universities fall into one of the main future framewo...

  17. STRUCTURE TENSOR IMAGE FILTERING USING RIEMANNIAN L1 AND L∞ CENTER-OF-MASS

    Directory of Open Access Journals (Sweden)

    Jesus Angulo

    2014-06-01

    Full Text Available Structure tensor images are obtained by a Gaussian smoothing of the dyadic product of gradient image. These images give at each pixel a n×n symmetric positive definite matrix SPD(n, representing the local orientation and the edge information. Processing such images requires appropriate algorithms working on the Riemannian manifold on the SPD(n matrices. This contribution deals with structure tensor image filtering based on Lp geometric averaging. In particular, L1 center-of-mass (Riemannian median or Fermat-Weber point and L∞ center-of-mass (Riemannian circumcenter can be obtained for structure tensors using recently proposed algorithms. Our contribution in this paper is to study the interest of L1 and L∞ Riemannian estimators for structure tensor image processing. In particular, we compare both for two image analysis tasks: (i structure tensor image denoising; (ii anomaly detection in structure tensor images.

  18. Non-Abelian tensor gauge fields and higher-spin extension of standard model

    International Nuclear Information System (INIS)

    Savvidy, G.

    2006-01-01

    We suggest an extension of the gauge principle which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large integer spin 1,2,l. Non-Abelian tensor gauge fields can be viewed as a unique gauge field with values in the infinite-dimensional current algebra associated with compact Lie group. The full Lagrangian exhibits also enhanced local gauge invariance with double number of gauge parameters which allows to eliminate all negative norm states of the nonsymmetric second-rank tensor gauge field, which describes therefore two polarizations of helicity-two massless charged tensor gauge boson and the helicity-zero ''axion'' The geometrical interpretation of the enhanced gauge symmetry with double number of gauge parameters is not yet known. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

  19. Variational optimization algorithms for uniform matrix product states

    Science.gov (United States)

    Zauner-Stauber, V.; Vanderstraeten, L.; Fishman, M. T.; Verstraete, F.; Haegeman, J.

    2018-01-01

    We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation.

  20. Quark-gluon mixing in pseudoscalar and tensor mesons

    International Nuclear Information System (INIS)

    Eremyan, Sh.S.; Nazaryan, A.E.

    1986-01-01

    A mixing model of quark-antiquark ang gluonium states in η, η', i(1440) pseudoscalar and f, f', Θ(1690) tensor mesons is considered. Description of and predictions for 68 two-particle decays with these particles taking part in them are obtained. It is shown that i(1440) by 85% consists of gluonium and Θ(1690) is a pure gluonic state. The quark-gluon and gluon-gluon couplings in the pseudoscalar sector are obtained to be stronger as compared to the corresponding ones in the tensor case

  1. Tensor-optimized shell model for the Li isotopes with a bare nucleon-nucleon interaction

    Science.gov (United States)

    Myo, Takayuki; Umeya, Atsushi; Toki, Hiroshi; Ikeda, Kiyomi

    2012-08-01

    We study the Li isotopes systematically in terms of the tensor-optimized shell model (TOSM) by using a bare nucleon-nucleon interaction as the AV8' interaction. The short-range correlation is treated in the unitary correlation operator method (UCOM). Using the TOSM + UCOM approach, we investigate the role of the tensor force on each spectrum of the Li isotopes. It is found that the tensor force produces quite a characteristic effect on various states in each spectrum and those spectra are affected considerably by the tensor force. The energy difference between the spin-orbit partner, the p1/2 and p3/2 orbits of the last neutron, in 5Li is caused by opposite roles of the tensor correlation. In 6Li, the spin-triplet state in the LS coupling configuration is favored energetically by the tensor force in comparison with jj coupling shell-model states. In 7,8,9Li, the low-lying states containing extra neutrons in the p3/2 orbit are favored energetically due to the large tensor contribution to allow the excitation from the 0s, orbit to the p1/2 orbit by the tensor force. Those three nuclei show the jj coupling character in their ground states which is different from 6Li.

  2. State regulation and power plant productivity: background and recommendations

    International Nuclear Information System (INIS)

    1980-09-01

    This report was prepared by representatives of several state regulatory agencies. It is a guide to some of the activities currently under way in state agencies to promote increased availability of electrical generating power plants. Standard measures of plant performance are defined and the nature of data bases that report such measures is discussed. It includes reviews of current state, federal, and industry programs to enhance power plant productivity and provides detailed outlines of programs in effect in California, Illinois, Michigan, New York, North Carolina, Ohio, and Texas. A number of actions are presented that could be adopted by state regulatory agencies, depending on local conditions. They include: develop a commission position or policy statement to encourage productivity improvements by utilities; coordinate state efforts with ongoing industry and government programs to improve the acquisition of power plant performance data and the maintenance of quality information systems; acquire the capability to perform independent analyses of power plant productivity; direct the establishment of productivity improvement programs, including explicit performance objectives for both existing and planned power plants, and a performance program; establish a program of incentives to motivate productivity improvement activities; and participate in ongoing efforts at all levels and initiate new actions to promote productivity improvements

  3. KMS states on Nica-Toeplitz algebras of product systems

    DEFF Research Database (Denmark)

    Hong, Jeong Hee; Larsen, Nadia S.; Szymanski, Wojciech

    2012-01-01

    We investigate KMS states of Fowler's Nica-Toeplitz algebra NT(X) associated to a compactly aligned product system X over a semigroup P of Hilbert bimodules. This analysis relies on restrictions of these states to the core algebra which satisfy appropriate scaling conditions. The concept of product...... system of finite type is introduced. If (G, P) is a lattice ordered group and X is a product system of finite type over P satisfying certain coherence properties, we construct KMS_beta states of NT(X) associated to a scalar dynamics from traces on the coefficient algebra of the product system. Our...... results were motivated by, and generalize some of the results of Laca and Raeburn obtained for the Toeplitz algebra of the affine semigroup over the natural numbers....

  4. Tensor glueball-meson mixing phenomenology

    International Nuclear Information System (INIS)

    Burakovsky, L.; Page, P.R.

    2000-01-01

    The overpopulated isoscalar tensor states are sifted using Schwinger-type mass relations. Two solutions are found: one where the glueball is the f J (2220), and one where the glueball is more distributed, with f 2 (1820) having the largest component. The f 2 (1565) and f J (1710) cannot be accommodated as glueball-(hybrid) meson mixtures in the absence of significant coupling to decay channels. f 2 '(1525)→ππ is in agreement with experiment. The f J (2220) decays neither flavour democratically nor is narrow. (orig.)

  5. Link prediction via generalized coupled tensor factorisation

    DEFF Research Database (Denmark)

    Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.

    2012-01-01

    and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com- mon latent factors using...... different loss functions. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links....

  6. Enhanced amylase production by fusarium solani in solid state fermentation

    International Nuclear Information System (INIS)

    Bakri, Y.; Jawhar, M.; Arabi, M.I.E.

    2014-01-01

    The present study illustrates the investigation carried out on the production of amylase by Fusarium species under solid state fermentation. All the tested Fusarium species were capable of producing amylase. A selected F. solani isolate SY7, showed the highest amylase production in solid state fermentation. Different substrates were screened for enzyme production. Among the several agronomic wastes, wheat bran supported the highest yield of amylase (141.18 U/g of dry substrate) after 3 days of incubation. Optimisation of the physical parameters revealed the optimum pH, temperature and moisture level for amylase production by the isolate as 8.0, 25 C and 70%, respectively. The above results indicate that the production of amylase by F. solani isolate SY7 could be improved by a further optimisation of the medium and culture conditions. (author)

  7. A Givental-like formula and bilinear identities for tensor models

    Energy Technology Data Exchange (ETDEWEB)

    Dartois, Stéphane [LIPN, Institut Galilée, CNRS UMR 7030, Université Paris 13,F-93430, Villetaneuse (France); Laboratoire de Physique Théorique, CNRS UMR 8627, Université Paris 11,91405 Orsay Cedex (France)

    2015-08-26

    In this paper we express some simple random tensor models in a Givental-like fashion i.e. as differential operators acting on a product of generic 1-Hermitian matrix models. Finally we derive Hirota’s equations for these tensor models. Our decomposition is a first step towards integrability of such models.

  8. Angular dependence of resonant inelastic x-ray scattering : A spherical tensor expansion

    NARCIS (Netherlands)

    Juhin, Amelie; Brouder, Christian; de Groot, Frank

    A spherical tensor expansion is carried out to express the resonant inelastic scattering cross-section as a sum of products of fundamental spectra with tensors involving wavevectors and polarization vectors of incident and scattered photons. The expression presented in this paper differs from that

  9. Measurement of mean rotation and strain-rate tensors by using stereoscopic PIV

    DEFF Research Database (Denmark)

    Özcan, Oktay; Meyer, Knud Erik; Larsen, Poul Scheel

    2005-01-01

    A technique is described for measuring the mean velocity gradient (rate-of-displacement) tensor by using a conventional stereoscopic particle image velocimetry (SPIV) system. Planar measurement of the mean vorticity vector, rate-of-rotation and rate-of-strain tensors and the production of turbule...

  10. State-Specific Prevalence of Tobacco Product Use Among Adults - United States, 2014-2015.

    Science.gov (United States)

    Odani, Satomi; Armour, Brian S; Graffunder, Corinne M; Willis, Gordon; Hartman, Anne M; Agaku, Israel T

    2018-01-26

    Despite recent declines in cigarette smoking prevalence, the tobacco product landscape has shifted to include emerging tobacco products* (1,2). Previous research has documented adult use of smokeless tobacco and cigarettes by state (3); however, state-specific data on other tobacco products are limited. To assess tobacco product use in the 50 U.S. states and the District of Columbia (DC), CDC and the National Cancer Institute analyzed self-reported use of six tobacco product types: cigarettes, cigars, regular pipes, water pipes, electronic cigarettes (e-cigarettes), and smokeless tobacco products among adults aged ≥18 years using data from the 2014-2015 Tobacco Use Supplement to the Current Population Survey (TUS-CPS). Prevalence of ever-use of any tobacco product ranged from 27.0% (Utah) to 55.4% (Wyoming). Current (every day or some days) use of any tobacco product ranged from 10.2% (California) to 27.7% (Wyoming). Cigarettes were the most common currently used tobacco product in all states and DC. Among current cigarette smokers, the proportion who currently used one or more other tobacco products ranged from 11.5% (Delaware) to 32.3% (Oregon). Differences in tobacco product use across states underscore the importance of implementing proven population-level strategies to reduce tobacco use and expanding these strategies to cover all forms of tobacco marketed in the United States. Such strategies could include comprehensive smoke-free policies, tobacco product price increases, anti-tobacco mass media campaigns, and barrier-free access to clinical smoking cessation resources (1,4).

  11. Spectral Tensor-Train Decomposition

    DEFF Research Database (Denmark)

    Bigoni, Daniele; Engsig-Karup, Allan Peter; Marzouk, Youssef M.

    2016-01-01

    The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT...... adaptive Smolyak approach. The method is also used to approximate the solution of an elliptic PDE with random input data. The open source software and examples presented in this work are available online (http://pypi.python.org/pypi/TensorToolbox/)....

  12. Tensors and second quantization

    NARCIS (Netherlands)

    Graaf, de J.

    2010-01-01

    Starting from a pair of vector spaces (formula) an inner product space and (formula), the space of linear mappings (formula), we construct a six-tuple (formula). Here (formula) is again an inner product space and (formula) the space of its linear mappings. It is required that (formula), as linear

  13. The 'gravitating' tensor in the dualistic theory

    International Nuclear Information System (INIS)

    Mahanta, M.N.

    1989-01-01

    The exact microscopic system of Einstein-type field equations of the dualistic gravitation theory is investigated as well as an analysis of the modified energy-momentum tensor or so called 'gravitating' tensor is presented

  14. Tensor calculus for physics a concise guide

    CERN Document Server

    Neuenschwander, Dwight E

    2015-01-01

    Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism...

  15. Mean template for tensor-based morphometry using deformation tensors.

    Science.gov (United States)

    Leporé, Natasha; Brun, Caroline; Pennec, Xavier; Chou, Yi-Yu; Lopez, Oscar L; Aizenstein, Howard J; Becker, James T; Toga, Arthur W; Thompson, Paul M

    2007-01-01

    Tensor-based morphometry (TBM) studies anatomical differences between brain images statistically, to identify regions that differ between groups, over time, or correlate with cognitive or clinical measures. Using a nonlinear registration algorithm, all images are mapped to a common space, and statistics are most commonly performed on the Jacobian determinant (local expansion factor) of the deformation fields. In, it was shown that the detection sensitivity of the standard TBM approach could be increased by using the full deformation tensors in a multivariate statistical analysis. Here we set out to improve the common space itself, by choosing the shape that minimizes a natural metric on the deformation tensors from that space to the population of control subjects. This method avoids statistical bias and should ease nonlinear registration of new subjects data to a template that is 'closest' to all subjects' anatomies. As deformation tensors are symmetric positive-definite matrices and do not form a vector space, all computations are performed in the log-Euclidean framework. The control brain B that is already the closest to 'average' is found. A gradient descent algorithm is then used to perform the minimization that iteratively deforms this template and obtains the mean shape. We apply our method to map the profile of anatomical differences in a dataset of 26 HIV/AIDS patients and 14 controls, via a log-Euclidean Hotelling's T2 test on the deformation tensors. These results are compared to the ones found using the 'best' control, B. Statistics on both shapes are evaluated using cumulative distribution functions of the p-values in maps of inter-group differences.

  16. Corrosion-product transport, oxidation state and remedial measures

    International Nuclear Information System (INIS)

    Sawicki, J.A.; Brett, M.E.; Tapping, R.L.

    1998-01-01

    The issues associated with monitoring and controlling corrosion-product transport (CPT) in the balance-of-plant (BOP) and steam generators (SG) of CANDU stations are briefly reviewed. The efforts are focused on minimizing corrosion of carbon steel, which is used extensively in the CANDU primary and secondary systems. Emphasis is placed on the corrosion-product oxidation state as a monitor of water chemistry effectiveness, and as a monitor of system corrosion effects. The discussion is based mostly on the results and observations from Ontario Hydro plants, and their comparisons with PWRs. The effects of low oxygen and elevated hydrazine chemistry are reviewed, as well as the effects of lay-up and various start-up conditions. Progress in monitoring electrochemical potential (ECP) at Ontario Hydro plants and its relationship to the oxidation state of corrosion products is reviewed. Observations on corrosion-product transport on the primary side of steam generators are also discussed. (author)

  17. Total Factor Productivity Convergence in German States Since Reunification

    DEFF Research Database (Denmark)

    Burda, Michael C.; Severgnini, Battista

    2018-01-01

    A quarter-century after reunification, labor productivity in the states of eastern Germany continues to lag systematically behind the West. Persistent gaps in total factor productivity (TFP) are the proximate cause; conventional and capital-free measurements confirm a sharp slowdown in TFP growth...... of managers, low startup intensity and the distribution of firm size in the East rather than R&D activities....

  18. The nonabelian tensor square of Bieberbach group of dimension five with dihedral point group of order eight

    Science.gov (United States)

    Fauzi, Wan Nor Farhana Wan Mohd; Idrus, Nor'ashiqin Mohd; Masri, Rohaidah; Sarmin, Nor Haniza

    2014-07-01

    The nonabelian tensor product was originated in homotopy theory as well as in algebraic K-theory. The nonabelian tensor square is a special case of the nonabelian tensor product where the product is defined if the two groups act on each other in a compatible way and their action are taken to be conjugation. In this paper, the computation of nonabelian tensor square of a Bieberbach group, which is a torsion free crystallographic group, of dimension five with dihedral point group of order eight is determined. Groups, Algorithms and Programming (GAP) software has been used to assist and verify the results.

  19. Reciprocal mass tensor : a general form

    International Nuclear Information System (INIS)

    Roy, C.L.

    1978-01-01

    Using the results of earlier treatment of wave packets, a general form of reciprocal mass tensor has been obtained. The elements of this tensor are seen to be dependent on momentum as well as space coordinates of the particle under consideration. The conditions under which the tensor would reduce to the usual space-independent form, are discussed and the impact of the space-dependence of this tensor on the motion of Bloch electrons, is examined. (author)

  20. A new deteriorated energy-momentum tensor

    International Nuclear Information System (INIS)

    Duff, M.J.

    1982-01-01

    The stress-tensor of a scalar field theory is not unique because of the possibility of adding an 'improvement term'. In supersymmetric field theories the stress-tensor will appear in a super-current multiplet along with the sypersymmetry current. The general question of the supercurrent multiplet for arbitrary deteriorated stress tensors and their relationship to supercurrent multiplets for models with gauge antisymmetric tensors is answered for various models of N = 1, 2 and 4 supersymmetry. (U.K.)

  1. Tensor categories and the mathematics of rational and logarithmic conformal field theory

    International Nuclear Information System (INIS)

    Huang, Yi-Zhi; Lepowsky, James

    2013-01-01

    We review the construction of braided tensor categories and modular tensor categories from representations of vertex operator algebras, which correspond to chiral algebras in physics. The extensive and general theory underlying this construction also establishes the operator product expansion for intertwining operators, which correspond to chiral vertex operators, and more generally, it establishes the logarithmic operator product expansion for logarithmic intertwining operators. We review the main ideas in the construction of the tensor product bifunctors and the associativity isomorphisms. For rational and logarithmic conformal field theories, we review the precise results that yield braided tensor categories, and in the rational case, modular tensor categories as well. In the case of rational conformal field theory, we also briefly discuss the construction of the modular tensor categories for the Wess–Zumino–Novikov–Witten models and, especially, a recent discovery concerning the proof of the fundamental rigidity property of the modular tensor categories for this important special case. In the case of logarithmic conformal field theory, we mention suitable categories of modules for the triplet W-algebras as an example of the applications of our general construction of the braided tensor category structure. (review)

  2. The direct tensor solution and higher-order acquisition schemes for generalized diffusion tensor imaging

    NARCIS (Netherlands)

    Akkerman, Erik M.

    2010-01-01

    Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional

  3. Fourth meeting entitled “Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data”

    CERN Document Server

    Vilanova, Anna; Burgeth, Bernhard; Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data

    2014-01-01

    Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties. Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discusses the current state of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs. The second Part, Representation and Processing of Higher-order Descriptors, describes a matrix representation of local phase, outlines mathematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI. Part III, Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to model and...

  4. Degenerate Perturbation Theory for Electronic g Tensors: Leading-Order Relativistic Effects.

    Science.gov (United States)

    Rinkevicius, Zilvinas; de Almeida, Katia Julia; Oprea, Cornel I; Vahtras, Olav; Ågren, Hans; Ruud, Kenneth

    2008-11-11

    A new approach for the evaluation of the leading-order relativistic corrections to the electronic g tensors of molecules with a doublet ground state is presented. The methodology is based on degenerate perturbation theory and includes all relevant contributions to the g tensor shift up to order O(α(4)) originating from the one-electron part of the Breit-Pauli Hamiltonian-that is, it allows for the treatment of scalar relativistic, spin-orbit, and mixed corrections to the spin and orbital Zeeman effects. This approach has been implemented in the framework of spin-restricted density functional theory and is in the present paper, as a first illustration of the theory, applied to study relativistic effects on electronic g tensors of dihalogen anion radicals X2(-) (X = F, Cl, Br, I). The results indicate that the spin-orbit interaction is responsible for the large parallel component of the g tensor shift of Br2(-) and I2(-), and furthermore that both the leading-order scalar relativistic and spin-orbit corrections are of minor importance for the perpendicular component of the g tensor in these molecules since they effectively cancel each other. In addition to investigating the g tensors of dihalogen anion radicals, we also critically examine the importance of various relativistic corrections to the electronic g tensor of linear molecules with Σ-type ground states and present a two-state model suitable for an approximate estimation of the g tensor in such molecules.

  5. Efficient Tensor Strategy for Recommendation

    Directory of Open Access Journals (Sweden)

    Aboagye Emelia Opoku

    2017-07-01

    Full Text Available The era of big data has witnessed the explosion of tensor datasets, and large scale Probabilistic Tensor Factorization (PTF analysis is important to accommodate such increasing trend of data. Sparsity, and Cold-Start are some of the inherent problems of recommender systems in the era of big data. This paper proposes a novel Sentiment-Based Probabilistic Tensor Analysis technique senti-PTF to address the problems. The propose framework first applies a Natural Language Processing technique to perform sentiment analysis taking advantage of the huge sums of textual data generated available from the social media which are predominantly left untouched. Although some current studies do employ review texts, many of them do not consider how sentiments in reviews influence recommendation algorithm for prediction. There is therefore this big data text analytics gap whose modeling is computationally expensive. From our experiments, our novel machine learning sentiment-based tensor analysis is computationally less expensive, and addresses the cold-start problem, for optimal recommendation prediction.

  6. Quantum chaos and holographic tensor models

    Energy Technology Data Exchange (ETDEWEB)

    Krishnan, Chethan [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India); Sanyal, Sambuddha [International Center for Theoretical Sciences, Tata Institute of Fundamental Research,Bangalore 560089 (India); Subramanian, P.N. Bala [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India)

    2017-03-10

    A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large-N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.

  7. Quantum chaos and holographic tensor models

    International Nuclear Information System (INIS)

    Krishnan, Chethan; Sanyal, Sambuddha; Subramanian, P.N. Bala

    2017-01-01

    A class of tensor models were recently outlined as potentially calculable examples of holography: their perturbative large-N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for quantum black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten tensor model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and quantum chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.

  8. Weyl tensors for asymmetric complex curvatures

    International Nuclear Information System (INIS)

    Oliveira, C.G.

    Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt

  9. Spherical Tensor Calculus for Local Adaptive Filtering

    Science.gov (United States)

    Reisert, Marco; Burkhardt, Hans

    In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.

  10. Properties of the stress tensor in more than two dimensions

    International Nuclear Information System (INIS)

    Cappelli, A.

    1988-03-01

    Some aspects of conformal invariance in more than two dimensions are analysed. In this case conformal (Weyl) transformations of the metric are not realized in general by coordinate transformations. The operator product expansion of the stress tensor is investigated by means of examples in the free bosonic and fermionic theories. The effective action for the general form of the trace anomaly is built in four dimensions and the Wess-Zumino consistency conditions are discussed. This gives the anomalous transformation law of the stress tensor and the relation to the Casimir effect in the geometry R x S 3 . The explicit computation of the bosonic partition function provides a check

  11. Simultaneous tensor decomposition and completion using factor priors.

    Science.gov (United States)

    Chen, Yi-Lei; Hsu, Chiou-Ting; Liao, Hong-Yuan Mark

    2014-03-01

    The success of research on matrix completion is evident in a variety of real-world applications. Tensor completion, which is a high-order extension of matrix completion, has also generated a great deal of research interest in recent years. Given a tensor with incomplete entries, existing methods use either factorization or completion schemes to recover the missing parts. However, as the number of missing entries increases, factorization schemes may overfit the model because of incorrectly predefined ranks, while completion schemes may fail to interpret the model factors. In this paper, we introduce a novel concept: complete the missing entries and simultaneously capture the underlying model structure. To this end, we propose a method called simultaneous tensor decomposition and completion (STDC) that combines a rank minimization technique with Tucker model decomposition. Moreover, as the model structure is implicitly included in the Tucker model, we use factor priors, which are usually known a priori in real-world tensor objects, to characterize the underlying joint-manifold drawn from the model factors. By exploiting this auxiliary information, our method leverages two classic schemes and accurately estimates the model factors and missing entries. We conducted experiments to empirically verify the convergence of our algorithm on synthetic data and evaluate its effectiveness on various kinds of real-world data. The results demonstrate the efficacy of the proposed method and its potential usage in tensor-based applications. It also outperforms state-of-the-art methods on multilinear model analysis and visual data completion tasks.

  12. Competitiveness of wood pulp production in different Brazilian states

    Directory of Open Access Journals (Sweden)

    Naisy Silva Soares

    2013-06-01

    Full Text Available This work aimed to analyze the competitiveness of wood pulp production in different Brazilian states, in May, 2008 (Minas Gerais, São Paulo, Espírito Santo and Bahia, using the Policy Analysis Matrix (PAM. The results obtained indicated that the private and social profitability of wood pulp production and commercialization was positive and greater in Bahia. The Brazilian companies were penalized by public policies adopted for the sector; the wood pulp production in São Paulo and Bahia were more competitive and less exposed to the negative effects of public policies that reduce the national company profits.

  13. Mesh Denoising based on Normal Voting Tensor and Binary Optimization.

    Science.gov (United States)

    Yadav, Sunil Kumar; Reitebuch, Ulrich; Polthier, Konrad

    2017-08-17

    This paper presents a two-stage mesh denoising algorithm. Unlike other traditional averaging approaches, our approach uses an element-based normal voting tensor to compute smooth surfaces. By introducing a binary optimization on the proposed tensor together with a local binary neighborhood concept, our algorithm better retains sharp features and produces smoother umbilical regions than previous approaches. On top of that, we provide a stochastic analysis on the different kinds of noise based on the average edge length. The quantitative results demonstrate that the performance of our method is better compared to state-of-the-art smoothing approaches.

  14. Relativistic New Yukawa-Like Potential and Tensor Coupling

    International Nuclear Information System (INIS)

    Ikhdair, S.M.; Hamzavi, M.

    2012-01-01

    We approximately solve the Dirac equation for a new suggested generalized inversely quadratic Yukawa potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number κ. In the framework of the spin and pseudo spin (p-spin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions, in closed form, by using the parametric Nikiforov-Uvarov method. The numerical results show that the Coulomb-like tensor interaction, -T/r, removes degeneracies between spin and p-spin state doublets. The Dirac solutions in the presence of exact spin symmetry are reduced to Schroedinger solutions for Yukawa and inversely quadratic Yukawa potentials. (author)

  15. Core Polarization and Tensor Coupling Effects on Magnetic Moments of Hypernuclei

    International Nuclear Information System (INIS)

    Jiang-Ming, Yao; Jie, Meng; Hong-Feng, Lü; Greg, Hillhouse

    2008-01-01

    Effects of core polarization and tensor coupling on the magnetic moments in Λ 13 C, Λ 17 O, and Λ 41 Ca Λ-hypernuclei are studied by employing the Dirac equation with scalar, vector and tensor potentials. It is found that the effect of core polarization on the magnetic moments is suppressed by Λ tensor coupling. The Λ tensor potential reduces the spin-orbit splitting of p Λ states considerably. However, almost the same magnetic moments are obtained using the hyperon wavefunction obtained via the Dirac equation either with or without the A tensor potential in the electromagnetic current vertex. The deviations of magnetic moments for p Λ states from the Schmidt values are found to increase with nuclear mass number. (nuclear physics)

  16. Tannase Production by Solid State Fermentation of Cashew Apple Bagasse

    Science.gov (United States)

    Podrigues, Tigressa H. S.; Dantas, Maria Alcilene A.; Pinto, Gustavo A. S.; Gonçalves, Luciana R. B.

    The ability of Aspergillus oryzae for the production of tannase by solid state fermentation was investigated using cashew apple bagasse (CAB) as substrate. The effect of initial water content was studied and maximum enzyme production was obtained when 60 mL of water was added to 100.0 g of CAB. The fungal strain was able to grow on CAB without any supplementation but a low enzyme activity was obtained, 0.576 U/g of dry substrate (gds). Optimization of process parameters such as supplementation with tannic acid, phosphorous, and different organic and inorganic nitrogen sources was studied. The addition of tannic acid affected the enzyme production and maximum tannase activity (2.40 U/gds) was obtained with 2.5% (w/w) supplementation. Supplementation with ammonium nitrate, peptone, and yeast extract exerted no influence on tannase production. Ammonium sulphate improved the enzyme production in 3.75-fold compared with control. Based on the experimental results, CAB is a promising substrate for solid state fermentation, enabling A. oryzae growth and the production of tannase, with a maximum activity of 3.42 U/gds and enzyme productivity of 128.5×10-3 U·gds -1·h-1.

  17. Micromechanics based framework with second-order damage tensors

    Science.gov (United States)

    Desmorat, R.; Desmorat, B.; Olive, M.; Kolev, B.

    2018-05-01

    The harmonic product of tensors---leading to the concept of harmonic factorization---has been defined in a previous work (Olive et al, 2017). In the practical case of 3D crack density measurements on thin or thick walled structures, this mathematical tool allows us to factorize the harmonic (irreducible) part of the fourth-order damage tensor as an harmonic square: an exact harmonic square in 2D, an harmonic square over the set of so-called mechanically accessible directions for measurements in the 3D case. The corresponding micro-mechanics framework based on second---instead of fourth---order damage tensors is derived. An illustrating example is provided showing how the proposed framework allows for the modeling of the so-called hydrostatic sensitivity up to high damage levels.

  18. A new Weyl-like tensor of geometric origin

    Science.gov (United States)

    Vishwakarma, Ram Gopal

    2018-04-01

    A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank tensor of the hierarchy possesses all the geometrical properties of the Weyl tensor.

  19. Youth tobacco product use in the United States.

    Science.gov (United States)

    Lee, Youn Ok; Hebert, Christine J; Nonnemaker, James M; Kim, Annice E

    2015-03-01

    Noncigarette tobacco products are increasingly popular among youth, especially cigarette smokers. Understanding multiple tobacco product use is necessary to assess the effects of tobacco products on population health. This study examines multiple tobacco product use and associated risk factors among US youth. Estimates of current use were calculated for cigarettes, cigars, smokeless tobacco, hookah, e-cigarettes, pipes, bidis, kreteks, snus, and dissolvable tobacco by using data from the 2012 National Youth Tobacco Survey (n = 24 658), a nationally representative sample of US middle and high school students. Associations between use patterns and demographic characteristics were examined by using multinomial logistic regression. Among youth, 14.7% currently use 1 or more tobacco products. Of these, 2.8% use cigarettes exclusively, and 4% use 1 noncigarette product exclusively; 2.7% use cigarettes with another product (dual use), and 4.3% use 3 or more products (polytobacco use). Twice as many youth use e-cigarettes alone than dual use with cigarettes. Among smokers, polytobacco use was significantly associated with male gender (adjusted relative risk ratio [aRRR] = 3.71), by using flavored products (aRRR = 6.09), nicotine dependence (aRRR = 1.91), tobacco marketing receptivity (aRRR = 2.52), and perceived prevalence of peer use of tobacco products (aRRR = 3.61, 5.73). More than twice as many youth in the United States currently use 2 or more tobacco products than cigarettes alone. Continued monitoring of tobacco use patterns is warranted, especially for e-cigarettes. Youth rates of multiple product use involving combustible products underscore needs for research assessing potential harms associated with these patterns. Copyright © 2015 by the American Academy of Pediatrics.

  20. Tobacco Product Use Among Adults - United States, 2015.

    Science.gov (United States)

    Phillips, Elyse; Wang, Teresa W; Husten, Corinne G; Corey, Catherine G; Apelberg, Benjamin J; Jamal, Ahmed; Homa, David M; King, Brian A

    2017-11-10

    Tobacco use remains the leading cause of preventable disease and death in the United States (1). Despite declining cigarette smoking prevalence among U.S. adults, shifts in the tobacco product landscape have occurred in recent years (2,3). Previous estimates of tobacco product use among U.S. adults were obtained from the National Adult Tobacco Survey, which ended after the 2013-2014 cycle. This year, CDC and the Food and Drug Administration (FDA) assessed the most recent national estimates of tobacco product use among adults aged ≥18 years using, for the first time, data from the 2015 National Health Interview Survey (NHIS), an annual, nationally representative, in-person survey of the noninstitutionalized U.S. civilian population. The 2015 NHIS adult core questionnaire included 33,672 adults aged ≥18 years, reflecting a 55.2% response rate. Data were weighted to adjust for differences in selection probability and nonresponse, and to provide nationally representative estimates. In 2015, 20.1 % of U.S. adults currently (every day or some days) used any tobacco product, 17.6% used any combustible tobacco product, and 3.9% used ≥2 tobacco products. By product, 15.1% of adults used cigarettes; 3.5% used electronic cigarettes (e-cigarettes); 3.4% used cigars, cigarillos, or filtered little cigars; 2.3% used smokeless tobacco; and 1.2% used regular pipes, water pipes, or hookahs.* Current use of any tobacco product was higher among males; persons aged product was 47.2% among adults with serious psychological distress compared with 19.2% among those without serious psychological distress. Proven population-level interventions that focus on the diversity of tobacco product use are important to reducing tobacco-related disease and death in the United States (1).

  1. economics of cucumber production in rivers state, nigeria

    African Journals Online (AJOL)

    2016-05-02

    May 2, 2016 ... Faculty of Agriculture, University of Port Harcourt, Rivers State, Nigeria ... The study aimed to determine the profitability of cucumber production in two local government .... more amenable to risk taking and change than non- ..... improve cucumber value chain, attract better prices ... management practices.

  2. Problems and Prospects of Pineapple Production in Enugu State ...

    African Journals Online (AJOL)

    The study identified problems and prospects of pineapple production in Enugu State of Nigeria. Purposive sampling technique was used to select eighty (80) pineapple farmers from two agricultural zones. Data were analyzed using percentage and mean score. Results showed that greater proportion of the farmers was ...

  3. Dairy production in some selected integrated farms in Sokoto State ...

    African Journals Online (AJOL)

    A survey of eight integrated farms in four local government areas of Sokoto state in north-western Nigeria revealed the following about dairy production on such farms:breed of cattle kept, Sokoto Gudali, Friesian, and Sahiwal; average dairy herd size,69.4 head; husbandry system was largely semi-intensive; milking was ...

  4. Effects of Climate Change on Poultry Production in Ondo State ...

    African Journals Online (AJOL)

    The study assessed the effects of climate change on poultry production in Ondo State, Nigeria. Eighty three (83) poultry farmers were interviewed to elicit relevant information in line with the objectives of the study. Descriptive statistics and inferential statistical tools were used for data analysis. Findings revealed that majority ...

  5. Braille in the United States: Its Production, Distribution, and Use.

    Science.gov (United States)

    Goldish, Louis Harvey

    The braille production system in the United States is described. Aspects treated are the following: the need for braille (the braille system), the market for braille (size and characteristics), sources of braille (producers and braille book source information), and present methods and costs of producing braille. Technological advances are…

  6. Resource Use Efficiency in Sweet Potato Production in Kwara State ...

    African Journals Online (AJOL)

    This paper examines resource use efficiency in sweet potato production in Offa and Oyun local government areas of Kwara State of Nigeria. Primary data were collected from one hundred sweet potato farmers who were selected from the two local government areas during the 2003/2004 farming season. The data was ...

  7. Amylase production under solid state fermentation by a bacterial ...

    African Journals Online (AJOL)

    This study was concerned with the screening of a suitable isolate and optimization of cultural conditions for the biosynthesis of thermostable amylase under solid state fermentation (SSF). Twenty seven isolates were screened for amylase production out of which one isolate designated as W74 showed maximal amylase ...

  8. Corrosion-product transport, oxidation state and remedial measures

    International Nuclear Information System (INIS)

    Sawicki, J.A.; Brett, M.E.; Tapping, R.L.

    1998-10-01

    The issues associated with monitoring and controlling corrosion-product transport (CPT) in the balance-of-plant (BOP) and steam generators (SG) of CANDU stations are briefly reviewed. Efforts are focused on minimizing corrosion of carbon steel, which is used extensively in the CANDU primary and secondary systems. Emphasis is placed on the corrosion-product oxidation state as a monitor of water chemistry effectiveness and as a monitor of system corrosion effects. The discussion is based mostly on the results of observations from Ontario Hydro plants, and their comparisons with pressurized-water reactors. The effects of low oxygen and elevated hydrazine chemistry are reviewed, as well as the effects of layup and various startup conditions. Progress in monitoring electrochemical potential (ECP) at Ontario Hydro plants and its relationship to the oxidation state of corrosion products is reviewed. Observations on CPT on the primary side of SGs are also discussed. (author)

  9. Production and spectroscopy of quarkonia states at the ATLAS experiment

    CERN Document Server

    Price, D; The ATLAS collaboration

    2014-01-01

    This presentation will cover ATLAS results in the domain of charmonium production, including J/psi, psi(2s) and chi_c states. The analyses discussed include double-differential production cross-section measurements of the J/psi, psi(2S) and P-wave charmonium states chi_cJ, extending upon previous measurements in precision and kinematic reach. Prompt and non-prompt modes are distinguished, as well as J/psi vs psi(2s) and the contribution to J/psi production from chi_c feed-down. Alongside the latter analysis, a competitive measurement of the branching fraction B± --> chi_c1 + K± was also performed. Results of the measurements are compared with the latest theoretical predictions from a variety of theoretical approaches.

  10. Simulating quantum systems on classical computers with matrix product states

    International Nuclear Information System (INIS)

    Kleine, Adrian

    2010-01-01

    In this thesis, the numerical simulation of strongly-interacting many-body quantum-mechanical systems using matrix product states (MPS) is considered. Matrix-Product-States are a novel representation of arbitrary quantum many-body states. Using quantum information theory, it is possible to show that Matrix-Product-States provide a polynomial-sized representation of one-dimensional quantum systems, thus allowing an efficient simulation of one-dimensional quantum system on classical computers. Matrix-Product-States form the conceptual framework of the density-matrix renormalization group (DMRG). After a general introduction in the first chapter of this thesis, the second chapter deals with Matrix-Product-States, focusing on the development of fast and stable algorithms. To obtain algorithms to efficiently calculate ground states, the density-matrix renormalization group is reformulated using the Matrix-Product-States framework. Further, time-dependent problems are considered. Two different algorithms are presented, one based on a Trotter decomposition of the time-evolution operator, the other one on Krylov subspaces. Finally, the evaluation of dynamical spectral functions is discussed, and a correction vector-based method is presented. In the following chapters, the methods presented in the second chapter, are applied to a number of different physical problems. The third chapter deals with the existence of chiral phases in isotropic one-dimensional quantum spin systems. A preceding analytical study based on a mean-field approach indicated the possible existence of those phases in an isotropic Heisenberg model with a frustrating zig-zag interaction and a magnetic field. In this thesis, the existence of the chiral phases is shown numerically by using Matrix-Product-States-based algorithms. In the fourth chapter, we propose an experiment using ultracold atomic gases in optical lattices, which allows a well controlled observation of the spin-charge separation (of

  11. Simulating quantum systems on classical computers with matrix product states

    Energy Technology Data Exchange (ETDEWEB)

    Kleine, Adrian

    2010-11-08

    In this thesis, the numerical simulation of strongly-interacting many-body quantum-mechanical systems using matrix product states (MPS) is considered. Matrix-Product-States are a novel representation of arbitrary quantum many-body states. Using quantum information theory, it is possible to show that Matrix-Product-States provide a polynomial-sized representation of one-dimensional quantum systems, thus allowing an efficient simulation of one-dimensional quantum system on classical computers. Matrix-Product-States form the conceptual framework of the density-matrix renormalization group (DMRG). After a general introduction in the first chapter of this thesis, the second chapter deals with Matrix-Product-States, focusing on the development of fast and stable algorithms. To obtain algorithms to efficiently calculate ground states, the density-matrix renormalization group is reformulated using the Matrix-Product-States framework. Further, time-dependent problems are considered. Two different algorithms are presented, one based on a Trotter decomposition of the time-evolution operator, the other one on Krylov subspaces. Finally, the evaluation of dynamical spectral functions is discussed, and a correction vector-based method is presented. In the following chapters, the methods presented in the second chapter, are applied to a number of different physical problems. The third chapter deals with the existence of chiral phases in isotropic one-dimensional quantum spin systems. A preceding analytical study based on a mean-field approach indicated the possible existence of those phases in an isotropic Heisenberg model with a frustrating zig-zag interaction and a magnetic field. In this thesis, the existence of the chiral phases is shown numerically by using Matrix-Product-States-based algorithms. In the fourth chapter, we propose an experiment using ultracold atomic gases in optical lattices, which allows a well controlled observation of the spin-charge separation (of

  12. Comparison of Magnetic Susceptibility Tensor and Diffusion Tensor of the Brain.

    Science.gov (United States)

    Li, Wei; Liu, Chunlei

    2013-10-01

    Susceptibility tensor imaging (STI) provides a novel approach for noninvasive assessment of the white matter pathways of the brain. Using mouse brain ex vivo , we compared STI with diffusion tensor imaging (DTI), in terms of tensor values, principal tensor values, anisotropy values, and tensor orientations. Despite the completely different biophysical underpinnings, magnetic susceptibility tensors and diffusion tensors show many similarities in the tensor and principal tensor images, for example, the tensors perpendicular to the fiber direction have the highest gray-white matter contrast, and the largest principal tensor is along the fiber direction. Comparison to DTI fractional anisotropy, the susceptibility anisotropy provides much higher sensitivity to the chemical composition of the white matter, especially myelin. The high sensitivity can be further enhanced with the perfusion of ProHance, a gadolinium-based contrast agent. Regarding the tensor orientations, the direction of the largest principal susceptibility tensor agrees with that of diffusion tensors in major white matter fiber bundles. The STI fiber tractography can reconstruct the fiber pathways for the whole corpus callosum and for white matter fiber bundles that are in close contact but in different orientations. There are some differences between susceptibility and diffusion tensor orientations, which are likely due to the limitations in the current STI reconstruction. With the development of more accurate reconstruction methods, STI holds the promise for probing the white matter micro-architectures with more anatomical details and higher chemical sensitivity.

  13. Tensor voting for robust color edge detection

    OpenAIRE

    Moreno, Rodrigo; García, Miguel Ángel; Puig, Domenec

    2014-01-01

    The final publication is available at Springer via http://dx.doi.org/10.1007/978-94-007-7584-8_9 This chapter proposes two robust color edge detection methods based on tensor voting. The first method is a direct adaptation of the classical tensor voting to color images where tensors are initialized with either the gradient or the local color structure tensor. The second method is based on an extension of tensor voting in which the encoding and voting processes are specifically tailored to ...

  14. The Physical Interpretation of the Lanczos Tensor

    OpenAIRE

    Roberts, Mark D.

    1999-01-01

    The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. The Lanczos tensor plays a similar role in general relativity to that of the vector potential in electro-magnetic theory. The Aharonov-Bohm effect shows that when quantum mechanics is applied to electro-magnetic theory the vector potential is dynamicall...

  15. Matrix product density operators: Renormalization fixed points and boundary theories

    Energy Technology Data Exchange (ETDEWEB)

    Cirac, J.I. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Pérez-García, D., E-mail: dperezga@ucm.es [Departamento de Análisis Matemático, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain); ICMAT, Nicolas Cabrera, Campus de Cantoblanco, 28049 Madrid (Spain); Schuch, N. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Verstraete, F. [Department of Physics and Astronomy, Ghent University (Belgium); Vienna Center for Quantum Technology, University of Vienna (Austria)

    2017-03-15

    We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).

  16. Robust estimation of adaptive tensors of curvature by tensor voting.

    Science.gov (United States)

    Tong, Wai-Shun; Tang, Chi-Keung

    2005-03-01

    Although curvature estimation from a given mesh or regularly sampled point set is a well-studied problem, it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise. Such input is ubiquitous in computer vision. In this paper, we propose a three-pass tensor voting algorithm to robustly estimate curvature tensors, from which accurate principal curvatures and directions can be calculated. Our quantitative estimation is an improvement over the previous two-pass algorithm, where only qualitative curvature estimation (sign of Gaussian curvature) is performed. To overcome misalignment errors, our improved method automatically corrects input point locations at subvoxel precision, which also rejects outliers that are uncorrectable. To adapt to different scales locally, we define the RadiusHit of a curvature tensor to quantify estimation accuracy and applicability. Our curvature estimation algorithm has been proven with detailed quantitative experiments, performing better in a variety of standard error metrics (percentage error in curvature magnitudes, absolute angle difference in curvature direction) in the presence of a large amount of misalignment noise.

  17. Antisymmetric tensor generalizations of affine vector fields.

    Science.gov (United States)

    Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro

    2016-02-01

    Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.

  18. PRODUCTION OF AN EXTRACELLULAR CELLOBIASE IN SOLID STATE FERMENTATION

    Directory of Open Access Journals (Sweden)

    Ruchi Agrawal

    2013-02-01

    Full Text Available The bioethanol production from lignocellulosic biomass has attracted wide interest globally in last decade. One of the main reasons for the high cost of bioethanol production from lignocellulosic biomass is the expensive enzymes involved in enzymatic hydrolysis of cellulose (cellulase. The utilization of agro-industrial waste as a potential substrate for producing enzymes may serve a dual purpose of reducing the environmental pollution along with producing a high value commercial product. Twelve different agro-industrial wastes were evaluated for extracellular cellobiose or β-glucosidase production by a mutant of Bacillus subtilis on solid state fermentations (SSF. The Citrus sinensis peel waste was found to be the most suitable substrate with highest BGL titre (35 U/gds. Optimum incubation time, inoculum size, moisture content and volume of buffer for enzyme extraction were 72 h, 40 % v/w, 10 mL and 20 mL respectively.

  19. China-United States Productivity Catch-Up

    DEFF Research Database (Denmark)

    Deng, Paul Duo; Jefferson, Gary H.

    China’s gap in industrial labor productivity with the United States has been steadily shrinking over recent decades. In this paper we examine the main sources of gap reduction and the potential for further catch-up. Using Chinese above-scale firm-level data during 1998-2007 period and BEA industry...... -level data in the US, we first document the respective rates of growth of labor productivity, gap reduction, and contributions to overall catch-up of China’s manufacturing sector during 1998-2007. We then aggregate the firm-level data to the 3-digit industry level to estimate a productivity gap...... reduction function and find that the key drivers for the productivity convergence are the initial technology gap, increased R&D spending, firm’s ownership restructuring, and industry level entry-exit ratio, a measure of competitive dynamism. A key finding is that the catch-up dynamic entails the break out...

  20. STATE INVESTMENT IN SCIENCE AND SCIENTIFIC PRODUCTIVITY OF UNIVERSITIES

    Directory of Open Access Journals (Sweden)

    Domagoj Karacic

    2016-06-01

    Full Text Available State investment in service activities of the public sector, as well as the financial returns analyzed from the aspect of service effectiveness and utilization of public goods, can be considered as one of the most significant dilemmas, especially in the field of education. When analyzing state investments, through investment in education and development of the university, we can conclude that state investments in scientific productivity of universities fall into one of the main future frameworks of measurability of universities efficiency. This criterion cannot be taken as the most important since universities are fundamentally divided into teaching and research activities. However, the concept of determination of the productivity of universities, from the aspect of the scientific activities of the teaching staff, has an increasingly important role due to the specified global criteria and conditions for career advancement of the teaching staff and positioning of the university in the education market. This paper intends to give the overview of the current situation of universities in Croatia, as well as the trends that would point out state role in financing of universities and indicate coherent criteria regarding the financing of scientific productivity of teaching stuff.

  1. Extended vector-tensor theories

    Energy Technology Data Exchange (ETDEWEB)

    Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)

    2017-01-01

    Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.

  2. Scalar-tensor linear inflation

    Energy Technology Data Exchange (ETDEWEB)

    Artymowski, Michał [Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków (Poland); Racioppi, Antonio, E-mail: Michal.Artymowski@uj.edu.pl, E-mail: Antonio.Racioppi@kbfi.ee [National Institute of Chemical Physics and Biophysics, Rävala 10, 10143 Tallinn (Estonia)

    2017-04-01

    We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f (φ) R /2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead to linear inflation in the strong coupling limit.

  3. The equation of state of predominant detonation products

    Science.gov (United States)

    Zaug, Joseph; Crowhurst, Jonathan; Bastea, Sorin; Fried, Laurence

    2009-06-01

    The equation of state of detonation products, when incorporated into an experimentally grounded thermochemical reaction algorithm can be used to predict the performance of explosives. Here we report laser based Impulsive Stimulated Light Scattering measurements of the speed of sound from a variety of polar and nonpolar detonation product supercritical fluids and mixtures. The speed of sound data are used to improve the exponential-six potentials employed within the Cheetah thermochemical code. We will discuss the improvements made to Cheetah in terms of predictions vs. measured performance data for common polymer blended explosives. Accurately computing the chemistry that occurs from reacted binder materials is one important step forward in our efforts.

  4. New inner products for physical states in BRST quantization

    International Nuclear Information System (INIS)

    Marnelius, R.; Oegren, M.

    1991-01-01

    In a BRST quantization involving operators with continuous eigenvalues the naive inner products of physical states are usually undefined. In order to include such cases we propose new inner products defined by , where ρ is an odd gauge-fixing operator. In this definition, which requires the use of dynamical Lagrange multipliers, the factor exp i[ρ,Q] is naturally provided by the choice of dynamics. Several examples are worked out. In particular it is shown that the worldline supersymmetric model for a massless spin-1/2 particle leads to fermions whose chiral projections have opposite norms. (orig.)

  5. All-at-once Optimization for Coupled Matrix and Tensor Factorizations

    DEFF Research Database (Denmark)

    Evrim, Acar Ataman; Kolda, Tamara G.; Dunlavy, Daniel M.

    2011-01-01

    .g., the person by person social network matrix or the restaurant by category matrix, and higher-order tensors, e.g., the "ratings" tensor of the form restaurant by meal by person. In this paper, we are particularly interested in fusing data sets with the goal of capturing their underlying latent structures. We...... formulate this problem as a coupled matrix and tensor factorization (CMTF) problem where heterogeneous data sets are modeled by fitting outer-product models to higher-order tensors and matrices in a coupled manner. Unlike traditional approaches solving this problem using alternating algorithms, we propose...... an all-at-once optimization approach called CMTF-OPT (CMTF-OPTimization), which is a gradient-based optimization approach for joint analysis of matrices and higher-order tensors. We also extend the algorithm to handle coupled incomplete data sets. Using numerical experiments, we demonstrate...

  6. The stress energy tensor of a locally supersymmetric quantum field on a curved spacetime

    International Nuclear Information System (INIS)

    Koehler, M.

    1995-04-01

    For an analogon of the free Wess-Zumino model on Ricci flat spacetimes, the relation between a conserved 'supercurrent' and the point-separated improved energy momentum tensor is investigated and a similar relation as on Minkowski space is established. The expectation value of the latter in any globally Hadamard product state is found to be a priori finite in the coincidence limit if the theory is massive. On arbitrary globally hyperbolic spacetimes the 'supercurrent' is shown to be a well defined operator valued distribution on the GNS Hilbertspace of any globally Hadamard product state. Viewed as a new field, all n-point distributions exist, giving a new example for a Wightman field on that manifold. Moreover, it is shown that this field satisfies a new wave front set spectrum condition in a nontrivial way. (orig.)

  7. Diffusion tensor optical coherence tomography

    Science.gov (United States)

    Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.

    2018-01-01

    In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.

  8. Liquid hydrogen production and commercial demand in the United States

    Science.gov (United States)

    Heydorn, Barbara

    1990-01-01

    Kennedy Space Center, the single largest purchaser of liquid hydrogen (LH2) in the United States, evaluated current and anticipated hydrogen production and consumption in the government and commercial sectors. Specific objectives of the study are as follows: (1) identify LH2 producers in the United States and Canada during 1980-1989 period; (2) compile information in expected changes in LH2 production capabilities over the 1990-2000 period; (3) describe how hydrogen is used in each consuming industry and estimate U.S. LH2 consumption for the chemicals, metals, electronics, fats and oil, and glass industries, and report data on a regional basis; (4) estimate historical and future consumption; and (5) assess the influence of international demands on U.S. plants.

  9. Nonperturbative production of multiboson states and quantum bubbles

    International Nuclear Information System (INIS)

    Gorsky, A.S.; Voloshin, M.B.

    1993-01-01

    The amplitude of production of n on-mass-shell scalar bosons by a highly virtual field φ is considered in a λφ 4 theory with weak coupling λ and spontaneously broken symmetry. The amplitude of this process is known to have an n exclamation point growth when the produced bosons are exactly at rest. Here it is shown that for n much-gt 1/λ the process goes through ''quantum bubbles,'' i.e., quantized droplets of a different vacuum phase, which are nonperturbative resonant states of the field φ. The bubbles provide a form factor for the production amplitude, which rapidly decreases above the threshold. As a result the probability of the process may be heavily suppressed and may decrease with energy E as exp(-constxE a ), where the power a depends on the number of space dimensions. Also discussed are the quantized states of bubbles and the amplitudes of their formation and decay

  10. Initial-State Graviton Radiation in Quantum Black Hole Production

    CERN Document Server

    AUTHOR|(CDS)2262067

    2017-01-01

    Monte Carlo simulation of quantum black hole production in the ATLAS experiment that allows for graviton radiation in the initial state is discussed and studied. It is concluded that, using trapped surface calculations and graviton emission, a black hole signal would be significant for Planck scales up to 4.5 TeV given a proton-proton luminosity of 37 fb$^{-1}$ in the 13 TeV LHC configuration.

  11. Sparse alignment for robust tensor learning.

    Science.gov (United States)

    Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming

    2014-10-01

    Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods.

  12. Design, production and initial state of the closure

    International Nuclear Information System (INIS)

    2010-12-01

    The report is included in a set of Production reports, presenting how the KBS-3 repository is designed, produced and inspected. The production reports are included in the safety report for the KBS-3 repository and repository facility. The report provides input on the initial state of the closure and plugs in underground openings other than deposition tunnels for the assessment of the long-term safety, SR-Site. The initial state refers to the properties of the engineered barriers once they have been finally placed in the KBS-3 repository and will not be further handled within the repository facility. In addition, the report provides some input to the operational safety report, SR-Operation, on how the closure and plugs shall be handled and installed. The report presents the design premises and reference designs of the closure and plugs and verifies their conformity to the design premises. It also briefly deals with the production of the closure and plugs. Finally, the initial state of the closure and plugs and their conformity to the reference designs and design premises are presented

  13. Design, production and initial state of the closure

    Energy Technology Data Exchange (ETDEWEB)

    2010-12-15

    The report is included in a set of Production reports, presenting how the KBS-3 repository is designed, produced and inspected. The production reports are included in the safety report for the KBS-3 repository and repository facility. The report provides input on the initial state of the closure and plugs in underground openings other than deposition tunnels for the assessment of the long-term safety, SR-Site. The initial state refers to the properties of the engineered barriers once they have been finally placed in the KBS-3 repository and will not be further handled within the repository facility. In addition, the report provides some input to the operational safety report, SR-Operation, on how the closure and plugs shall be handled and installed. The report presents the design premises and reference designs of the closure and plugs and verifies their conformity to the design premises. It also briefly deals with the production of the closure and plugs. Finally, the initial state of the closure and plugs and their conformity to the reference designs and design premises are presented

  14. Transposes, L-Eigenvalues and Invariants of Third Order Tensors

    OpenAIRE

    Qi, Liqun

    2017-01-01

    Third order tensors have wide applications in mechanics, physics and engineering. The most famous and useful third order tensor is the piezoelectric tensor, which plays a key role in the piezoelectric effect, first discovered by Curie brothers. On the other hand, the Levi-Civita tensor is famous in tensor calculus. In this paper, we study third order tensors and (third order) hypermatrices systematically, by regarding a third order tensor as a linear operator which transforms a second order t...

  15. ENERGY USE ANALYSIS FOR RICE PRODUCTION IN NASARAWA STATE, NIGERIA

    Directory of Open Access Journals (Sweden)

    Hussaini Yusuf Ibrahim

    2012-12-01

    Full Text Available The study was conducted to analyze energy use for in rice production in Nasarawa state Nigeria using a sample of 120 randomly selected rice farmers. Energy productivity, energy efficiency and specific energy were computed and simple descriptive statistics was used for data analysis. The energy use pattern shows that, rice production consumed an average total energy of 12906.8 MJha-1, with herbicide energy input contributing the largest share (53.55 %. Human labour had the least share (0.74 % of the total energy input used. The energy productivity, Specific energy and energy efficiency were 0.3 MJ-1, 3.6 MJ-1 and 4.1 respectively. A total of 10925.0 MJ of energy was used in the form of indirect energy and 1981.8MJ was in the direct form of energy. Non-renewable energy forms contributed the largest share (80.63 % of the total energy input used for rice production in the study area. Rice production in the study area was observed to be mainly dependent on non-renewable and indirect energy input especially herbicide. Thus, the study recommends the introduction of integrated weed management system in order to reduce cost and dependence on a non-renewable input for weed control.

  16. Microbial production of hyaluronic acid: current state, challenges, and perspectives

    Directory of Open Access Journals (Sweden)

    Liu Long

    2011-11-01

    Full Text Available Abstract Hyaluronic acid (HA is a natural and linear polymer composed of repeating disaccharide units of β-1, 3-N-acetyl glucosamine and β-1, 4-glucuronic acid with a molecular weight up to 6 million Daltons. With excellent viscoelasticity, high moisture retention capacity, and high biocompatibility, HA finds a wide-range of applications in medicine, cosmetics, and nutraceuticals. Traditionally HA was extracted from rooster combs, and now it is mainly produced via streptococcal fermentation. Recently the production of HA via recombinant systems has received increasing interest due to the avoidance of potential toxins. This work summarizes the research history and current commercial market of HA, and then deeply analyzes the current state of microbial production of HA by Streptococcus zooepidemicus and recombinant systems, and finally discusses the challenges facing microbial HA production and proposes several research outlines to meet the challenges.

  17. Commonwealth and state controls over uranium exploration and production

    International Nuclear Information System (INIS)

    Nicholson, R.D.

    1979-01-01

    This survey of Commonwealth and State controls relating to uranium exploration and production in Australia shows that legal controls can be imposed at the following points: on licensing or on the grant of an authority to mine by the Commonwealth; by application of a Commonwealth Code of Practice if it is applicable; by the Commonwealth as a condition to approval for export; by the Commonwealth with respect to foreign investment approval; by the Commonwealth or a state in a government agreement relating to the particular development; by the application of a state code of practice where legislation is made on that behalf and by the application of local government requirements to the extent they are not modified by government agreement. There is potential for much overlap and duplication

  18. Optimal matrix product states for the Heisenberg spin chain

    International Nuclear Information System (INIS)

    Latorre, Jose I; Pico, Vicent

    2009-01-01

    We present some exact results for the optimal matrix product state (MPS) approximation to the ground state of the infinite isotropic Heisenberg spin-1/2 chain. Our approach is based on the systematic use of Schmidt decompositions to reduce the problem of approximating for the ground state of a spin chain to an analytical minimization. This allows one to show that results of standard simulations, e.g. density matrix renormalization group and infinite time evolving block decimation, do correspond to the result obtained by this minimization strategy and, thus, both methods deliver optimal MPS with the same energy but, otherwise, different properties. We also find that translational and rotational symmetries cannot be maintained simultaneously by the MPS ansatz of minimum energy and present explicit constructions for each case. Furthermore, we analyze symmetry restoration and quantify it to uncover new scaling relations. The method we propose can be extended to any translational invariant Hamiltonian

  19. Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings.

    Science.gov (United States)

    Iwasaki, Tohru; Furukawa, Tetsuo

    2016-05-01

    In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures. Copyright © 2016 Elsevier Ltd. All rights reserved.

  20. Applications of tensor functions in creep mechanics

    International Nuclear Information System (INIS)

    Betten, J.

    1991-01-01

    Within this contribution a short survey is given of some recent advances in the mathematical modelling of materials behaviour under creep conditions. The mechanical behaviour of anisotropic solids requires a suitable mathematical modelling. The properties of tensor functions with several argument tensors constitute a rational basis for a consistent mathematical modelling of complex material behaviour. This paper presents certain principles, methods, and recent successfull applications of tensor functions in solid mechanics. The rules for specifying irreducible sets of tensor invariants and tensor generators for material tensors of rank two and four are also discussed. Furthermore, it is very important that the scalar coefficients in constitutive and evolutional equations are determined as functions of the integrity basis and experimental data. It is explained in detail that these coefficients can be determined by using tensorial interpolation methods. Some examples for practical use are discussed. (orig./RHM)

  1. Seamless warping of diffusion tensor fields

    DEFF Research Database (Denmark)

    Xu, Dongrong; Hao, Xuejun; Bansal, Ravi

    2008-01-01

    To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping...... of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot...... transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT...

  2. The Topology of Symmetric Tensor Fields

    Science.gov (United States)

    Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval

    1997-01-01

    Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

  3. On improving the efficiency of tensor voting

    OpenAIRE

    Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim

    2011-01-01

    This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor v...

  4. The Riemann-Lovelock Curvature Tensor

    OpenAIRE

    Kastor, David

    2012-01-01

    In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D

  5. The 1/ N Expansion of Tensor Models with Two Symmetric Tensors

    Science.gov (United States)

    Gurau, Razvan

    2018-06-01

    It is well known that tensor models for a tensor with no symmetry admit a 1/ N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/ N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/ N expansion dominated by melonic graphs.

  6. Design, production and initial state of the canister

    Energy Technology Data Exchange (ETDEWEB)

    Cederqvist, Lars; Johansson, Magnus; Leskinen, Nina; Ronneteg, Ulf

    2010-12-15

    The report is included in a set of Production reports, presenting how the KBS-3 repository is designed, produced and inspected. The set of reports is included in the safety report for the KBS-3 repository and repository facility.The report provides input on the initial state of the canisters to the assessment of the long-term safety, SR-Site. The initial state refers to the properties of the engineered barriers once they have been finally placed in the KBS-3 repository and will not be further handled within the repository facility. In addition, the report provides input to the operational safety report, SR-Operation, on how the canisters shall be handled and disposed. The report presents the design premises and reference design of the canister and verifies the conformity of the reference design to the design premises. The production methods and the ability to produce canisters according to the reference design are described. Finally, the initial state of the canisters and their conformity to the reference design and design premises are presented

  7. Design, production and initial state of the canister

    International Nuclear Information System (INIS)

    Cederqvist, Lars; Johansson, Magnus; Leskinen, Nina; Ronneteg, Ulf

    2010-12-01

    The report is included in a set of Production reports, presenting how the KBS-3 repository is designed, produced and inspected. The set of reports is included in the safety report for the KBS-3 repository and repository facility.The report provides input on the initial state of the canisters to the assessment of the long-term safety, SR-Site. The initial state refers to the properties of the engineered barriers once they have been finally placed in the KBS-3 repository and will not be further handled within the repository facility. In addition, the report provides input to the operational safety report, SR-Operation, on how the canisters shall be handled and disposed. The report presents the design premises and reference design of the canister and verifies the conformity of the reference design to the design premises. The production methods and the ability to produce canisters according to the reference design are described. Finally, the initial state of the canisters and their conformity to the reference design and design premises are presented

  8. Directory of cyclotrons used for radionuclide production in Member States

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1998-03-01

    The directory of cyclotrons used for radionuclide production is an update of the data base on cyclotrons that was compiled in 1983 by the International Atomic Energy Agency. The directory contains technical, utilization and administrative information supplied to the IAEA as of October 1997. The directory was prepared through information collected by questionnaires sent to institutions that either have a cyclotron, or that were identified to be in the process of installation of a cyclotron. The directory contains 206 entries for cyclotrons operating in 34 Member States. The largest concentration of cyclotrons for radionuclide production are located in the United States of America (66), Japan (33) and Germany (22). The largest number of cyclotrons for a single country is the United States of America. The expansion in number of cyclotrons during the last decade has been driven by the advent of advances in medical imaging instrumentation (PET, SPET and more recently 511 KeV emission tomography); introduction of user friendly compact medical cyclotrons from several companies that manufacture cyclotrons; and recent decisions that {sup 15}O-oxygen PET studies in Japan, and {sup 18}F-FDG PET studies in Germany are eligible for reimbursement by government or insurance companies.

  9. Directory of cyclotrons used for radionuclide production in Member States

    International Nuclear Information System (INIS)

    1998-03-01

    The directory of cyclotrons used for radionuclide production is an update of the data base on cyclotrons that was compiled in 1983 by the International Atomic Energy Agency. The directory contains technical, utilization and administrative information supplied to the IAEA as of October 1997. The directory was prepared through information collected by questionnaires sent to institutions that either have a cyclotron, or that were identified to be in the process of installation of a cyclotron. The directory contains 206 entries for cyclotrons operating in 34 Member States. The largest concentration of cyclotrons for radionuclide production are located in the United States of America (66), Japan (33) and Germany (22). The largest number of cyclotrons for a single country is the United States of America. The expansion in number of cyclotrons during the last decade has been driven by the advent of advances in medical imaging instrumentation (PET, SPET and more recently 511 KeV emission tomography); introduction of user friendly compact medical cyclotrons from several companies that manufacture cyclotrons; and recent decisions that 15 O-oxygen PET studies in Japan, and 18 F-FDG PET studies in Germany are eligible for reimbursement by government or insurance companies

  10. Design, production and initial state of the buffer

    Energy Technology Data Exchange (ETDEWEB)

    Boerjesson, Lennart; Gunnarsson, David; Johannesson, Lars-Erik; Jonsson, Esther

    2010-12-15

    The report is included in a set of Production reports, presenting how the KBS-3 repository is designed, produced and inspected. The set of reports is included in the safety report for the KBS-3 repository and repository facility. The report provides input on the initial state of the buffer for the assessment of the long-term safety, SR-Site. The initial state refers to the properties of the engineered barriers once they have been finally placed in the KBS-3 repository and will not be further handled within the repository facility. In addition, the report provides input to the operational safety report, SR-Operation, on how the buffer shall be handled and installed. The report presents the design premises and reference design of the buffer and verifies the conformity of the reference design to the design premises. It also describes the production of the buffer, from excavation and delivery of buffer material to installation in the deposition hole. Finally, the initial state of the buffer and its conformity to the reference design and design premises is presented

  11. Dictionary-Based Tensor Canonical Polyadic Decomposition

    Science.gov (United States)

    Cohen, Jeremy Emile; Gillis, Nicolas

    2018-04-01

    To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images.

  12. Bayesian regularization of diffusion tensor images

    DEFF Research Database (Denmark)

    Frandsen, Jesper; Hobolth, Asger; Østergaard, Leif

    2007-01-01

    Diffusion tensor imaging (DTI) is a powerful tool in the study of the course of nerve fibre bundles in the human brain. Using DTI, the local fibre orientation in each image voxel can be described by a diffusion tensor which is constructed from local measurements of diffusion coefficients along...... several directions. The measured diffusion coefficients and thereby the diffusion tensors are subject to noise, leading to possibly flawed representations of the three dimensional fibre bundles. In this paper we develop a Bayesian procedure for regularizing the diffusion tensor field, fully utilizing...

  13. A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY

    OpenAIRE

    SASAKURA, NAOKI

    2010-01-01

    Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config...

  14. New results for algebraic tensor reduction of Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Fleischer, Jochem [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Yundin, Valery [Copenhagen Univ. (Denmark). Niels Bohr International Academy and Discovery Center

    2012-02-15

    We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5- point Gram determinants and inverse small 4-point Gram determinants are treated by expansions in higher-dimensional 3-point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7-point functions is discussed. In the present approach one needs for the reductions a (d +2)-dimensional scalar 5-point function in addition to the usual scalar basis of 1- to 4-point functions in the generic dimension d=4-2{epsilon}. When exploiting the four-dimensionality of the kinematics, this basis is sufficient. We indicate how the (d+2)-dimensional 5-point function can be evaluated. (orig.)

  15. New results for algebraic tensor reduction of Feynman integrals

    International Nuclear Information System (INIS)

    Fleischer, Jochem; Yundin, Valery

    2012-02-01

    We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5- point Gram determinants and inverse small 4-point Gram determinants are treated by expansions in higher-dimensional 3-point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7-point functions is discussed. In the present approach one needs for the reductions a (d +2)-dimensional scalar 5-point function in addition to the usual scalar basis of 1- to 4-point functions in the generic dimension d=4-2ε. When exploiting the four-dimensionality of the kinematics, this basis is sufficient. We indicate how the (d+2)-dimensional 5-point function can be evaluated. (orig.)

  16. Partition-based Collaborative Tensor Factorization for POI Recommendation

    Institute of Scientific and Technical Information of China (English)

    Wenjing Luan; Guanjun Liu; Changjun Jiang; Liang Qi

    2017-01-01

    The rapid development of location-based social networks (LBSNs) provides people with an opportunity of better understanding their mobility behavior which enables them to decide their next location.For example,it can help travelers to choose where to go next,or recommend salesmen the most potential places to deliver advertisements or sell products.In this paper,a method for recommending points of interest (POIs) is proposed based on a collaborative tensor factorization (CTF) technique.Firstly,a generalized objective function is constructed for collaboratively factorizing a tensor with several feature matrices.Secondly,a 3-mode tensor is used to model all users' check-in behaviors,and three feature matrices are extracted to characterize the time distribution,category distribution and POI correlation,respectively.Thirdly,each user's preference to a POI at a specific time can be estimated by using CTF.In order to further improve the recommendation accuracy,PCTF (Partitionbased CTF) is proposed to fill the missing entries of a tensor after clustering its every mode.Experiments on a real checkin database show that the proposed method can provide more accurate location recommendation.

  17. Cα chemical shift tensors in helical peptides by dipolar-modulated chemical shift recoupling NMR

    International Nuclear Information System (INIS)

    Yao Xiaolan; Yamaguchi, Satoru; Hong Mei

    2002-01-01

    The Cα chemical shift tensors of proteins contain information on the backbone conformation. We have determined the magnitude and orientation of the Cα chemical shift tensors of two peptides with α-helical torsion angles: the Ala residue in G*AL (φ=-65.7 deg., ψ=-40 deg.), and the Val residue in GG*V (φ=-81.5 deg., ψ=-50.7 deg.). The magnitude of the tensors was determined from quasi-static powder patterns recoupled under magic-angle spinning, while the orientation of the tensors was extracted from Cα-Hα and Cα-N dipolar modulated powder patterns. The helical Ala Cα chemical shift tensor has a span of 36 ppm and an asymmetry parameter of 0.89. Its σ 11 axis is 116 deg. ± 5 deg. from the Cα-Hα bond while the σ 22 axis is 40 deg. ± 5 deg. from the Cα-N bond. The Val tensor has an anisotropic span of 25 ppm and an asymmetry parameter of 0.33, both much smaller than the values for β-sheet Val found recently (Yao and Hong, 2002). The Val σ 33 axis is tilted by 115 deg. ± 5 deg. from the Cα-Hα bond and 98 deg. ± 5 deg. from the Cα-N bond. These represent the first completely experimentally determined Cα chemical shift tensors of helical peptides. Using an icosahedral representation, we compared the experimental chemical shift tensors with quantum chemical calculations and found overall good agreement. These solid-state chemical shift tensors confirm the observation from cross-correlated relaxation experiments that the projection of the Cα chemical shift tensor onto the Cα-Hα bond is much smaller in α-helices than in β-sheets

  18. Dirac tensor with heavy photon

    Energy Technology Data Exchange (ETDEWEB)

    Bytev, V.V.; Kuraev, E.A. [Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Scherbakova, E.S. [Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik

    2012-01-15

    For the large-angles hard photon emission by initial leptons in process of high energy annihilation of e{sup +}e{sup -} {yields} to hadrons the Dirac tensor is obtained, taking into account the lowest order radiative corrections. The case of large-angles emission of two hard photons by initial leptons is considered. This result is being completed by the kinematics case of collinear hard photons emission as well as soft virtual and real photons and can be used for construction of Monte-Carlo generators. (orig.)

  19. A Tensor Statistical Model for Quantifying Dynamic Functional Connectivity.

    Science.gov (United States)

    Zhu, Yingying; Zhu, Xiaofeng; Kim, Minjeong; Yan, Jin; Wu, Guorong

    2017-06-01

    Functional connectivity (FC) has been widely investigated in many imaging-based neuroscience and clinical studies. Since functional Magnetic Resonance Image (MRI) signal is just an indirect reflection of brain activity, it is difficult to accurately quantify the FC strength only based on signal correlation. To address this limitation, we propose a learning-based tensor model to derive high sensitivity and specificity connectome biomarkers at the individual level from resting-state fMRI images. First, we propose a learning-based approach to estimate the intrinsic functional connectivity. In addition to the low level region-to-region signal correlation, latent module-to-module connection is also estimated and used to provide high level heuristics for measuring connectivity strength. Furthermore, sparsity constraint is employed to automatically remove the spurious connections, thus alleviating the issue of searching for optimal threshold. Second, we integrate our learning-based approach with the sliding-window technique to further reveal the dynamics of functional connectivity. Specifically, we stack the functional connectivity matrix within each sliding window and form a 3D tensor where the third dimension denotes for time. Then we obtain dynamic functional connectivity (dFC) for each individual subject by simultaneously estimating the within-sliding-window functional connectivity and characterizing the across-sliding-window temporal dynamics. Third, in order to enhance the robustness of the connectome patterns extracted from dFC, we extend the individual-based 3D tensors to a population-based 4D tensor (with the fourth dimension stands for the training subjects) and learn the statistics of connectome patterns via 4D tensor analysis. Since our 4D tensor model jointly (1) optimizes dFC for each training subject and (2) captures the principle connectome patterns, our statistical model gains more statistical power of representing new subject than current state

  20. Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms

    Science.gov (United States)

    Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.

    2016-07-01

    Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

  1. Simulations of Shor's algorithm using matrix product states

    Science.gov (United States)

    Wang, D. S.; Hill, Charles D.; Hollenberg, L. C. L.

    2017-07-01

    We show that under the matrix product state formalism the states produced in Shor's algorithm can be represented using O(\\max (4lr^2, 2^{2l})) space, where l is the number of bits in the number to factorise and r is the order and the solution to the related order-finding problem. The reduction in space compared to an amplitude formalism approach is significant, allowing simulations as large as 42 qubits to be run on a single processor with 32 GB RAM. This approach is readily adapted to a distributed memory environment, and we have simulated a 45-qubit case using 8 cores with 16 GB RAM in approximately 1 h.

  2. Zirconia powders production by precipitation: state-of-art review

    International Nuclear Information System (INIS)

    Oliveira, Ana Paula Almeida de; Torem, Mauricio Leonardo

    1994-01-01

    The important role played by zirconia in advanced ceramics can be attributed to its excellent wear and corrosion resistance and refractory character. The polymorphic nature of zirconia made the controlled addition of stabilizing oxides or the constraining effect of a dense ceramics matrix necessary to maintain high parameters had a significant influence on powder properties and on compacted powder behaviour in sintering. Particle shape and size, purity and crystalline structure were specially influenced by precipitation parameters. Therefore, this work presented a review of the state of the art in zirconia powder production and in the recent research on precipitation of that powder. (author)

  3. Eta products, BPS states and K3 surfaces

    Energy Technology Data Exchange (ETDEWEB)

    He, Yang-Hui [Department of Mathematics, City University,London, EC1V 0HB (United Kingdom); School of Physics, NanKai University,Tianjin, 300071 (China); Merton College, University of Oxford,Oxford, OX14JD (United Kingdom); McKay, John [Department of Mathematics and Statistics, Concordia University,1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8 (Canada)

    2014-01-22

    Inspired by the multiplicative nature of the Ramanujan modular discriminant, Δ, we consider physical realizations of certain multiplicative products over the Dedekind eta-function in two parallel directions: the generating function of BPS states in certain heterotic orbifolds and elliptic K3 surfaces associated to congruence subgroups of the modular group. We show that they are, after string duality to type II, the same K3 surfaces admitting Nikulin automorphisms. In due course, we will present identities arising from q-expansions as well as relations to the sporadic Mathieu group M{sub 24}.

  4. Quasi-degenerate perturbation theory using matrix product states

    International Nuclear Information System (INIS)

    Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali

    2016-01-01

    In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner’s 2n + 1 rule. Further, our formulation satisfies Granovsky’s requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost

  5. Quasi-degenerate perturbation theory using matrix product states

    Energy Technology Data Exchange (ETDEWEB)

    Sharma, Sandeep, E-mail: sanshar@gmail.com; Jeanmairet, Guillaume [Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart (Germany); Alavi, Ali, E-mail: a.alavi@fkf.mpg.de [Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart (Germany); Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW (United Kingdom)

    2016-01-21

    In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner’s 2n + 1 rule. Further, our formulation satisfies Granovsky’s requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.

  6. Quasi-degenerate perturbation theory using matrix product states

    Science.gov (United States)

    Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali

    2016-01-01

    In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner's 2n + 1 rule. Further, our formulation satisfies Granovsky's requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.

  7. A solution for tensor reduction of one-loop N-point functions with N{>=}6

    Energy Technology Data Exchange (ETDEWEB)

    Fleischer, J. [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2011-11-15

    Collisions at the LHC produce many-particle final states, and for precise predictions the one-loop N-point corrections are needed. We study here the tensor reduction for Feynman integrals with N{>=}6. A general, recursive solution by Binoth et al. expresses N-point Feynman integrals of rank R in terms of (N-1)-point Feynman integrals of rank (R-1) (for N{>=}6). We show that the coefficients can be obtained analytically from suitable representations of the metric tensor. Contractions of the tensor integrals with external momenta can be efficiently expressed as well. We consider our approach particularly well suited for automatization. (orig.)

  8. Relativistic symmetries in the Hulthén scalar—vector—tensor interactions

    International Nuclear Information System (INIS)

    Hamzavi Majid; Rajabi Ali Akbar

    2013-01-01

    In the presence of spin and pseudospin (p-spin) symmetries, the approximate analytical bound states of the Dirac equation for scalar—vector—tensor Hulthén potentials are obtained with any arbitrary spin—orbit coupling number κ using the Pekeris approximation. The Hulthén tensor interaction is studied instead of the commonly used Coulomb or linear terms. The generalized parametric Nikiforov—Uvarov (NU) method is used to obtain energy eigenvalues and corresponding wave functions in their closed forms. It is shown that tensor interaction removes degeneracy between spin and p-spin doublets. Some numerical results are also given. (general)

  9. 3D reconstruction of tensors and vectors

    International Nuclear Information System (INIS)

    Defrise, Michel; Gullberg, Grant T.

    2005-01-01

    Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields

  10. Raman scattering tensors of tyrosine.

    Science.gov (United States)

    Tsuboi, M; Ezaki, Y; Aida, M; Suzuki, M; Yimit, A; Ushizawa, K; Ueda, T

    1998-01-01

    Polarized Raman scattering measurements have been made of a single crystal of L-tyrosine by the use of a Raman microscope with the 488.0-nm exciting beam from an argon ion laser. The L-tyrosine crystal belongs to the space group P2(1)2(1)2(1) (orthorhombic), and Raman scattering intensities corresponding to the aa, bb, cc, ab and ac components of the crystal Raman tensor have been determined for each prominent Raman band. A similar set of measurements has been made of L-tyrosine-d4, in which four hydrogen atoms on the benzene ring are replaced by deuterium atoms. The effects of NH3-->ND3 and OH-->OD on the Raman spectrum have also been examined. In addition, depolarization ratios of some bands of L-tyrosine in aqueous solutions of pH 13 and pH 1 were examined. For comparison with these experimental results, on the other hand, ab initio molecular orbital calculations have been made of the normal modes of vibration and their associated polarizability oscillations of the L-tyrosine molecule. On the basis of these experimental data and by referring to the results of the calculations, discussions have been presented on the Raman tensors associated to some Raman bands, including those at 829 cm-1 (benzene ring breathing), 642 cm-1 (benzene ring deformation), and 432 cm-1 (C alpha-C beta-C gamma bending).

  11. Secondary Metabolites Production by Solid-State Fermentation

    Directory of Open Access Journals (Sweden)

    Barrios-González, J.

    2005-01-01

    Full Text Available Microbial secondary metabolites are useful high value products with an enormous range of biological activities. Moreover, the past two decades have been a phase of rapid discovery of new activities and development of major compounds for use in different industrial fields, mainly pharmaceuticals, cosmetics, food, agriculture and farming. Many of these metabolites could be produced advantageously in industry by solid–state fermentation (SSF. Two types of SSF can be distinguished, depending on the nature of the solid phase used: 1 Solid cultures of one support-substrate phase in which solid phase is constituted by a material that assumes, simultaneously, the functions of support and of nutrients source; and 2 Solid cultures of two substrate-support phases: solid phase is constituted by an inert support impregnated with a liquid medium. Besides good production performance, two phases systems have provided a convenient model for basic studies. Studies in our laboratory, as well as in others, have shown that physiology of idiophase (production phase in SSF share several similarities with the physiology in liquid medium, so similar strategies must be adapted for efficient production processes. However, our studies indicate the need to develop special strains for SSF since overproducing strains, generated for liquid fermentation, cannot be relied upon to perform well in SSF. On the other hand, there are important parameters, specific for SSF, that have to be optimized (pretreatment, initial moisture content, medium concentration and aeration. Respiration studies of secondary metabolites SSF, performed in our laboratory, have shown more subtle aspects of efficient production in SSF. This indicates that there are certain particularities of physiology in SSF that represent the point that needs a better understanding, and that promise to generate knowledge that will be the basis for efficient processes development and control strategies, as well as for

  12. Tensor-optimized antisymmetrized molecular dynamics as a successive variational method in nuclear many-body system

    Energy Technology Data Exchange (ETDEWEB)

    Myo, Takayuki, E-mail: takayuki.myo@oit.ac.jp [General Education, Faculty of Engineering, Osaka Institute of Technology, Osaka 535-8585 (Japan); Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047 (Japan); Toki, Hiroshi [Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047 (Japan); Ikeda, Kiyomi [RIKEN Nishina Center, Wako, Saitama 351-0198 (Japan); Horiuchi, Hisashi [Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047 (Japan); Suhara, Tadahiro [Matsue College of Technology, Matsue 690-8518 (Japan)

    2017-06-10

    We study the tensor-optimized antisymmetrized molecular dynamics (TOAMD) as a successive variational method in many-body systems with strong interaction for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiples are operated to the AMD state as the variational wave function. The total wave function is expressed as the sum of all the components and the variational space can be increased successively with the multiple correlation functions to achieve convergence. All the necessary matrix elements of many-body operators, consisting of the multiple correlation functions and the Hamiltonian, are expressed analytically using the Gaussian integral formula. In this paper we show the results of TOAMD with up to the double products of the correlation functions for the s-shell nuclei, {sup 3}H and {sup 4}He, using the nucleon–nucleon interaction AV8′. It is found that the energies and Hamiltonian components of two nuclei converge rapidly with respect to the multiple of correlation functions. This result indicates the efficiency of TOAMD for the power series expansion in terms of the tensor and short-range correlation functions.

  13. Equations of state of detonation products: ammonia and methane

    Science.gov (United States)

    Lang, John; Dattelbaum, Dana; Goodwin, Peter; Garcia, Daniel; Coe, Joshua; Leiding, Jeffery; Gibson, Lloyd; Bartram, Brian

    2015-06-01

    Ammonia (NH3) and methane (CH4) are two principal product gases resulting from explosives detonation, and the decomposition of other organic materials under shockwave loading (such as foams). Accurate thermodynamic descriptions of these gases are important for understanding the detonation performance of high explosives. However, shock compression data often do not exist for molecular species in the dense gas phase, and are limited in the fluid phase. Here, we present equation of state measurements of elevated initial density ammonia and methane gases dynamically compressed in gas-gun driven plate impact experiments. Pressure and density of the shocked gases on the principal Hugoniot were determined from direct particle velocity and shock wave velocity measurements recorded using optical velocimetry (Photonic Doppler velocimetry (PDV) and VISAR (velocity interferometer system for any reflector)). Streak spectroscopy and 5-color pyrometry were further used to measure the emission from the shocked gases, from which the temperatures of the shocked gases were estimated. Up to 0.07 GPa, ammonia was not observed to ionize, with temperature remaining below 7000 K. These results provide quantitative measurements of the Hugoniot locus for improving equations of state models of detonation products.

  14. Composite antisymmetric tensor bosons in a four-fermion interaction model

    International Nuclear Information System (INIS)

    Dmitrasinovic, V.

    2000-01-01

    We discuss the phenomenological consequences of the U A (1) symmetry-breaking two-flavour four-fermion antisymmetric (AS) Lorentz tensor interaction Lagrangians. We use the recently developed methods that respect the 'duality' symmetry of this interaction. Starting from the Fierz transform of the two-flavour 't Hooft interaction (a four-fermion Lagrangian with AS tensor interaction terms augmented by Nambu and Jona-Lasinio (NJL)-type Lorentz scalar interaction responsible for dynamical symmetry breaking and quark mass generation), we find the following. (a) Four antisymmetric tensor and four AS pseudotensor bosons exist which satisfy a mass relation previously derived for scalar and pseudoscalar mesons from the 't Hooft interaction. (b) Antisymmetric tensor bosons mix with vector bosons via one-fermion-loop effective couplings so that both kinds of bosons have their masses shifted and the fermions (quarks) acquire anomalous magnetic moment form factors that explicitly violate chiral symmetry. (c) The mixing of massive AS tensor fields with vector fields leads to two sets of spin-1 states. The second set of spin-1 mesons is heavy and has not been observed. Moreover, at least one member of this second set is tachyonic, under standard assumptions about the source and strength of the AS tensor interaction. The tachyonic state also shows up as a pole in the space-like region of the electromagnetic form factors. (d) The mixing of axial-vector fields with antisymmetric tensor bosons is proportional to the (small) isospin-breaking up-down quark mass difference, so the mixing-induced mass shift is negligible. (e) The AS tensor version of the Veneziano-Witten U A (1) symmetry-breaking interaction does not lead to tachyons, or any AS tensor field propagation to leading order in N C . (author)

  15. An introduction to tensor calculus, relativity and cosmology /3rd edition/

    Science.gov (United States)

    Lawden, D. F.

    This textbook introduction to the principles of special relativity proceeds within the context of cartesian tensors. Newton's laws of motion are reviewed, as are the Lorentz transformations, Minkowski space-time, and the Fitzgerald contraction. Orthogonal transformations are described, and invariants, gradients, tensor derivatives, contraction, scalar products, divergence, pseudotensors, vector products, and curl are defined. Special relativity mechanics are explored in terms of mass, momentum, the force vector, the Lorentz transformation equations for force, calculations for photons and neutrinos, the development of the Lagrange and Hamilton equations, and the energy-momentum tensor. Electrodynamics is investigated, together with general tensor calculus and Riemmanian space. The General Theory of Relativity is presented, along with applications to astrophysical phenomena such as black holes and gravitational waves. Finally, analytical discussions of cosmological problems are reviewed, particularly Einstein, de Sitter, and Friedmann universes, redshifts, event horizons, and the redshift.

  16. The total position-spread tensor: Spin partition

    International Nuclear Information System (INIS)

    El Khatib, Muammar; Evangelisti, Stefano; Leininger, Thierry; Brea, Oriana; Fertitta, Edoardo; Bendazzoli, Gian Luigi

    2015-01-01

    The Total Position Spread (TPS) tensor, defined as the second moment cumulant of the position operator, is a key quantity to describe the mobility of electrons in a molecule or an extended system. In the present investigation, the partition of the TPS tensor according to spin variables is derived and discussed. It is shown that, while the spin-summed TPS gives information on charge mobility, the spin-partitioned TPS tensor becomes a powerful tool that provides information about spin fluctuations. The case of the hydrogen molecule is treated, both analytically, by using a 1s Slater-type orbital, and numerically, at Full Configuration Interaction (FCI) level with a V6Z basis set. It is found that, for very large inter-nuclear distances, the partitioned tensor growths quadratically with the distance in some of the low-lying electronic states. This fact is related to the presence of entanglement in the wave function. Non-dimerized open chains described by a model Hubbard Hamiltonian and linear hydrogen chains H n (n ≥ 2), composed of equally spaced atoms, are also studied at FCI level. The hydrogen systems show the presence of marked maxima for the spin-summed TPS (corresponding to a high charge mobility) when the inter-nuclear distance is about 2 bohrs. This fact can be associated to the presence of a Mott transition occurring in this region. The spin-partitioned TPS tensor, on the other hand, has a quadratical growth at long distances, a fact that corresponds to the high spin mobility in a magnetic system

  17. Gravitational Metric Tensor Exterior to Rotating Homogeneous ...

    African Journals Online (AJOL)

    The covariant and contravariant metric tensors exterior to a homogeneous spherical body rotating uniformly about a common φ axis with constant angular velocity ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is ...

  18. Differential invariants for higher-rank tensors. A progress report

    International Nuclear Information System (INIS)

    Tapial, V.

    2004-07-01

    We outline the construction of differential invariants for higher-rank tensors. In section 2 we outline the general method for the construction of differential invariants. A first result is that the simplest tensor differential invariant contains derivatives of the same order as the rank of the tensor. In section 3 we review the construction for the first-rank tensors (vectors) and second-rank tensors (metrics). In section 4 we outline the same construction for higher-rank tensors. (author)

  19. Beyond Low Rank: A Data-Adaptive Tensor Completion Method

    OpenAIRE

    Zhang, Lei; Wei, Wei; Shi, Qinfeng; Shen, Chunhua; Hengel, Anton van den; Zhang, Yanning

    2017-01-01

    Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor data which only approximately fulfils the low-rank requirement. To address these two issues, we develop a data-adaptive tensor completion model which explicitly represents both the low-rank and non-low-rank structures in a latent tensor. Representing the no...

  20. Unique characterization of the Bel-Robinson tensor

    International Nuclear Information System (INIS)

    Bergqvist, G; Lankinen, P

    2004-01-01

    We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors

  1. Tensor completion and low-n-rank tensor recovery via convex optimization

    International Nuclear Information System (INIS)

    Gandy, Silvia; Yamada, Isao; Recht, Benjamin

    2011-01-01

    In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas–Rachford splitting technique and its dual variant, the alternating direction method of multipliers

  2. On the energy-momentum tensor in non-linear σ-models with torsion

    International Nuclear Information System (INIS)

    Dorn, H.; Otto, H.J.

    1987-10-01

    We study the renormalization properties of the energy-momentum tensor in a σ-model with torsion. Our normal product version contains besides the classical expression and the trace anomaly an off diagonal term proportional to the squared torsion. Specialized to a group manifold this term is crucial to reproduce the correct perturbative expansion of the energy-momentum tensor in Sugawara form. (orig.)

  3. Anisotropic Conductivity Tensor Imaging of In Vivo Canine Brain Using DT-MREIT.

    Science.gov (United States)

    Jeong, Woo Chul; Sajib, Saurav Z K; Katoch, Nitish; Kim, Hyung Joong; Kwon, Oh In; Woo, Eung Je

    2017-01-01

    We present in vivo images of anisotropic electrical conductivity tensor distributions inside canine brains using diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT). The conductivity tensor is represented as a product of an ion mobility tensor and a scale factor of ion concentrations. Incorporating directional mobility information from water diffusion tensors, we developed a stable process to reconstruct anisotropic conductivity tensor images from measured magnetic flux density data using an MRI scanner. Devising a new image reconstruction algorithm, we reconstructed anisotropic conductivity tensor images of two canine brains with a pixel size of 1.25 mm. Though the reconstructed conductivity values matched well in general with those measured by using invasive probing methods, there were some discrepancies as well. The degree of white matter anisotropy was 2 to 4.5, which is smaller than previous findings of 5 to 10. The reconstructed conductivity value of the cerebrospinal fluid was about 1.3 S/m, which is smaller than previous measurements of about 1.8 S/m. Future studies of in vivo imaging experiments with disease models should follow this initial trial to validate clinical significance of DT-MREIT as a new diagnostic imaging modality. Applications in modeling and simulation studies of bioelectromagnetic phenomena including source imaging and electrical stimulation are also promising.

  4. The tensor part of the Skyrme energy density functional. I. Spherical nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Lesinski, T.; Meyer, J. [Universite de Lyon, F-69003 Lyon (France)]|[Institut de Physique Nucleaire de Lyon, CNRS/IN2P3, Universite Lyon 1, F-69622 Villeurbanne (France); Bender, M. [DSM/DAPNIA/SPhN, CEA Saclay, F-91191 Gif-sur-Yvette Cedex (France)]|[Universite Bordeaux, CNRS/IN2P3, Centre d' Etudes Nucleaires de Bordeaux Gradignan, UMR5797, Chemin du Solarium, BP120, F-33175 Gradignan (France); Bennaceur, K. [Universite de Lyon, F-69003 Lyon (France)]|[Institut de Physique Nucleaire de Lyon, CNRS/IN2P3, Universite Lyon 1, F-69622 Villeurbanne (France)]|[DSM/DAPNIA/SPhN, CEA Saclay, F-91191 Gif-sur-Yvette Cedex (France); Duguet, T. [National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States)

    2007-04-15

    We perform a systematic study of the impact of the J-vector{sup 2} tensor term in the Skyrme energy functional on properties of spherical nuclei. In the Skyrme energy functional, the tensor terms originate both from zero-range central and tensor forces. We build a set of 36 parameterizations which cover a wide range of the parameter space of the isoscalar and isovector tensor term coupling constants with a fit protocol very similar to that of the successful SLy parameterizations. We analyze the impact of the tensor terms on a large variety of observables in spherical mean-field calculations, such as the spin-orbit splittings and single-particle spectra of doubly-magic nuclei, the evolution of spin-orbit splittings along chains of semi-magic nuclei, mass residuals of spherical nuclei, and known anomalies of radii. The major findings of our study are (i) tensor terms should not be added perturbatively to existing parameterizations, a complete refit of the entire parameter set is imperative. (ii) The free variation of the tensor terms does not lower the {chi}{sup 2} within a standard Skyrme energy functional. (iii) For certain regions of the parameter space of their coupling constants, the tensor terms lead to instabilities of the spherical shell structure, or even the coexistence of two configurations with different spherical shell structure. (iv) The standard spin-orbit interaction does not scale properly with the principal quantum number, such that single-particle states with one or several nodes have too large spin-orbit splittings, while those of node-less intruder levels are tentatively too small. Tensor terms with realistic coupling constants cannot cure this problem. (v) Positive values of the coupling constants of proton-neutron and like-particle tensor terms allow for a qualitative description of the evolution of spin-orbit splittings in chains of Ca, Ni and Sn isotopes. (vi) For the same values of the tensor term coupling constants, however, the overall

  5. Weyl curvature tensor in static spherical sources

    International Nuclear Information System (INIS)

    Ponce de Leon, J.

    1988-01-01

    The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed

  6. On Lovelock analogs of the Riemann tensor

    Science.gov (United States)

    Camanho, Xián O.; Dadhich, Naresh

    2016-03-01

    It is possible to define an analog of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analog of the Einstein tensor. Interestingly there exist two parallel but distinct such analogs and the main purpose of this note is to reconcile both formulations. In addition we will introduce a simple tensor identity and use it to show that any pure Lovelock vacuum in odd d=2N+1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in the presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes.

  7. Dissipation consistent fabric tensor definition from DEM to continuum for granular media

    Science.gov (United States)

    Li, X. S.; Dafalias, Y. F.

    2015-05-01

    In elastoplastic soil models aimed at capturing the impact of fabric anisotropy, a necessary ingredient is a measure of anisotropic fabric in the form of an evolving tensor. While it is possible to formulate such a fabric tensor based on indirect phenomenological observations at the continuum level, it is more effective and insightful to have the tensor defined first based on direct particle level microstructural observations and subsequently deduce a corresponding continuum definition. A practical means able to provide such observations, at least in the context of fabric evolution mechanisms, is the discrete element method (DEM). Some DEM defined fabric tensors such as the one based on the statistics of interparticle contact normals have already gained widespread acceptance as a quantitative measure of fabric anisotropy among researchers of granular material behavior. On the other hand, a fabric tensor in continuum elastoplastic modeling has been treated as a tensor-valued internal variable whose evolution must be properly linked to physical dissipation. Accordingly, the adaptation of a DEM fabric tensor definition to a continuum constitutive modeling theory must be thermodynamically consistent in regards to dissipation mechanisms. The present paper addresses this issue in detail, brings up possible pitfalls if such consistency is violated and proposes remedies and guidelines for such adaptation within a recently developed Anisotropic Critical State Theory (ACST) for granular materials.

  8. Tri-Clustered Tensor Completion for Social-Aware Image Tag Refinement.

    Science.gov (United States)

    Tang, Jinhui; Shu, Xiangbo; Qi, Guo-Jun; Li, Zechao; Wang, Meng; Yan, Shuicheng; Jain, Ramesh

    2017-08-01

    Social image tag refinement, which aims to improve tag quality by automatically completing the missing tags and rectifying the noise-corrupted ones, is an essential component for social image search. Conventional approaches mainly focus on exploring the visual and tag information, without considering the user information, which often reveals important hints on the (in)correct tags of social images. Towards this end, we propose a novel tri-clustered tensor completion framework to collaboratively explore these three kinds of information to improve the performance of social image tag refinement. Specifically, the inter-relations among users, images and tags are modeled by a tensor, and the intra-relations between users, images and tags are explored by three regularizations respectively. To address the challenges of the super-sparse and large-scale tensor factorization that demands expensive computing and memory cost, we propose a novel tri-clustering method to divide the tensor into a certain number of sub-tensors by simultaneously clustering users, images and tags into a bunch of tri-clusters. And then we investigate two strategies to complete these sub-tensors by considering (in)dependence between the sub-tensors. Experimental results on a real-world social image database demonstrate the superiority of the proposed method compared with the state-of-the-art methods.

  9. Using MODIS NDVI products for vegetation state monitoring on the oil production territory in Western Siberia

    OpenAIRE

    Kovalev, Anton; Tokareva, Olga Sergeevna

    2016-01-01

    Article describes the results of using remote sensing data for vegetation state monitoring on the oil field territories in Western Siberia. We used MODIS data product providing the normalized difference vegetation index (NDVI) values. Average NDVI values of each studied area were calculated for the period from 2010 to 2015 with one year interval for June, July and August. Analysis was carried out via an open tool of geographic information system QGIS used for spatial analysis and calculation ...

  10. Evidence for Nuclear Tensor Polarization of Deuterium Molecules in Storage Cells

    International Nuclear Information System (INIS)

    van den Brand, J.; Bulten, H.; Zhou, Z.; Unal, O.; van den Brand, J.; Ferro-Luzzi, M.; Botto, T.; Bouwhuis, M.; Heimberg, P.; de Jager, C.; de Lange, D.; Nooren, G.; Papadakis, N.; Passchier, I.; Poolman, H.; Steijger, J.; Vodinas, N.; de Vries, H.; van den Brand, J.; Ferro-Luzzi, M.; Lang, J.; Alarcon, R.; Dolfini, S.; Ent, R.; Higinbotham, D.

    1997-01-01

    Deuterium molecules were obtained by recombination, on a copper surface, of deuterium atoms prepared in specific hyperfine states. The molecules were stored for about 5ms in an open-ended cylindrical cell, placed in a 23mT magnetic field, and their tensor polarization was measured by elastic scattering of 704MeV electrons. The results of the measurements are consistent with the deuterium molecules retaining the tensor polarization of the initial atoms. copyright 1997 The American Physical Society

  11. Central Production of Two-Pseudoscalar Final States at COMPASS

    CERN Document Server

    Alexander Austregesilo

    2013-01-01

    COMPASS is a fixed-target experiment at CERN SPS which focused on light-quark meson spectroscopy during the data-taking periods in 2008 and 2009. The central exclusive production of glueball candidates is studied with a 190GeV/c proton beam impinging on a liquid hydrogen target. We select centrally produced systems with two pseudo-scalar mesons in the final state. The decay of this system is decomposed in terms of partial waves, with particular attention paid to the inherent mathematical ambiguities of the amplitude analysis. We show that simple parametrisation are able to describe the mass dependence of the fit results with sensible Breit-Wigner parameters.

  12. Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.

    Science.gov (United States)

    Khoromskaia, Venera; Khoromskij, Boris N

    2015-12-21

    We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.

  13. High resolution production water footprints of the United States

    Science.gov (United States)

    Marston, L.; Yufei, A.; Konar, M.; Mekonnen, M.; Hoekstra, A. Y.

    2017-12-01

    The United States is the largest producer and consumer of goods and services in the world. Rainfall, surface water supplies, and groundwater aquifers represent a fundamental input to this economic production. Despite the importance of water resources to economic activity, we do not have consistent information on water use for specific locations and economic sectors. A national, high-resolution database of water use by sector would provide insight into US utilization and dependence on water resources for economic production. To this end, we calculate the water footprint of over 500 food, energy, mining, services, and manufacturing industries and goods produced in the US. To do this, we employ a data intensive approach that integrates water footprint and input-output techniques into a novel methodological framework. This approach enables us to present the most detailed and comprehensive water footprint analysis of any country to date. This study broadly contributes to our understanding of water in the US economy, enables supply chain managers to assess direct and indirect water dependencies, and provides opportunities to reduce water use through benchmarking.

  14. Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.

    Science.gov (United States)

    Bengua, Johann A; Phien, Ho N; Tuan, Hoang Duong; Do, Minh N

    2017-05-01

    This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.

  15. Multipartite fully nonlocal quantum states

    International Nuclear Information System (INIS)

    Almeida, Mafalda L.; Cavalcanti, Daniel; Scarani, Valerio; Acin, Antonio

    2010-01-01

    We present a general method for characterizing the quantum correlations obtained after local measurements on multipartite systems. Sufficient conditions for a quantum system to be fully nonlocal according to a given partition, as well as being (genuinely) multipartite fully nonlocal, are derived. These conditions allow us to identify all completely connected graph states as multipartite fully nonlocal quantum states. Moreover, we show that this feature can also be observed in mixed states: the tensor product of five copies of the Smolin state, a biseparable and bound entangled state, is multipartite fully nonlocal.

  16. Tensor network method for reversible classical computation

    Science.gov (United States)

    Yang, Zhi-Cheng; Kourtis, Stefanos; Chamon, Claudio; Mucciolo, Eduardo R.; Ruckenstein, Andrei E.

    2018-03-01

    We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017), 10.1038/ncomms15303]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.

  17. On improving the efficiency of tensor voting.

    Science.gov (United States)

    Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim

    2011-11-01

    This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor voting and the stick component of the plate tensor voting must reinforce surfaceness, the plate components of both the plate and ball tensor voting must boost curveness, whereas junctionness must be strengthened by the ball component of the ball tensor voting. Two new parameters have been proposed for the second formulation in order to control the potentially conflictive influence of the stick component of the plate vote and the ball component of the ball vote. Results show that the proposed formulations can be used in applications where efficiency is an issue since they have a complexity of order O(1). Moreover, the second proposed formulation has been shown to be more appropriate than the original tensor voting for estimating saliencies by appropriately setting the two new parameters.

  18. Conformal field theories and tensor categories. Proceedings

    Energy Technology Data Exchange (ETDEWEB)

    Bai, Chengming [Nankai Univ., Tianjin (China). Chern Institute of Mathematics; Fuchs, Juergen [Karlstad Univ. (Sweden). Theoretical Physics; Huang, Yi-Zhi [Rutgers Univ., Piscataway, NJ (United States). Dept. of Mathematics; Kong, Liang [Tsinghua Univ., Beijing (China). Inst. for Advanced Study; Runkel, Ingo; Schweigert, Christoph (eds.) [Hamburg Univ. (Germany). Dept. of Mathematics

    2014-08-01

    First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

  19. Conformal field theories and tensor categories. Proceedings

    International Nuclear Information System (INIS)

    Bai, Chengming; Fuchs, Juergen; Huang, Yi-Zhi; Kong, Liang; Runkel, Ingo; Schweigert, Christoph

    2014-01-01

    First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

  20. Alabama's forest products industry: performance and contribution to the State's economy, 1970 to 1980.

    Science.gov (United States)

    Wilbur R. Maki; Con H Schallau; Bennett B. Foster; Clair H. Redmond

    1986-01-01

    Employment and earnings in Alabama's forest products industry, like those of most Southern States, grew significantly between 1970 and 1980. The forest products industry accounted for a larger share of the State's economic base. in 1980 than in 1970. Of the 13 Southern States, only 5 had more forest products industry employment than Alabama. Moreover, during...

  1. One-loop tensor Feynman integral reduction with signed minors

    International Nuclear Information System (INIS)

    Fleischer, J.; Yundin, V.

    2011-12-01

    We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms of a basis of scalar integrals, which is provided by an external library, e.g. QCDLoop. We shortly describe installation and use of PJFry. Examples for numerical results are shown, including a special treatment for small or vanishing inverse four-point Gram determinants. An extremely efficient application of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically in a systematic way. The final expressions for the numerical evaluation are then compact combinations of the contributing basic scalar functions. (orig.)

  2. One-loop tensor Feynman integral reduction with signed minors

    Energy Technology Data Exchange (ETDEWEB)

    Fleischer, J. [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Yundin, V. [Copenhagen Univ. (Denmark). Niels Bohr International Academy and Discovery Center

    2011-12-15

    We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms of a basis of scalar integrals, which is provided by an external library, e.g. QCDLoop. We shortly describe installation and use of PJFry. Examples for numerical results are shown, including a special treatment for small or vanishing inverse four-point Gram determinants. An extremely efficient application of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically in a systematic way. The final expressions for the numerical evaluation are then compact combinations of the contributing basic scalar functions. (orig.)

  3. Fragmentation of tensor polarized deuterons into cumulative pions

    International Nuclear Information System (INIS)

    Afanas'ev, S.; Arkhipov, V.; Bondarev, V.

    1998-01-01

    The tensor analyzing power T 20 of the reaction d polarized + A → π - (0 0 ) + X has been measured in the fragmentation of 9 GeV tensor polarized deuterons into pions with momenta from 3.5 to 5.3 GeV/c on hydrogen, beryllium and carbon targets. This kinematic range corresponds to the region of cumulative hadron production with the cumulative variable x c from 1.08 to 1.76. The values of T 20 have been found to be small and consistent with positive values. This contradicts the predictions based on a direct mechanism assuming NN collision between a high momentum nucleon in the deuteron and a target nucleon (NN → NNπ)

  4. Visual Tracking via Feature Tensor Multimanifold Discriminate Analysis

    Directory of Open Access Journals (Sweden)

    Ting-quan Deng

    2014-01-01

    Full Text Available In the visual tracking scenarios, if there are multiple objects, due to the interference of similar objects, tracking may fail in the progress of occlusion to separation. To address this problem, this paper proposed a visual tracking algorithm with discrimination through multimanifold learning. Color-gradient-based feature tensor was used to describe object appearance for accommodation of partial occlusion. A prior multimanifold tensor dataset is established through the template matching tracking algorithm. For the purpose of discrimination, tensor distance was defined to determine the intramanifold and intermanifold neighborhood relationship in multimanifold space. Then multimanifold discriminate analysis was employed to construct multilinear projection matrices of submanifolds. Finally, object states were obtained by combining with sequence inference. Meanwhile, the multimanifold dataset and manifold learning embedded projection should be updated online. Experiments were conducted on two real visual surveillance sequences to evaluate the proposed algorithm with three state-of-the-art tracking methods qualitatively and quantitatively. Experimental results show that the proposed algorithm can achieve effective and robust effect in multi-similar-object mutual occlusion scenarios.

  5. Anisotropy of the fluorine chemical shift tensor in UF6

    International Nuclear Information System (INIS)

    Rigny, P.

    1965-04-01

    An 19 F magnetic resonance study of polycrystalline UF 6 is presented. The low temperature complex line can be analyzed as the superposition of two distinct lines, which is attributed to a distortion of the UF 6 octahedron in the solid. The shape of the two components is studied. Their width is much larger than the theoretical dipolar width, and must be explained by large anisotropies of the fluorine chemical shift tensors. The resulting shape functions of the powder spectra are determined. The values of the parameters of the chemical shift tensors yield estimates of the characters of the U-F bonds, and this gives some information on the ground state electronic wave function of the UF 6 molecule in the solid. (author) [fr

  6. Tensor-Dictionary Learning with Deep Kruskal-Factor Analysis

    Energy Technology Data Exchange (ETDEWEB)

    Stevens, Andrew J.; Pu, Yunchen; Sun, Yannan; Spell, Gregory; Carin, Lawrence

    2017-04-20

    We introduce new dictionary learning methods for tensor-variate data of any order. We represent each data item as a sum of Kruskal decomposed dictionary atoms within the framework of beta-process factor analysis (BPFA). Our model is nonparametric and can infer the tensor-rank of each dictionary atom. This Kruskal-Factor Analysis (KFA) is a natural generalization of BPFA. We also extend KFA to a deep convolutional setting and develop online learning methods. We test our approach on image processing and classification tasks achieving state of the art results for 2D & 3D inpainting and Caltech 101. The experiments also show that atom-rank impacts both overcompleteness and sparsity.

  7. Monocular Visual Odometry Based on Trifocal Tensor Constraint

    Science.gov (United States)

    Chen, Y. J.; Yang, G. L.; Jiang, Y. X.; Liu, X. Y.

    2018-02-01

    For the problem of real-time precise localization in the urban street, a monocular visual odometry based on Extend Kalman fusion of optical-flow tracking and trifocal tensor constraint is proposed. To diminish the influence of moving object, such as pedestrian, we estimate the motion of the camera by extracting the features on the ground, which improves the robustness of the system. The observation equation based on trifocal tensor constraint is derived, which can form the Kalman filter alone with the state transition equation. An Extend Kalman filter is employed to cope with the nonlinear system. Experimental results demonstrate that, compares with Yu’s 2-step EKF method, the algorithm is more accurate which meets the needs of real-time accurate localization in cities.

  8. Tensor harmonic analysis on homogenous space

    International Nuclear Information System (INIS)

    Wrobel, G.

    1997-01-01

    The Hilbert space of tensor functions on a homogenous space with the compact stability group is considered. The functions are decomposed onto a sum of tensor plane waves (defined in the text), components of which are transformed by irreducible representations of the appropriate transformation group. The orthogonality relation and the completeness relation for tensor plane waves are found. The decomposition constitutes a unitary transformation, which allows to obtain the Parseval equality. The Fourier components can be calculated by means of the Fourier transformation, the form of which is given explicitly. (author)

  9. Abelian gauge theories with tensor gauge fields

    International Nuclear Information System (INIS)

    Kapuscik, E.

    1984-01-01

    Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author)

  10. Local Tensor Radiation Conditions For Elastic Waves

    DEFF Research Database (Denmark)

    Krenk, S.; Kirkegaard, Poul Henning

    2001-01-01

    A local boundary condition is formulated, representing radiation of elastic waves from an arbitrary point source. The boundary condition takes the form of a tensor relation between the stress at a point on an arbitrarily oriented section and the velocity and displacement vectors at the point....... The tensor relation generalizes the traditional normal incidence impedance condition by accounting for the angle between wave propagation and the surface normal and by including a generalized stiffness term due to spreading of the waves. The effectiveness of the local tensor radiation condition...

  11. Scalable Tensor Factorizations with Missing Data

    DEFF Research Database (Denmark)

    Acar, Evrim; Dunlavy, Daniel M.; Kolda, Tamara G.

    2010-01-01

    of missing data, many important data sets will be discarded or improperly analyzed. Therefore, we need a robust and scalable approach for factorizing multi-way arrays (i.e., tensors) in the presence of missing data. We focus on one of the most well-known tensor factorizations, CANDECOMP/PARAFAC (CP...... is shown to successfully factor tensors with noise and up to 70% missing data. Moreover, our approach is significantly faster than the leading alternative and scales to larger problems. To show the real-world usefulness of CP-WOPT, we illustrate its applicability on a novel EEG (electroencephalogram...

  12. Surface tensor estimation from linear sections

    DEFF Research Database (Denmark)

    Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel

    From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....

  13. Surface tensor estimation from linear sections

    DEFF Research Database (Denmark)

    Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel

    2015-01-01

    From Crofton’s formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....

  14. Scalable tensor factorizations for incomplete data

    DEFF Research Database (Denmark)

    Acar, Evrim; Dunlavy, Daniel M.; KOlda, Tamara G.

    2011-01-01

    to factorize data sets with missing values with the goal of capturing the underlying latent structure of the data and possibly reconstructing missing values (i.e., tensor completion). We focus on one of the most well-known tensor factorizations that captures multi-linear structure, CANDECOMP/PARAFAC (CP...... experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000 × 1000 × 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP...

  15. Tensor decomposition in electronic structure calculations on 3D Cartesian grids

    International Nuclear Information System (INIS)

    Khoromskij, B.N.; Khoromskaia, V.; Chinnamsetty, S.R.; Flad, H.-J.

    2009-01-01

    In this paper, we investigate a novel approach based on the combination of Tucker-type and canonical tensor decomposition techniques for the efficient numerical approximation of functions and operators in electronic structure calculations. In particular, we study applicability of tensor approximations for the numerical solution of Hartree-Fock and Kohn-Sham equations on 3D Cartesian grids. We show that the orthogonal Tucker-type tensor approximation of electron density and Hartree potential of simple molecules leads to low tensor rank representations. This enables an efficient tensor-product convolution scheme for the computation of the Hartree potential using a collocation-type approximation via piecewise constant basis functions on a uniform nxnxn grid. Combined with the Richardson extrapolation, our approach exhibits O(h 3 ) convergence in the grid-size h=O(n -1 ). Moreover, this requires O(3rn+r 3 ) storage, where r denotes the Tucker rank of the electron density with r=O(logn), almost uniformly in n. For example, calculations of the Coulomb matrix and the Hartree-Fock energy for the CH 4 molecule, with a pseudopotential on the C atom, achieved accuracies of the order of 10 -6 hartree with a grid-size n of several hundreds. Since the tensor-product convolution in 3D is performed via 1D convolution transforms, our scheme markedly outperforms the 3D-FFT in both the computing time and storage requirements.

  16. Norm overlap between many-body states: Uncorrelated overlap between arbitrary Bogoliubov product states

    Science.gov (United States)

    Bally, B.; Duguet, T.

    2018-02-01

    Background: State-of-the-art multi-reference energy density functional calculations require the computation of norm overlaps between different Bogoliubov quasiparticle many-body states. It is only recently that the efficient and unambiguous calculation of such norm kernels has become available under the form of Pfaffians [L. M. Robledo, Phys. Rev. C 79, 021302 (2009), 10.1103/PhysRevC.79.021302]. Recently developed particle-number-restored Bogoliubov coupled-cluster (PNR-BCC) and particle-number-restored Bogoliubov many-body perturbation (PNR-BMBPT) ab initio theories [T. Duguet and A. Signoracci, J. Phys. G 44, 015103 (2017), 10.1088/0954-3899/44/1/015103] make use of generalized norm kernels incorporating explicit many-body correlations. In PNR-BCC and PNR-BMBPT, the Bogoliubov states involved in the norm kernels differ specifically via a global gauge rotation. Purpose: The goal of this work is threefold. We wish (i) to propose and implement an alternative to the Pfaffian method to compute unambiguously the norm overlap between arbitrary Bogoliubov quasiparticle states, (ii) to extend the first point to explicitly correlated norm kernels, and (iii) to scrutinize the analytical content of the correlated norm kernels employed in PNR-BMBPT. Point (i) constitutes the purpose of the present paper while points (ii) and (iii) are addressed in a forthcoming paper. Methods: We generalize the method used in another work [T. Duguet and A. Signoracci, J. Phys. G 44, 015103 (2017), 10.1088/0954-3899/44/1/015103] in such a way that it is applicable to kernels involving arbitrary pairs of Bogoliubov states. The formalism is presently explicated in detail in the case of the uncorrelated overlap between arbitrary Bogoliubov states. The power of the method is numerically illustrated and benchmarked against known results on the basis of toy models of increasing complexity. Results: The norm overlap between arbitrary Bogoliubov product states is obtained under a closed

  17. A closed-form solution to tensor voting: theory and applications.

    Science.gov (United States)

    Wu, Tai-Pang; Yeung, Sai-Kit; Jia, Jiaya; Tang, Chi-Keung; Medioni, Gérard

    2012-08-01

    We prove a closed-form solution to tensor voting (CFTV): Given a point set in any dimensions, our closed-form solution provides an exact, continuous, and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence in structure propagation. We then embed structure-aware tensor into expectation maximization (EM) for optimizing a single linear structure to achieve efficient and robust parameter estimation. Specifically, our EMTV algorithm optimizes both the tensor and fitting parameters and does not require random sampling consensus typically used in existing robust statistical techniques. We performed quantitative evaluation on its accuracy and robustness, showing that EMTV performs better than the original TV and other state-of-the-art techniques in fundamental matrix estimation for multiview stereo matching. The extensions of CFTV and EMTV for extracting multiple and nonlinear structures are underway.

  18. Labour Arrangements in Cassava Production in Oyo State, Nigeria

    Directory of Open Access Journals (Sweden)

    Abila, N.

    2012-01-01

    Full Text Available The study examined the effects of labour arrangements on the profitability of cassava enterprises in Oyo North Area of Oyo State, Nigeria. A multi-stage sampling technique was adopted for data collection, while data were analysed using descriptive statistics and budgetary analysis. The results show that the prevalent labour arrangements for cassava enterprises are: a combination of Family, Hired and Contract labour (38.9%; Family-Hired labour (27.8%; Family-Contract labour (31.1%. The gross margin per hectares across labour arrangements are N279481.99 (all-labour, N286044.24 (family-hired, N216940.10 (familycontract, and N235000.00 (family only. The returns on a naira invested on variable costs across different labour arrangements for cassava enterprises are N2.04 (all-labour, N3.66 (family-hired, N2.37 (familycontract, and N2.61 (family only. This implies that a unit (N1 variable cost in the various labour arrangements of all-labour, family/hired, family/contract and family only in cassava production will yield a marginal return of N3.04, N3.66, N2.37 and N2.61 respectively. Family-hired labour arrangement yields higher marginal return per unit of manday and one naira spent than all other arrangements. The study recommends among others the application of laboursaving technologies and an optimum combination of various labour arrangements to reduce the cost of labour used in cassava production.

  19. General projective relativity and the vector-tensor gravitational field

    International Nuclear Information System (INIS)

    Arcidiacono, G.

    1986-01-01

    In the general projective relativity, the induced 4-dimensional metric is symmetric in three cases, and we obtain the vector-tensor, the scalar-tensor, and the scalar-vector-tensor theories of gravitation. In this work we examine the vector-tensor theory, similar to the Veblen's theory, but with a different physical interpretation

  20. Tucker tensor analysis of Matern functions in spatial statistics

    KAUST Repository

    Litvinenko, Alexander

    2018-04-20

    Low-rank Tucker tensor methods in spatial statistics 1. Motivation: improve statistical models 2. Motivation: disadvantages of matrices 3. Tools: Tucker tensor format 4. Tensor approximation of Matern covariance function via FFT 5. Typical statistical operations in Tucker tensor format 6. Numerical experiments

  1. TensorFlow Agents: Efficient Batched Reinforcement Learning in TensorFlow

    OpenAIRE

    Hafner, Danijar; Davidson, James; Vanhoucke, Vincent

    2017-01-01

    We introduce TensorFlow Agents, an efficient infrastructure paradigm for building parallel reinforcement learning algorithms in TensorFlow. We simulate multiple environments in parallel, and group them to perform the neural network computation on a batch rather than individual observations. This allows the TensorFlow execution engine to parallelize computation, without the need for manual synchronization. Environments are stepped in separate Python processes to progress them in parallel witho...

  2. Scaling net ecosystem production and net biome production over a heterogeneous region in the Western United States

    Science.gov (United States)

    D.P. Turner; W.D. Ritts; B.E. Law; W.B. Cohen; Z. Yan; T. Hudiburg; J.L. Campbell; M. Duane

    2007-01-01

    Bottom-up scaling of net ecosystem production (NEP) and net biome production (NBP) was used to generate a carbon budget for a large heterogeneous region (the state of Oregon, 2.5x105 km2 ) in the Western United States. Landsat resolution (30 m) remote sensing provided the basis for mapping land cover and disturbance history...

  3. Economics of Waterleaf (Talinumtriangulare Production in Akwa Ibom State, Nigeria

    Directory of Open Access Journals (Sweden)

    Anselm A. Enete

    2010-03-01

    Full Text Available This study analyzed the profitability level of waterleaf production in three selected agricultural zones of Akwa Ibom State, Nigeria. The study was based on primary data obtained from a random sample of 60 waterleaf farmers and analyzed using descriptive statistics, profitability ratios and regression analysis. The result of the analysis shows that the majority (90% of the farmers had some level of formal education. Labour had the highest percentage (58% of total cost of production, suggesting that waterleaf production was labour intensive in the area.  The average net income per hectare per waterleaf production cycle was N322,413 while the average total cost was N89,307.18. Labour cost constituted the highest percentage of total variable cost. The profitability index (0.78, rate of returns on investment (361%, rate of returns on variable cost (482%, and operating ratio (0.21 suggest that waterleaf production was profitable in the study area. The identified major factors that enhance the output of waterleaf were the application of poultry manure, bigger household size (cheap labour, level of education of the farmer and level of capital. These observations underscore the need for the provision of credit facilities and some kind of adult education programme for the farmers. These will respectively ensure that they apply the right quantity of purchased inputs (like fertilizers, hired labour and capital in their production process and improve their human capital.Cette étude a porté sur l’analyse du taux de rentabilité de la production de grassé dans trois régions agricoles de l’état d’Akwa Ibom, au Nigeria. Des données primaires obtenues à partir d’un échantillon aléatoire de 60 cultivateurs de grassé ont été analysées à l’aide de statistiques descriptives, de ratios de rentabilité et d’une analyse de régression. Les résultats montrent que la majorité (90 % des cultivateurs a un certain degré d’éducation formelle

  4. Reconstruction of convex bodies from surface tensors

    DEFF Research Database (Denmark)

    Kousholt, Astrid; Kiderlen, Markus

    . The output of the reconstruction algorithm is a polytope P, where the surface tensors of P and K are identical up to rank s. We establish a stability result based on a generalization of Wirtinger’s inequality that shows that for large s, two convex bodies are close in shape when they have identical surface...... that are translates of each other. An algorithm for reconstructing an unknown convex body in R 2 from its surface tensors up to a certain rank is presented. Using the reconstruction algorithm, the shape of an unknown convex body can be approximated when only a finite number s of surface tensors are available...... tensors up to rank s. This is used to establish consistency of the developed reconstruction algorithm....

  5. Reconstruction of convex bodies from surface tensors

    DEFF Research Database (Denmark)

    Kousholt, Astrid; Kiderlen, Markus

    2016-01-01

    We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise...... of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes and allows for noisy...... measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise...

  6. Energy-momentum tensor in scalar QED

    International Nuclear Information System (INIS)

    Joglekar, S.D.; Misra, A.

    1988-01-01

    We consider the renormalization of the energy-momentum tensor in scalar quantum electrodynamics. We show the need for adding an improvement term to the conventional energy-momentum tensor. We consider two possible forms for the improvement term: (i) one in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be obtained from an action that is a finite function of bare quantities); (ii) one in which the improvement coefficient is a finite quantity, i.e., a finite function of renormalized parameters. We establish a negative result; viz., neither form leads to a finite energy-momentum tensor to O(e 2 λ/sup n/). .AE

  7. Unsupervised Tensor Mining for Big Data Practitioners.

    Science.gov (United States)

    Papalexakis, Evangelos E; Faloutsos, Christos

    2016-09-01

    Multiaspect data are ubiquitous in modern Big Data applications. For instance, different aspects of a social network are the different types of communication between people, the time stamp of each interaction, and the location associated to each individual. How can we jointly model all those aspects and leverage the additional information that they introduce to our analysis? Tensors, which are multidimensional extensions of matrices, are a principled and mathematically sound way of modeling such multiaspect data. In this article, our goal is to popularize tensors and tensor decompositions to Big Data practitioners by demonstrating their effectiveness, outlining challenges that pertain to their application in Big Data scenarios, and presenting our recent work that tackles those challenges. We view this work as a step toward a fully automated, unsupervised tensor mining tool that can be easily and broadly adopted by practitioners in academia and industry.

  8. Potentials for transverse trace-free tensors

    International Nuclear Information System (INIS)

    Conboye, Rory; Murchadha, Niall Ó

    2014-01-01

    In constructing and understanding initial conditions in the 3 + 1 formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point. However, finding an expression for a TT tensor depending on only two scalar functions is a non-trivial task. Assuming either axial or translational symmetry, expressions depending on two scalar potentials alone are derived here for all TT tensors in flat 3-space. In a more general spatial slice, only one of these potentials is found, the same potential given in (Baker and Puzio 1999 Phys. Rev. D 59 044030) and (Dain 2001 Phys. Rev. D 64 124002), with the remaining equations reduced to a partial differential equation, depending on boundary conditions for a solution. As an exercise, we also derive the potentials which give the Bowen-York curvature tensor in flat space. (paper)

  9. Correlators in tensor models from character calculus

    Directory of Open Access Journals (Sweden)

    A. Mironov

    2017-11-01

    Full Text Available We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.

  10. Loop optimization for tensor network renormalization

    Science.gov (United States)

    Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang

    We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.

  11. An introduction to linear algebra and tensors

    CERN Document Server

    Akivis, M A; Silverman, Richard A

    1978-01-01

    Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.

  12. Algebraic classification of the conformal tensor

    International Nuclear Information System (INIS)

    Ares de Parga, Gonzalo; Chavoya, O.; Lopez B, J.L.; Ovando Z, Gerardo

    1989-01-01

    Starting from the Petrov matrix method, we deduce a new algorithm (adaptable to computers), within the Newman-Penrose formalism, to obtain the algebraic type of the Weyl tensor in general relativity. (author)

  13. Effects of tensor forces in nuclei

    International Nuclear Information System (INIS)

    Tanihata, Isao

    2013-01-01

    Recent studies of nuclei far from the stability line have revealed drastic changes in nuclear orbitals and reported the appearance of new magic numbers and the disappearance of magic numbers observed at the stability line. One of the important reasons for such changes is considered to be because of the effect of tensor forces on nuclear structure. Although the role of tensor forces in binding very light nuclei such as deuterons and 4 He has been known, direct experimental evidence for the effect on nuclear structure is scarce. In this paper, I review known effects of tensor forces in nuclei and then discuss the recently raised question of s–p wave mixing in a halo nucleus of 11 Li. Following these reviews, the development of a new experiment to see the high-momentum components due to the tensor forces is discussed and some of the new data are presented. (paper)

  14. The energy–momentum tensor(s in classical gauge theories

    Directory of Open Access Journals (Sweden)

    Daniel N. Blaschke

    2016-11-01

    Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.

  15. Geometric decomposition of the conformation tensor in viscoelastic turbulence

    Science.gov (United States)

    Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.

    2018-05-01

    This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.

  16. The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r(4)) scaling.

    Science.gov (United States)

    Shenvi, Neil; van Aggelen, Helen; Yang, Yang; Yang, Weitao; Schwerdtfeger, Christine; Mazziotti, David

    2013-08-07

    Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral tensor and the two-particle excitation amplitudes used in the parametric 2-electron reduced density matrix (p2RDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r(4)), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the standard p2RDM algorithm, somewhere between that of CCSD and CCSD(T).

  17. Estimation of Uncertainties of Full Moment Tensors

    Science.gov (United States)

    2017-10-06

    For our moment tensor inversions, we use the ‘cut-and-paste’ ( CAP ) code of Zhu and Helmberger (1996) and Zhu and Ben-Zion (2013), with some...modifications. For the misfit function we use an L1 norm Silwal and Tape (2016), and we incorporate the number of misfitting polarities into the waveform... norm of the eigenvalue triple provides the magnitude of the moment tensor, leaving two free parameters to define the source type. In the same year

  18. Superconformal tensor calculus in five dimensions

    International Nuclear Information System (INIS)

    Fujita, Tomoyuki; Ohashi, Keisuke

    2001-01-01

    We present a full superconformal tensor calculus in five spacetime dimensions in which the Weyl multiplet has 32 Bose plus 32 Fermi degrees of freedom. It is derived using dimensional reduction from the 6D superconformal tensor calculus. We present two types of 32+32 Weyl multiplets, a vector multiplet, linear multiplet, hypermultiplet and nonlinear multiplet. Their superconformal transformation laws and the embedding and invariant action formulas are given. (author)

  19. Geometrical foundations of tensor calculus and relativity

    OpenAIRE

    Schuller , Frédéric; Lorent , Vincent

    2006-01-01

    Manifolds, particularly space curves: basic notions 1 The first groundform, the covariant metric tensor 11 The second groundform, Meusnier's theorem 19 Transformation groups in the plane 28 Co- and contravariant components for a special affine transformation in the plane 29 Surface vectors 32 Elements of tensor calculus 36 Generalization of the first groundform to the space 46 The covariant (absolute) derivation 57 Examples from elasticity theory 61 Geodesic lines 63 Main curvatur...

  20. Diffusion tensor MRI: clinical applications

    International Nuclear Information System (INIS)

    Meli, Francisco; Romero, Carlos; Carpintiero, Silvina; Salvatico, Rosana; Lambre, Hector; Vila, Jose

    2005-01-01

    Purpose: To evaluate the usefulness of diffusion-tensor imaging (DTI) on different neurological diseases, and to know if this technique shows additional information than conventional Magnetic Resonance Imaging (MRI). Materials and method: Eight patients, with neurological diseases (five patients with brain tumors, one with multiple sclerosis (MS), one with variant Creutzfeldt-Jakob disease (vCJD) and the other with delayed CO intoxication were evaluated. A MR scanner of 1.5 T was used and conventional sequences and DTI with twenty-five directions were done. Quantitative maps were gotten, where the fractional anisotropy (FA) through regions of interest (ROIs) in specific anatomic area were quantified (i.e.: internal and external capsules, frontal and temporal bundles, corpus fibers). Results: In the patients with brain tumors, there was a decrease of FA on intra and peritumoral fibers. Some of them had a disruption in their pattern. In patients with MS and CO intoxication, partial interruption along white matter bundles was demonstrated. However, a 'mismatch' between the findings of FLAIR, Diffusion-weighted images (DWI) and DTI, in the case of CO intoxication, was seen. Conclusions: DTI gave more information compared to conventional sequences about ultrastructural brain tissue in almost all the diseases above mentioned. Therefore, there is a work in progress about DTI acquisition, to evaluate a new technique, called tractography. (author)

  1. Mixed symmetry tensors in the worldline formalism

    Energy Technology Data Exchange (ETDEWEB)

    Corradini, Olindo [Dipartimento di Scienze Fisiche, Informatiche e Matematiche,Università degli Studi di Modena e Reggio Emilia, via Campi 213/A, I-41125 Modena (Italy); INFN - Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy); Edwards, James P. [Department of Mathematical Sciences, University of Bath,Claverton Down, Bath BA2 7AY (United Kingdom)

    2016-05-10

    We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which — by adding a suitable Chern-Simons term to the particle action — can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U(F) “flavour” symmetry on the worldline particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young tableau. In particular the occupation numbers of the wavefunction — i.e. the lengths of the columns (rows) of the Young tableau — are fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We suggest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.

  2. Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

    Science.gov (United States)

    Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian

    The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.

  3. The gauge-invariant canonical energy-momentum tensor

    Science.gov (United States)

    Lorcé, Cédric

    2016-03-01

    The canonical energy-momentum tensor is often considered as a purely academic object because of its gauge dependence. However, it has recently been realized that canonical quantities can in fact be defined in a gauge-invariant way provided that strict locality is abandoned, the non-local aspect being dictacted in high-energy physics by the factorization theorems. Using the general techniques for the parametrization of non-local parton correlators, we provide for the first time a complete parametrization of the energy-momentum tensor (generalizing the purely local parametrizations of Ji and Bakker-Leader-Trueman used for the kinetic energy-momentum tensor) and identify explicitly the parts accessible from measurable two-parton distribution functions (TMDs and GPDs). As by-products, we confirm the absence of model-independent relations between TMDs and parton orbital angular momentum, recover in a much simpler way the Burkardt sum rule and derive three similar new sum rules expressing the conservation of transverse momentum.

  4. The gauge-invariant canonical energy-momentum tensor

    International Nuclear Information System (INIS)

    Lorce, C.

    2016-01-01

    The canonical energy-momentum tensor is often considered as a purely academic object because of its gauge dependence. However, it has recently been realized that canonical quantities can in fact be defined in a gauge-invariant way provided that strict locality is abandoned, the non-local aspect being dictated in high-energy physics by the factorization theorems. Using the general techniques for the parametrization of non-local parton correlators, we provide for the first time a complete parametrization of the energy-momentum tensor (generalizing the purely local parametrizations of Ji and Bakker-Leader-Trueman used for the kinetic energy-momentum tensor) and identify explicitly the parts accessible from measurable two-parton distribution functions (TMD and GPD). As by-products, we confirm the absence of model-independent relations between TMDs and parton orbital angular momentum, recover in a much simpler way the Burkardt sum rule and derive 3 similar new sum rules expressing the conservation of transverse momentum. (author)

  5. 9 CFR 381.209 - Returned United States inspected and marked poultry products; exemption.

    Science.gov (United States)

    2010-01-01

    ... PRODUCTS INSPECTION AND VOLUNTARY INSPECTION AND CERTIFICATION POULTRY PRODUCTS INSPECTION REGULATIONS... 9 Animals and Animal Products 2 2010-01-01 2010-01-01 false Returned United States inspected and marked poultry products; exemption. 381.209 Section 381.209 Animals and Animal Products FOOD SAFETY AND...

  6. On the concircular curvature tensor of Riemannian manifolds

    International Nuclear Information System (INIS)

    Rahman, M.S.; Lal, S.

    1990-06-01

    Definition of the concircular curvature tensor, Z hijk , along with Z-tensor, Z ij , is given and some properties of Z hijk are described. Tensors identical with Z hijk are shown. A necessary and sufficient condition that a Riemannian V n has zero Z-tensor is found. A number of theorems on concircular symmetric space, concircular recurrent space (Z n -space) and Z n -space with zero Z-tensor are deduced. (author). 6 refs

  7. (Ln-bar, g)-spaces. Special tensor fields

    International Nuclear Information System (INIS)

    Manoff, S.; Dimitrov, B.

    1998-01-01

    The Kronecker tensor field, the contraction tensor field, as well as the multi-Kronecker and multi-contraction tensor fields are determined and the action of the covariant differential operator, the Lie differential operator, the curvature operator, and the deviation operator on these tensor fields is established. The commutation relations between the operators Sym and Asym and the covariant and Lie differential operators are considered acting on symmetric and antisymmetric tensor fields over (L n bar, g)-spaces

  8. 75 FR 13345 - Pricing for Certain 2010 United States Mint Products

    Science.gov (United States)

    2010-03-19

    ... DEPARTMENT OF THE TREASURY United States Mint Pricing for Certain 2010 United States Mint Products AGENCY: United States Mint, Department of the Treasury. ACTION: Notice. SUMMARY: The United States Mint is announcing the price of the 2010 United States Mint Presidential $1 Coin and First Spouse Medal...

  9. New successive variational method of tensor-optimized antisymmetrized molecular dynamics for nuclear many-body systems

    Science.gov (United States)

    Myo, Takayuki; Toki, Hiroshi; Ikeda, Kiyomi; Horiuchi, Hisashi; Suhara, Tadahiro

    2017-07-01

    We recently proposed a new variational theory of “tensor-optimized antisymmetrized molecular dynamics” (TOAMD), which treats the strong interaction explicitly for finite nuclei [T. Myo et al., Prog. Theor. Exp. Phys. 2015, 073D02 (2015)]. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiple products are successively operated to the AMD state. The correlated Hamiltonian is expanded into many-body operators by using the cluster expansion and all the resulting operators are taken into account in the calculation without any truncation. We show detailed results for TOAMD with the nucleon-nucleon interaction AV8‧ for s-shell nuclei. The binding energy and the Hamiltonian components are successively converged to exact values of the few-body calculations. We also apply TOAMD to the Malfliet-Tjon central potential having a strong short-range repulsion. TOAMD can treat the short-range correlation and provided accurate energies of s-shell nuclei, reproducing the results of few-body calculations. It turns out that the numerical accuracy of TOAMD with double products of the correlation functions is beyond the variational Monte Carlo method with Jastrow's product-type correlation functions.

  10. Semi-Supervised Tensor-Based Graph Embedding Learning and Its Application to Visual Discriminant Tracking.

    Science.gov (United States)

    Hu, Weiming; Gao, Jin; Xing, Junliang; Zhang, Chao; Maybank, Stephen

    2017-01-01

    An appearance model adaptable to changes in object appearance is critical in visual object tracking. In this paper, we treat an image patch as a two-order tensor which preserves the original image structure. We design two graphs for characterizing the intrinsic local geometrical structure of the tensor samples of the object and the background. Graph embedding is used to reduce the dimensions of the tensors while preserving the structure of the graphs. Then, a discriminant embedding space is constructed. We prove two propositions for finding the transformation matrices which are used to map the original tensor samples to the tensor-based graph embedding space. In order to encode more discriminant information in the embedding space, we propose a transfer-learning- based semi-supervised strategy to iteratively adjust the embedding space into which discriminative information obtained from earlier times is transferred. We apply the proposed semi-supervised tensor-based graph embedding learning algorithm to visual tracking. The new tracking algorithm captures an object's appearance characteristics during tracking and uses a particle filter to estimate the optimal object state. Experimental results on the CVPR 2013 benchmark dataset demonstrate the effectiveness of the proposed tracking algorithm.

  11. Boosting aquaculture production systems in Osun state: Role of ...

    African Journals Online (AJOL)

    This scenario leaves a high percentage of the population who depend on fish and fish products food insecure, and thus, the need to boost aquaculture production to argument the supply from the wild. The study therefore looks into the possibility of boosting the production systems through the use of micro-credit and ...

  12. Economic sustainability of sheabutter production in Kwara state ...

    African Journals Online (AJOL)

    Production of sheabutter has the economic potentials in sustaining income generation for rural dwellers. The potentials of shea nuts productivity could only be achieved when technical efficiency of the processing becomes relevant. The study examines the patterns, efficiency and productivity of processing harvested shea ...

  13. A high performance data parallel tensor contraction framework: Application to coupled electro-mechanics

    Science.gov (United States)

    Poya, Roman; Gil, Antonio J.; Ortigosa, Rogelio

    2017-07-01

    The paper presents aspects of implementation of a new high performance tensor contraction framework for the numerical analysis of coupled and multi-physics problems on streaming architectures. In addition to explicit SIMD instructions and smart expression templates, the framework introduces domain specific constructs for the tensor cross product and its associated algebra recently rediscovered by Bonet et al. (2015, 2016) in the context of solid mechanics. The two key ingredients of the presented expression template engine are as follows. First, the capability to mathematically transform complex chains of operations to simpler equivalent expressions, while potentially avoiding routes with higher levels of computational complexity and, second, to perform a compile time depth-first or breadth-first search to find the optimal contraction indices of a large tensor network in order to minimise the number of floating point operations. For optimisations of tensor contraction such as loop transformation, loop fusion and data locality optimisations, the framework relies heavily on compile time technologies rather than source-to-source translation or JIT techniques. Every aspect of the framework is examined through relevant performance benchmarks, including the impact of data parallelism on the performance of isomorphic and nonisomorphic tensor products, the FLOP and memory I/O optimality in the evaluation of tensor networks, the compilation cost and memory footprint of the framework and the performance of tensor cross product kernels. The framework is then applied to finite element analysis of coupled electro-mechanical problems to assess the speed-ups achieved in kernel-based numerical integration of complex electroelastic energy functionals. In this context, domain-aware expression templates combined with SIMD instructions are shown to provide a significant speed-up over the classical low-level style programming techniques.

  14. By-products from the biodiesel chain as a substrate to citric acid production by solid-state fermentation.

    Science.gov (United States)

    Schneider, Manuella; Zimmer, Gabriela F; Cremonese, Ezequiel B; de C de S Schneider, Rosana; Corbellini, Valeriano A

    2014-07-01

    In this study, we propose the use of tung cake for the production of organic acids, with an emphasis on citric acid by solid-state fermentation. We evaluated the conditions of production and the by-products from the biodiesel chain as raw materials involved in this bioprocess. First, we standardized the conditions of solid-state fermentation in tung cake with and without residual fat and with different concentrations of glycerine using the fungus Aspergillus niger The solid-state fermentation process was monitored for 7 days considering the biomass growth and pH level. Citric acid production was determined by high-performance liquid chromatography. Fungal development was better in the crude tung cake, consisting of 20% glycerine. The highest citric acid yield was 350 g kg(-1) of biomass. Therefore, the solid-state fermentation of the tung cake with glycerine led to citric acid production using the Aspergillus niger fungus. © The Author(s) 2014.

  15. On the (1,1)-tensor bundle with Cheeger–Gromoll type metric

    Indian Academy of Sciences (India)

    The main purpose of the present paper is to construct Riemannian almost product structures on the (1, 1)-tensor bundle equipped with Cheeger–Gromoll type metric over a Riemannian manifold and present some results concerning these structures. Keywords. Almost product structure; Cheeger–Gromoll type metric; metric ...

  16. An Adaptive Spectrally Weighted Structure Tensor Applied to Tensor Anisotropic Nonlinear Diffusion for Hyperspectral Images

    Science.gov (United States)

    Marin Quintero, Maider J.

    2013-01-01

    The structure tensor for vector valued images is most often defined as the average of the scalar structure tensors in each band. The problem with this definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result non-edge pixels can be reinforced and edges can be weakened…

  17. Generalized tensor-based morphometry of HIV/AIDS using multivariate statistics on deformation tensors.

    Science.gov (United States)

    Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M

    2008-01-01

    This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.

  18. Modified weak energy condition for the energy momentum tensor in quantum field theory

    International Nuclear Information System (INIS)

    Latorre, J.

    1998-01-01

    The weak energy condition is known to fail in general when applied to expectation values of the energy momentum tensor in flat space quantum field theory. It is shown how the usual counter arguments against its validity are no longer applicable if the states vertical stroke ψ right angle for which the expectation value is considered are restricted to a suitably defined subspace. A possible natural restriction on vertical stroke ψ right angle is suggested and illustrated by two quantum mechanical examples based on a simple perturbed harmonic oscillator Hamiltonian. The proposed alternative quantum weak energy condition is applied to states formed by the action of the scalar, vector and the energy momentum tensor operators on the vacuum. We assume conformal invariance in order to determine almost uniquely three-point functions involving the energy momentum tensor in terms of a few parameters. The positivity conditions lead to non-trivial inequalities for these parameters. They are satisfied in free field theories, except in one case for dimensions close to two. Further restrictions on vertical stroke ψ right angle are suggested which remove this problem. The inequalities which follow from considering the state formed by applying the energy momentum tensor to the vacuum are shown to imply that the coefficient of the topological term in the expectation value of the trace of the energy momentum tensor in an arbitrary curved space background is positive, in accord with calculations in free field theories. (orig.)

  19. Using MODIS NDVI products for vegetation state monitoring on the oil production territory in Western Siberia

    Directory of Open Access Journals (Sweden)

    Kovalev Anton

    2016-01-01

    Full Text Available Article describes the results of using remote sensing data for vegetation state monitoring on the oil field territories in Western Siberia. We used MODIS data product providing the normalized difference vegetation index (NDVI values. Average NDVI values of each studied area were calculated for the period from 2010 to 2015 with one year interval for June, July and August. Analysis was carried out via an open tool of geographic information system QGIS used for spatial analysis and calculation of statistical parameters within chosen polygons. Results are presented in graphs showing the variation of NDVI for each study area and explaining the changes in trend lines for each field. It is shown that the majority of graphs are similar in shape which is caused by similar weather conditions. To confirm these results, we have conducted data analysis including temperature conditions and information about the accidents for each area. Abnormal changes in NDVI values revealed an emergency situation on the Priobskoe oil field caused by the flood in 2015. To sum up, the research results show that vegetation of studied areas is in a sufficiently stable state.

  20. Shifting stream planform state decreases stream productivity yet increases riparian animal production

    Science.gov (United States)

    Venarsky, Michael P.; Walters, David M.; Hall, Robert O.; Livers, Bridget; Wohl, Ellen

    2018-01-01

    In the Colorado Front Range (USA), disturbance history dictates stream planform. Undisturbed, old-growth streams have multiple channels and large amounts of wood and depositional habitat. Disturbed streams (wildfires and logging tested how these opposing stream states influenced organic matter, benthic macroinvertebrate secondary production, emerging aquatic insect flux, and riparian spider biomass. Organic matter and macroinvertebrate production did not differ among sites per unit area (m−2), but values were 2 ×–21 × higher in undisturbed reaches per unit of stream valley (m−1 valley) because total stream area was higher in undisturbed reaches. Insect emergence was similar among streams at the per unit area and per unit of stream valley. However, rescaling insect emergence to per meter of stream bank showed that the emerging insect biomass reaching the stream bank was lower in undisturbed sites because multi-channel reaches had 3 × more stream bank than single-channel reaches. Riparian spider biomass followed the same pattern as emerging aquatic insects, and we attribute this to bottom-up limitation caused by the multi-channeled undisturbed sites diluting prey quantity (emerging insects) reaching the stream bank (riparian spider habitat). These results show that historic landscape disturbances continue to influence stream and riparian communities in the Colorado Front Range. However, these legacy effects are only weakly influencing habitat-specific function and instead are primarily influencing stream–riparian community productivity by dictating both stream planform (total stream area, total stream bank length) and the proportional distribution of specific habitat types (pools vs riffles).

  1. Observation of vector and tensor light shifts in 87Rb using near-resonant, stimulated Raman spectroscopy

    Science.gov (United States)

    Hu, Qing-Qing; Freier, Christian; Sun, Yuan; Leykauf, Bastian; Schkolnik, Vladimir; Yang, Jun; Krutzik, Markus; Peters, Achim

    2018-01-01

    We present the derivation of the frequency-dependent scalar, vector, and tensor dynamical polarizabilities for the two hyperfine levels of the 87Rb atom 5 s ground state. Based on the characterization of the dynamical polarizabilities, we analyze and measure the differential vector and tensor light shift between the 5 s ground-state sublevels with near-resonant, stimulated Raman transitions. These results clarify that the tensor polarizabilities for the ground states of alkali atoms are absent when the light field is far detuned from the atomic resonance and the total electronic angular momentum J is a good quantum number. In the near-resonant case, the light shifts are nontrivial and the determination of the frequency-dependent vector and tensor dynamic polarizabilities will help to achieve higher fidelities for applications of neutral atoms in quantum information and precision measurements.

  2. Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Krtous, Pavel [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Kubiznak, David [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Page, Don N. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada); Frolov, Valeri P. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada)

    2007-02-15

    From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 {<=} j {<=} k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)

  3. Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

    International Nuclear Information System (INIS)

    Krtous, Pavel; Kubiznak, David; Page, Don N.; Frolov, Valeri P.

    2007-01-01

    From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 ≤ j ≤ k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)

  4. Effective field theory approaches for tensor potentials

    Energy Technology Data Exchange (ETDEWEB)

    Jansen, Maximilian

    2016-11-14

    Effective field theories are a widely used tool to study physical systems at low energies. We apply them to systematically analyze two and three particles interacting via tensor potentials. Two examples are addressed: pion interactions for anti D{sup 0}D{sup *0} scattering to dynamically generate the X(3872) and dipole interactions for two and three bosons at low energies. For the former, the one-pion exchange and for the latter, the long-range dipole force induce a tensor-like structure of the potential. We apply perturbative as well as non-perturbative methods to determine low-energy observables. The X(3872) is of major interest in modern high-energy physics. Its exotic characteristics require approaches outside the range of the quark model for baryons and mesons. Effective field theories represent such methods and provide access to its peculiar nature. We interpret the X(3872) as a hadronic molecule consisting of neutral D and D{sup *} mesons. It is possible to apply an effective field theory with perturbative pions. Within this framework, we address chiral as well as finite volume extrapolations for low-energy observables, such as the binding energy and the scattering length. We show that the two-point correlation function for the D{sup *0} meson has to be resummed to cure infrared divergences. Moreover, next-to-leading order coupling constants, which were introduced by power counting arguments, appear to be essential to renormalize the scattering amplitude. The binding energy as well as the scattering length display a moderate dependence on the light quark masses. The X(3872) is most likely deeper bound for large light quark masses. In a finite volume on the other hand, the binding energy significantly increases. The dependence on the light quark masses and the volume size can be simultaneously obtained. For bosonic dipoles we apply a non-perturbative, numerical approach. We solve the Lippmann-Schwinger equation for the two-dipole system and the Faddeev

  5. Eckart frame vibration-rotation Hamiltonians: Contravariant metric tensor

    International Nuclear Information System (INIS)

    Pesonen, Janne

    2014-01-01

    Eckart frame is a unique embedding in the theory of molecular vibrations and rotations. It is defined by the condition that the Coriolis coupling of the reference structure of the molecule is zero for every choice of the shape coordinates. It is far from trivial to set up Eckart kinetic energy operators (KEOs), when the shape of the molecule is described by curvilinear coordinates. In order to obtain the KEO, one needs to set up the corresponding contravariant metric tensor. Here, I derive explicitly the Eckart frame rotational measuring vectors. Their inner products with themselves give the rotational elements, and their inner products with the vibrational measuring vectors (which, in the absence of constraints, are the mass-weighted gradients of the shape coordinates) give the Coriolis elements of the contravariant metric tensor. The vibrational elements are given as the inner products of the vibrational measuring vectors with themselves, and these elements do not depend on the choice of the body-frame. The present approach has the advantage that it does not depend on any particular choice of the shape coordinates, but it can be used in conjunction with all shape coordinates. Furthermore, it does not involve evaluation of covariant metric tensors, chain rules of derivation, or numerical differentiation, and it can be easily modified if there are constraints on the shape of the molecule. Both the planar and non-planar reference structures are accounted for. The present method is particular suitable for numerical work. Its computational implementation is outlined in an example, where I discuss how to evaluate vibration-rotation energies and eigenfunctions of a general N-atomic molecule, the shape of which is described by a set of local polyspherical coordinates

  6. Productivity Effects of United States Multinational Enterprises : The Roles of Market Orientation and Regional Integration

    NARCIS (Netherlands)

    Smeets, Roger; Wei, Yingqi

    2010-01-01

    Smeets R. and Wei Y. Productivity effects of United States multinational enterprises: the roles of market orientation and regional integration, Regional Studies. This paper considers the role of market orientation and regional integration in foreign direct investment (FDI) productivity effects.

  7. Susceptibility tensor imaging (STI) of the brain.

    Science.gov (United States)

    Li, Wei; Liu, Chunlei; Duong, Timothy Q; van Zijl, Peter C M; Li, Xu

    2017-04-01

    Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility and magnetic susceptibility anisotropy can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping to remove such dependence. Similar to diffusion tensor imaging, STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of the susceptibility anisotropy in brain white matter is myelin. Another unique feature of the susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in the myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

  8. Susceptibility Tensor Imaging (STI) of the Brain

    Science.gov (United States)

    Li, Wei; Liu, Chunlei; Duong, Timothy Q.; van Zijl, Peter C.M.; Li, Xu

    2016-01-01

    Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility (MMS) and magnetic susceptibility anisotropy (MSA) can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping (QSM) to remove such dependence. Similar to diffusion tensor imaging (DTI), STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of susceptibility anisotropy in brain white matter is myelin. Another unique feature of susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. PMID:27120169

  9. Off-shell N = 2 tensor supermultiplets

    International Nuclear Information System (INIS)

    Wit, Bernard de; Saueressig, Frank

    2006-01-01

    A multiplet calculus is presented for an arbitrary number n of N = 2 tensor supermultiplets. For rigid supersymmetry the known couplings are reproduced. In the superconformal case the target spaces parametrized by the scalar fields are cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant potentials, subject to certain constraints. The coupling to conformal supergravity enables the derivation of a large class of supergravity Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing the tensor fields into scalars leads to hypermultiplets with hyperkaehler or quaternion-Kaehler target spaces with at least n abelian isometries. It is demonstrated how to use the calculus for the construction of Lagrangians containing higher-derivative couplings of tensor multiplets. For the application of the c-map between vector and tensor supermultiplets to Lagrangians with higher-order derivatives, an off-shell version of this map is proposed. Various other implications of the results are discussed. As an example an elegant derivation of the classification of 4-dimensional quaternion-Kaehler manifolds with two commuting isometries is given

  10. Economic Analysis Of Cassava Production In Akwa Ibom State ...

    African Journals Online (AJOL)

    ... encourage farmers to use recommended rate of fertilizer application, improved varieties of cassava stem for increased efficiency and increased cassava production in the country since there is availability of markets for Nigeria cassava products( chips/pellets) in China, Netherlands, Germany, Belgium and Luxembourg.

  11. Resources Use Efficiency In Food Crop Production In Ekiti State ...

    African Journals Online (AJOL)

    Marginal value productivity of resources were computed and compared with the acquisition/prices of these resources. Result of regression analysis indicates that farm size, fertilizer and purchased inputs were significant inputs that accounted for variation in the output of food crops. The Marginal Value Product (MVP) of all ...

  12. State and trends of oil crops production in China

    Directory of Open Access Journals (Sweden)

    Yang Tiankui

    2016-11-01

    Full Text Available This paper attempts to present a full picture of current situation and future trends of Chinese oil crop production. The total oil crop production remained broadly constant during 2011–2014. The top three oil crops are soybean, peanut and rapeseed, together accounting for more than 70% of total oil crop production. The area under cultivation and the production of peanuts will keep steadily increasing because most Chinese like its pleasant roasted flavor. Because of their high content in polyunsaturated fatty acids and the natural minor functional components in their oils, more attention is being paid to sunflower seed and rice bran. The diminishing availability of arable land and concern over the security of edible oil supplies is driving both a change in cultivation structure of crops and improvements in the efficiency of oilseed production in China.

  13. Profitability of Snail Production in Osun State,Nigeria | Baba ...

    African Journals Online (AJOL)

    The study determined the features and profitability of snail farming in Osun State. To achieve the study objectives, 20 snail farmers each were randomly selected from Osogbo, Iwo and Ife-Ijesa townships, where majority of snail farmers in the State were located. Data collected from the farmers were analysed using ...

  14. role of mass media in agricultural productivity in adamawa state

    African Journals Online (AJOL)

    BARTH

    2011-09-12

    Sep 12, 2011 ... LTD PRINTED IN NIGERIA ISSN 1596-2903 ... The study examined the role of mass media in agriculture in ..... television are cost of the hardware, cost of maintenance ... Government Area of Kebbi State: A case study of state ...

  15. High charge state heavy ion production from a PIG source

    International Nuclear Information System (INIS)

    Bex, L.; Clark, D.J.; Ellsworth, C.E.; Flood, W.S.; Gough, R.A.; Holley, W.R.; Meriwether, J.R.; Morris, D.

    1975-03-01

    The comparison of pulsed vs. dc arc operation for nitrogen and argon shows a shift in charge distribution toward the higher charge states for the pulsed case. Tests with various magnetic field shapes along the arc column show a significant increase in high charge state output for a uniform field compared to the case with a field low at the cathodes. (U.S.)

  16. Low charge state heavy ion production with sub-nanosecond laser.

    Science.gov (United States)

    Kanesue, T; Kumaki, M; Ikeda, S; Okamura, M

    2016-02-01

    We have investigated laser ablation plasma of various species using nanosecond and sub-nanosecond lasers for both high and low charge state ion productions. We found that with sub-nanosecond laser, the generated plasma has a long tail which has low charge state ions determined by an electrostatic ion analyzer even under the laser irradiation condition for highly charged ion production. This can be caused by insufficient laser absorption in plasma plume. This property might be suitable for low charge state ion production. We used a nanosecond laser and a sub-nanosecond laser for low charge state ion production to investigate the difference of generated plasma using the Zirconium target.

  17. Low charge state heavy ion production with sub-nanosecond laser

    Energy Technology Data Exchange (ETDEWEB)

    Kanesue, T., E-mail: tkanesue@bnl.gov; Okamura, M. [Collider-Accelerator Department, Brookhaven National Laboratory, Upton, New York 11973 (United States); Kumaki, M. [Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555 (Japan); Nishina Center for Accelerator-Based Science, RIKEN, Saitama 351-0198 (Japan); Ikeda, S. [Nishina Center for Accelerator-Based Science, RIKEN, Saitama 351-0198 (Japan); Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Kanagawa 226-8503 (Japan)

    2016-02-15

    We have investigated laser ablation plasma of various species using nanosecond and sub-nanosecond lasers for both high and low charge state ion productions. We found that with sub-nanosecond laser, the generated plasma has a long tail which has low charge state ions determined by an electrostatic ion analyzer even under the laser irradiation condition for highly charged ion production. This can be caused by insufficient laser absorption in plasma plume. This property might be suitable for low charge state ion production. We used a nanosecond laser and a sub-nanosecond laser for low charge state ion production to investigate the difference of generated plasma using the Zirconium target.

  18. TensorPack: a Maple-based software package for the manipulation of algebraic expressions of tensors in general relativity

    International Nuclear Information System (INIS)

    Huf, P A; Carminati, J

    2015-01-01

    In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment. (paper)

  19. Quantum stress tensor in Schwarzschild space-time

    International Nuclear Information System (INIS)

    Howard, K.W.; Candelas, P.

    1984-01-01

    The vacuum expectation value of the stress-energy tensor for the Hartle-Hawking state in Schwartzschild space-time has been calculated for the conformal scalar field. separates naturally into the sum of two terms. The first coincides with an approximate expression suggested by Page. The second term is a ''remainder'' that may be evaluated numerically. The total expression is in good qualitative agreement with Page's approximation. These results are at variance with earlier results given by Fawcett whose error is explained

  20. Energy-momentum tensor in the fermion-pairing model

    International Nuclear Information System (INIS)

    Kawati, S.; Miyata, H.

    1980-01-01

    The symmetric energy-momentum tensor for the self-interacting fermion theory (psi-barpsi) 2 is expressed in terms of the collective mode within the Hartree approximation. The divergent part of the energy-momentum tensor for the fermion theory induces an effective energy-momentum tensor for the collective mode, and this effective energy-momentum tensor automatically has the Callan-Coleman-Jackiw improved form. The renormalized energy-momentum tensor is structurally equivalent to the Callan-Coleman-Jackiw improved tensor for the Yukawa theory