On the BV formalism of open superstring field theory in the large Hilbert space

NASA Astrophysics Data System (ADS)

Matsunaga, Hiroaki; Nomura, Mitsuru

2018-05-01

We construct several BV master actions for open superstring field theory in the large Hilbert space. First, we show that a naive use of the conventional BV approach breaks down at the third order of the antifield number expansion, although it enables us to define a simple "string antibracket" taking the Darboux form as spacetime antibrackets. This fact implies that in the large Hilbert space, "string fields-antifields" should be reassembled to obtain master actions in a simple manner. We determine the assembly of the string anti-fields on the basis of Berkovits' constrained BV approach, and give solutions to the master equation defined by Dirac antibrackets on the constrained string field-antifield space. It is expected that partial gauge-fixing enables us to relate superstring field theories based on the large and small Hilbert spaces directly: reassembling string fields-antifields is rather natural from this point of view. Finally, inspired by these results, we revisit the conventional BV approach and construct a BV master action based on the minimal set of string fields-antifields.

Uniform sparse bounds for discrete quadratic phase Hilbert transforms

NASA Astrophysics Data System (ADS)

Kesler, Robert; Arias, Darío Mena

2017-09-01

For each α \\in T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions f : Z → C according to H^{α }f(n):= \\sum _{m ≠ 0} e^{iα m^2} f(n - m)/m. We prove that, uniformly in α \\in T , there is a sparse bound for the bilinear form < H^{α } f , g > for every pair of finitely supported functions f,g : Z→ C . The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Hölder classes.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Donnelly, William; Wong, Gabriel

What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large N. The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space. Here, we derive the modular Hamiltonian for themore » Hartle-Hawking state and show that the corresponding reduced density matrix describes a thermal ensemble of open strings ending on an object at the entangling surface that we call an entanglement brane, or E-brane.« less

Leibniz algebroids, generalized Bismut connections and Einstein-Hilbert actions

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Vysoký, Jan

2015-11-01

Connection, torsion and curvature are introduced for general (local) Leibniz algebroids. Generalized Bismut connection on TM ⊕ΛpT∗ M is an example leading to a scalar curvature of the form R +H2 for a closed (p + 2) -form H.

Hilbert-Huang Transform: A Spectral Analysis Tool Applied to Sunspot Number and Total Solar Irradiance Variations, as well as Near-Surface Atmospheric Variables

NASA Astrophysics Data System (ADS)

Barnhart, B. L.; Eichinger, W. E.; Prueger, J. H.

2010-12-01

Hilbert-Huang transform (HHT) is a relatively new data analysis tool which is used to analyze nonstationary and nonlinear time series data. It consists of an algorithm, called empirical mode decomposition (EMD), which extracts the cyclic components embedded within time series data, as well as Hilbert spectral analysis (HSA) which displays the time and frequency dependent energy contributions from each component in the form of a spectrogram. The method can be considered a generalized form of Fourier analysis which can describe the intrinsic cycles of data with basis functions whose amplitudes and phases may vary with time. The HHT will be introduced and compared to current spectral analysis tools such as Fourier analysis, short-time Fourier analysis, wavelet analysis and Wigner-Ville distributions. A number of applications are also presented which demonstrate the strengths and limitations of the tool, including analyzing sunspot number variability and total solar irradiance proxies as well as global averaged temperature and carbon dioxide concentration. Also, near-surface atmospheric quantities such as temperature and wind velocity are analyzed to demonstrate the nonstationarity of the atmosphere.

Computer implemented empirical mode decomposition method, apparatus, and article of manufacture for two-dimensional signals

NASA Technical Reports Server (NTRS)

Huang, Norden E. (Inventor)

2001-01-01

A computer implemented method of processing two-dimensional physical signals includes five basic components and the associated presentation techniques of the results. The first component decomposes the two-dimensional signal into one-dimensional profiles. The second component is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF's) from each profile based on local extrema and/or curvature extrema. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the profiles. In the third component, the IMF's of each profile are then subjected to a Hilbert Transform. The fourth component collates the Hilbert transformed IMF's of the profiles to form a two-dimensional Hilbert Spectrum. A fifth component manipulates the IMF's by, for example, filtering the two-dimensional signal by reconstructing the two-dimensional signal from selected IMF(s).

Interference in the classical probabilistic model and its representation in complex Hilbert space

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei Yu.

2005-10-01

The notion of a context (complex of physical conditions, that is to say: specification of the measurement setup) is basic in this paper.We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present already in a latent form in the classical Kolmogorov probability model. However, this model should be considered as a calculus of contextual probabilities. In our approach it is forbidden to consider abstract context independent probabilities: “first context and only then probability”. We construct the representation of the general contextual probabilistic dynamics in the complex Hilbert space. Thus dynamics of the wave function (in particular, Schrödinger's dynamics) can be considered as Hilbert space projections of a realistic dynamics in a “prespace”. The basic condition for representing of the prespace-dynamics is the law of statistical conservation of energy-conservation of probabilities. In general the Hilbert space projection of the “prespace” dynamics can be nonlinear and even irreversible (but it is always unitary). Methods developed in this paper can be applied not only to quantum mechanics, but also to classical statistical mechanics. The main quantum-like structures (e.g., interference of probabilities) might be found in some models of classical statistical mechanics. Quantum-like probabilistic behavior can be demonstrated by biological systems. In particular, it was recently found in some psychological experiments.

Covariant symplectic structure of the complex Monge-Ampère equation

NASA Astrophysics Data System (ADS)

Nutku, Y.

2000-04-01

The complex Monge-Ampère equation is invariant under arbitrary holomorphic changes of the independent variables with unit Jacobian. We present its variational formulation where the action remains invariant under this infinite group. The new Lagrangian enables us to obtain the first symplectic 2-form for the complex Monge-Ampère equation in the framework of the covariant Witten-Zuckerman approach to symplectic structure. We base our considerations on a reformulation of the Witten-Zuckerman theory in terms of holomorphic differential forms. The first closed and conserved Witten-Zuckerman symplectic 2-form for the complex Monge-Ampère equation is obtained in arbitrary dimension and for all cases elliptic, hyperbolic and homogeneous. The connection of the complex Monge-Ampère equation with Ricci-flat Kähler geometry suggests the use of the Hilbert action principle as an alternative variational formulation. However, we point out that Hilbert's Lagrangian is a divergence for Kähler metrics and serves as a topological invariant rather than yielding the Euclideanized Einstein field equations. Nevertheless, since the Witten-Zuckerman theory employs only the boundary terms in the first variation of the action, Hilbert's Lagrangian can be used to obtain the second Witten-Zuckerman symplectic 2-form. This symplectic 2-form vanishes on shell, thus defining a Lagrangian submanifold. In its derivation the connection of the second symplectic 2-form with the complex Monge-Ampère equation is indirect but we show that it satisfies all the properties required of a symplectic 2-form for the complex elliptic, or hyperbolic Monge-Ampère equation when the dimension of the complex manifold is 3 or higher. The complex Monge-Ampère equation admits covariant bisymplectic structure for complex dimension 3, or higher. However, in the physically interesting case of n=2 we have only one symplectic 2-form. The extension of these results to the case of complex Monge-Ampère-Liouville equation is also presented.

Entanglement branes in a two-dimensional string theory

DOE PAGES

Donnelly, William; Wong, Gabriel

2017-09-20

What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large N. The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space. Here, we derive the modular Hamiltonian for themore » Hartle-Hawking state and show that the corresponding reduced density matrix describes a thermal ensemble of open strings ending on an object at the entangling surface that we call an entanglement brane, or E-brane.« less

Unitary Quantum Relativity. (Work in Progress)

NASA Astrophysics Data System (ADS)

Finkelstein, David Ritz

2017-01-01

A quantum universe is expressed as a finite unitary relativistic quantum computer network. Its addresses are subject to quantum superposition as well as its memory. It has no exact mathematical model. It Its Hilbert space of input processes is also a Clifford algebra with a modular architecture of many ranks. A fundamental fermion is a quantum computer element whose quantum address belongs to the rank below. The least significant figures of its address define its spin and flavor. The most significant figures of it adress define its orbital variables. Gauging arises from the same quantification as space-time. This blurs star images only slightly, but perhaps measurably. General relativity is an approximation that splits nature into an emptiness with a high symmetry that is broken by a filling of lower symmetry. Action principles result from self-organization pf the vacuum.

Janus configurations with SL(2, ℤ)-duality twists, strings on mapping tori and a tridiagonal determinant formula

NASA Astrophysics Data System (ADS)

Ganor, Ori J.; Moore, Nathan P.; Sun, Hao-Yu; Torres-Chicon, Nesty R.

2014-07-01

We develop an equivalence between two Hilbert spaces: (i) the space of states of U(1) n Chern-Simons theory with a certain class of tridiagonal matrices of coupling constants (with corners) on T 2; and (ii) the space of ground states of strings on an associated mapping torus with T 2 fiber. The equivalence is deduced by studying the space of ground states of SL(2, ℤ)-twisted circle compactifications of U(1) gauge theory, connected with a Janus configuration, and further compactified on T 2. The equality of dimensions of the two Hilbert spaces (i) and (ii) is equivalent to a known identity on determinants of tridiagonal matrices with corners. The equivalence of operator algebras acting on the two Hilbert spaces follows from a relation between the Smith normal form of the Chern-Simons coupling constant matrix and the isometry group of the mapping torus, as well as the torsion part of its first homology group.

Canonical quantization of classical mechanics in curvilinear coordinates. Invariant quantization procedure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Błaszak, Maciej, E-mail: blaszakm@amu.edu.pl; Domański, Ziemowit, E-mail: ziemowit@amu.edu.pl

In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. An explicit form of position and momentum operators as well as their appropriate ordering in arbitrary curvilinear coordinates is demonstrated. Finally, the extension of presented formalism onto non-flat case and related ambiguities of the process of quantization are discussed. -- Highlights: •An invariant quantization procedure of classical mechanics on the phase space over flat configuration space is presented. •The passage tomore » an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. •Explicit form of position and momentum operators and their appropriate ordering in curvilinear coordinates is shown. •The invariant form of Hamiltonian operators quadratic and cubic in momenta is derived. •The extension of presented formalism onto non-flat case and related ambiguities of the quantization process are discussed.« less

Power Spectral Density and Hilbert Transform

DTIC Science & Technology

2016-12-01

Fourier transform, Hilbert transform, digital filter , SDR 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18. NUMBER...terms. A very good approximation to the ideal Hilbert transform is a low-pass finite impulse response (FIR) filter . In Fig. 7, we show a real signal...220), converted to an analytic signal using a 255-tap Hilbert transform low-pass filter . For an ideal Hilbert

Genetics Home Reference: spondyloperipheral dysplasia

MedlinePlus

... type of collagen in the body. Instead of forming collagen molecules, the abnormal COL2A1 protein builds up ... for This Page Zabel B, Hilbert K, Stöss H, Superti-Furga A, Spranger J, Winterpacht A. A ...

Constraint-Free Theories of Gravitation

NASA Technical Reports Server (NTRS)

Estabrook, Frank B.; Robinson, R. Steve; Wahlquist, Hugo D.

1998-01-01

Lovelock actions (more precisely, extended Gauss-Bonnet forms) when varied as Cartan forms on subspaces of higher dimensional flat Riemannian manifolds, generate well set, causal exterior differential systems. In particular, the Einstein- Hilbert action 4-form, varied on a 4 dimensional subspace of E(sub 10) yields a well set generalized theory of gravity having no constraints. Rcci-flat solutions are selected by initial conditions on a bounding 3-space.

de Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity

NASA Astrophysics Data System (ADS)

Bao, Ning; Cao, ChunJun; Carroll, Sean M.; Chatwin-Davies, Aidan

2017-12-01

We investigate the proposed connection between de Sitter spacetime and the multiscale entanglement renormalization ansatz (MERA) tensor network, and ask what can be learned via such a construction. We show that the quantum state obeys a cosmic no-hair theorem: the reduced density operator describing a causal patch of the MERA asymptotes to a fixed point of a quantum channel, just as spacetimes with a positive cosmological constant asymptote to de Sitter space. The MERA is potentially compatible with a weak form of complementarity (local physics only describes single patches at a time, but the overall Hilbert space is infinite dimensional) or, with certain specific modifications to the tensor structure, a strong form (the entire theory describes only a single patch plus its horizon, in a finite-dimensional Hilbert space). We also suggest that de Sitter evolution has an interpretation in terms of circuit complexity, as has been conjectured for anti-de Sitter space.

Einstein Meets Hilbert: At the Crossroads of Physics and Mathematics

NASA Astrophysics Data System (ADS)

Rowe, David E.

One of the most famous episodes in the early history of general relativity involves the ``race'' in November 1915 between Albert Einstein and David Hilbert to uncover the ``correct'' form for the ten gravitational field equations. In light of recent archival findings, however, this story now has become a topic of renewed interest and controversy among historians of physics and mathematics. Drawing on recent studies and newly found sources, the present essay takes up this familiar tale from a new perspective, one that has seldom received due attention in the standard literature, namely, the mathematical issues at the heart of Einstein's theory. Told from this angle, the leading actors are Einstein's collaborator Marcel Grossmann, his critic Tullio Levi-Civita, his competitor David Hilbert, and several other mathematicians, many of them connected with Hilbert's Göttingen colleagues such as Hermann Weyl, Felix Klein, and Emmy Noether. As Einstein was the first to admit, Göttingen was far more important than Berlin as an active center for research in general relativity. Any account which, like this one, tries to understand both the actions and motives of the leading players must confront the problem of interpreting the rather sparse documentary evidence available. The interpretation offered herein, whatever its merits, aims first and foremost to show how mathematical issues deeply permeated the early history of general relativity.

Computing Instantaneous Frequency by normalizing Hilbert Transform

NASA Technical Reports Server (NTRS)

Huang, Norden E. (Inventor)

2005-01-01

This invention presents Normalized Amplitude Hilbert Transform (NAHT) and Normalized Hilbert Transform(NHT), both of which are new methods for computing Instantaneous Frequency. This method is designed specifically to circumvent the limitation set by the Bedorsian and Nuttal Theorems, and to provide a sharp local measure of error when the quadrature and the Hilbert Transform do not agree. Motivation for this method is that straightforward application of the Hilbert Transform followed by taking the derivative of the phase-angle as the Instantaneous Frequency (IF) leads to a common mistake made up to this date. In order to make the Hilbert Transform method work, the data has to obey certain restrictions.

Computing Instantaneous Frequency by normalizing Hilbert Transform

DOEpatents

Huang, Norden E.

2005-05-31

This invention presents Normalized Amplitude Hilbert Transform (NAHT) and Normalized Hilbert Transform(NHT), both of which are new methods for computing Instantaneous Frequency. This method is designed specifically to circumvent the limitation set by the Bedorsian and Nuttal Theorems, and to provide a sharp local measure of error when the quadrature and the Hilbert Transform do not agree. Motivation for this method is that straightforward application of the Hilbert Transform followed by taking the derivative of the phase-angle as the Instantaneous Frequency (IF) leads to a common mistake made up to this date. In order to make the Hilbert Transform method work, the data has to obey certain restrictions.

Argyres-Douglas theories, chiral algebras and wild Hitchin characters

NASA Astrophysics Data System (ADS)

Fredrickson, Laura; Pei, Du; Yan, Wenbin; Ye, Ke

2018-01-01

We use Coulomb branch indices of Argyres-Douglas theories on S 1 × L( k, 1) to quantize moduli spaces M_H of wild/irregular Hitchin systems. In particular, we obtain formulae for the "wild Hitchin characters" — the graded dimensions of the Hilbert spaces from quantization — for four infinite families of M_H , giving access to many interesting geometric and topological data of these moduli spaces. We observe that the wild Hitchin characters can always be written as a sum over fixed points in M_H under the U(1) Hitchin action, and a limit of them can be identified with matrix elements of the modular transform ST k S in certain two-dimensional chiral algebras. Although naturally fitting into the geometric Langlands program, the appearance of chiral algebras, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising.

Tool Wear Feature Extraction Based on Hilbert Marginal Spectrum

NASA Astrophysics Data System (ADS)

Guan, Shan; Song, Weijie; Pang, Hongyang

2017-09-01

In the metal cutting process, the signal contains a wealth of tool wear state information. A tool wear signal’s analysis and feature extraction method based on Hilbert marginal spectrum is proposed. Firstly, the tool wear signal was decomposed by empirical mode decomposition algorithm and the intrinsic mode functions including the main information were screened out by the correlation coefficient and the variance contribution rate. Secondly, Hilbert transform was performed on the main intrinsic mode functions. Hilbert time-frequency spectrum and Hilbert marginal spectrum were obtained by Hilbert transform. Finally, Amplitude domain indexes were extracted on the basis of the Hilbert marginal spectrum and they structured recognition feature vector of tool wear state. The research results show that the extracted features can effectively characterize the different wear state of the tool, which provides a basis for monitoring tool wear condition.

Geometry of spin coherent states

NASA Astrophysics Data System (ADS)

Chryssomalakos, C.; Guzmán-González, E.; Serrano-Ensástiga, E.

2018-04-01

Spin states of maximal projection along some direction in space are called (spin) coherent, and are, in many respects, the ‘most classical’ available. For any spin s, the spin coherent states form a 2-sphere in the projective Hilbert space \

On the emergence of the structure of physics

NASA Astrophysics Data System (ADS)

Majid, S.

2018-04-01

We consider Hilbert's problem of the axioms of physics at a qualitative or conceptual level. This is more pressing than ever as we seek to understand how both general relativity and quantum theory could emerge from some deeper theory of quantum gravity, and in this regard I have previously proposed a principle of self-duality or quantum Born reciprocity as a key structure. Here, I outline some of my recent work around the idea of quantum space-time as motivated by this non-standard philosophy, including a new toy model of gravity on a space-time consisting of four points forming a square. This article is part of the theme issue `Hilbert's sixth problem'.

On the emergence of the structure of physics.

PubMed

Majid, S

2018-04-28

We consider Hilbert's problem of the axioms of physics at a qualitative or conceptual level. This is more pressing than ever as we seek to understand how both general relativity and quantum theory could emerge from some deeper theory of quantum gravity, and in this regard I have previously proposed a principle of self-duality or quantum Born reciprocity as a key structure. Here, I outline some of my recent work around the idea of quantum space-time as motivated by this non-standard philosophy, including a new toy model of gravity on a space-time consisting of four points forming a square.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Self-entanglement and the dissociation of homonuclear diatomic molecules

DOE PAGES

Gonis, A.; Zhang, X. -G.; Nicholson, D. M.; ...

2014-01-14

The concept of self-entanglement is introduced to describe a mixed state or ensemble density as a pure state in an augmented Hilbert space formed by the products of the individual states forming a mixed state (or ensemble). We use this representation of mixed states to show that upon dissociation a neutral homonuclear diatomic molecule will separate into two neutral atoms.

Multiple D3-Instantons and Mock Modular Forms I

NASA Astrophysics Data System (ADS)

Alexandrov, Sergei; Banerjee, Sibasish; Manschot, Jan; Pioline, Boris

2017-07-01

We study D3-instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold. In a previous work, consistency of D3-instantons with S-duality was established at first order in the instanton expansion, using the modular properties of the M5-brane elliptic genus. We extend this analysis to the two-instanton level, where wall-crossing phenomena start playing a role. We focus on the contact potential, an analogue of the Kähler potential which must transform as a modular form under S-duality. We show that it can be expressed in terms of a suitable modification of the partition function of D4-D2-D0 BPS black holes, constructed out of the generating function of MSW invariants (the latter coincide with Donaldson-Thomas invariants in a particular chamber). Modular invariance of the contact potential then requires that, in the case where the D3-brane wraps a reducible divisor, the generating function of MSW invariants must transform as a vector-valued mock modular form, with a specific modular completion built from the MSW invariants of the constituents. Physically, this gives a powerful constraint on the degeneracies of BPS black holes. Mathematically, our result gives a universal prediction for the modular properties of Donaldson-Thomas invariants of pure two-dimensional sheaves.

ICASE Semiannual Report

DTIC Science & Technology

1991-05-01

Greenberg and B. Lubachevsky (AT& T, Bell Laboratories). We have developed algorithms suitable for simulating a general class of stack replacement policy al...systems of conservation laws. Finally, we began to study various edge detectors based on the (truncated) Hilbert trans- form, in the context of spectral

The Standard Model in noncommutative geometry: fundamental fermions as internal forms

NASA Astrophysics Data System (ADS)

Dąbrowski, Ludwik; D'Andrea, Francesco; Sitarz, Andrzej

2018-05-01

Given the algebra, Hilbert space H, grading and real structure of the finite spectral triple of the Standard Model, we classify all possible Dirac operators such that H is a self-Morita equivalence bimodule for the associated Clifford algebra.

Multiple D3-Instantons and Mock Modular Forms II

NASA Astrophysics Data System (ADS)

Alexandrov, Sergei; Banerjee, Sibasish; Manschot, Jan; Pioline, Boris

2018-03-01

We analyze the modular properties of D3-brane instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold. In Part I, we found a necessary condition for the existence of an isometric action of S-duality on this moduli space: the generating function of DT invariants in the large volume attractor chamber must be a vector-valued mock modular form with specified modular properties. In this work, we prove that this condition is also sufficient at two-instanton order. This is achieved by producing a holomorphic action of {SL(2,Z)} on the twistor space which preserves the holomorphic contact structure. The key step is to cancel the anomalous modular variation of the Darboux coordinates by a local holomorphic contact transformation, which is generated by a suitable indefinite theta series. For this purpose we introduce a new family of theta series of signature (2, n - 2), find their modular completion, and conjecture sufficient conditions for their convergence, which may be of independent mathematical interest.

Terahertz bandwidth all-optical Hilbert transformers based on long-period gratings.

PubMed

Ashrafi, Reza; Azaña, José

2012-07-01

A novel, all-optical design for implementing terahertz (THz) bandwidth real-time Hilbert transformers is proposed and numerically demonstrated. An all-optical Hilbert transformer can be implemented using a uniform-period long-period grating (LPG) with a properly designed amplitude-only grating apodization profile, incorporating a single π-phase shift in the middle of the grating length. The designed LPG-based Hilbert transformers can be practically implemented using either fiber-optic or integrated-waveguide technologies. As a generalization, photonic fractional Hilbert transformers are also designed based on the same optical platform. In this general case, the resulting LPGs have multiple π-phase shifts along the grating length. Our numerical simulations confirm that all-optical Hilbert transformers capable of processing arbitrary optical signals with bandwidths well in the THz range can be implemented using feasible fiber/waveguide LPG designs.

Aeroelastic Flight Data Analysis with the Hilbert-Huang Algorithm

NASA Technical Reports Server (NTRS)

Brenner, Martin J.; Prazenica, Chad

2006-01-01

This report investigates the utility of the Hilbert Huang transform for the analysis of aeroelastic flight data. It is well known that the classical Hilbert transform can be used for time-frequency analysis of functions or signals. Unfortunately, the Hilbert transform can only be effectively applied to an extremely small class of signals, namely those that are characterized by a single frequency component at any instant in time. The recently-developed Hilbert Huang algorithm addresses the limitations of the classical Hilbert transform through a process known as empirical mode decomposition. Using this approach, the data is filtered into a series of intrinsic mode functions, each of which admits a well-behaved Hilbert transform. In this manner, the Hilbert Huang algorithm affords time-frequency analysis of a large class of signals. This powerful tool has been applied in the analysis of scientific data, structural system identification, mechanical system fault detection, and even image processing. The purpose of this report is to demonstrate the potential applications of the Hilbert Huang algorithm for the analysis of aeroelastic systems, with improvements such as localized online processing. Applications for correlations between system input and output, and amongst output sensors, are discussed to characterize the time-varying amplitude and frequency correlations present in the various components of multiple data channels. Online stability analyses and modal identification are also presented. Examples are given using aeroelastic test data from the F-18 Active Aeroelastic Wing airplane, an Aerostructures Test Wing, and pitch plunge simulation.

Aeroelastic Flight Data Analysis with the Hilbert-Huang Algorithm

NASA Technical Reports Server (NTRS)

Brenner, Marty; Prazenica, Chad

2005-01-01

This paper investigates the utility of the Hilbert-Huang transform for the analysis of aeroelastic flight data. It is well known that the classical Hilbert transform can be used for time-frequency analysis of functions or signals. Unfortunately, the Hilbert transform can only be effectively applied to an extremely small class of signals, namely those that are characterized by a single frequency component at any instant in time. The recently-developed Hilbert-Huang algorithm addresses the limitations of the classical Hilbert transform through a process known as empirical mode decomposition. Using this approach, the data is filtered into a series of intrinsic mode functions, each of which admits a well-behaved Hilbert transform. In this manner, the Hilbert-Huang algorithm affords time-frequency analysis of a large class of signals. This powerful tool has been applied in the analysis of scientific data, structural system identification, mechanical system fault detection, and even image processing. The purpose of this paper is to demonstrate the potential applications of the Hilbert-Huang algorithm for the analysis of aeroelastic systems, with improvements such as localized/online processing. Applications for correlations between system input and output, and amongst output sensors, are discussed to characterize the time-varying amplitude and frequency correlations present in the various components of multiple data channels. Online stability analyses and modal identification are also presented. Examples are given using aeroelastic test data from the F/A-18 Active Aeroelastic Wing aircraft, an Aerostructures Test Wing, and pitch-plunge simulation.

Hilbert's sixth problem and the failure of the Boltzmann to Euler limit

NASA Astrophysics Data System (ADS)

Slemrod, Marshall

2018-04-01

This paper addresses the main issue of Hilbert's sixth problem, namely the rigorous passage of solutions to the mesoscopic Boltzmann equation to macroscopic solutions of the Euler equations of compressible gas dynamics. The results of the paper are that (i) in general Hilbert's program will fail because of the appearance of van der Waals-Korteweg capillarity terms in a macroscopic description of motion of a gas, and (ii) the van der Waals-Korteweg theory itself might satisfy Hilbert's quest for a map from the `atomistic view' to the laws of motion of continua. This article is part of the theme issue `Hilbert's sixth problem'.

Modular organization and hospital performance.

PubMed

Kuntz, Ludwig; Vera, Antonio

2007-02-01

The concept of modularization represents a modern form of organization, which contains the vertical disaggregation of the firm and the use of market mechanisms within hierarchies. The objective of this paper is to examine whether the use of modular structures has a positive effect on hospital performance. The empirical section makes use of multiple regression analyses and leads to the main result that modularization does not have a positive effect on hospital performance. However, the analysis also finds out positive efficiency effects of two central ideas of modularization, namely process orientation and internal market mechanisms.

Instantaneous frequency time analysis of physiology signals: The application of pregnant women’s radial artery pulse signals

NASA Astrophysics Data System (ADS)

Su, Zhi-Yuan; Wang, Chuan-Chen; Wu, Tzuyin; Wang, Yeng-Tseng; Tang, Feng-Cheng

2008-01-01

This study used the Hilbert-Huang transform, a recently developed, instantaneous frequency-time analysis, to analyze radial artery pulse signals taken from women in their 36th week of pregnancy and after pregnancy. The acquired instantaneous frequency-time spectrum (Hilbert spectrum) is further compared with the Morlet wavelet spectrum. Results indicate that the Hilbert spectrum is especially suitable for analyzing the time series of non-stationary radial artery pulse signals since, in the Hilbert-Huang transform, signals are decomposed into different mode functions in accordance with signal’s local time scale. Therefore, the Hilbert spectrum contains more detailed information than the Morlet wavelet spectrum. From the Hilbert spectrum, we can see that radial artery pulse signals taken from women in their 36th week of pregnancy and after pregnancy have different patterns. This approach could be applied to facilitate non-invasive diagnosis of fetus’ physiological signals in the future.

Quantum probability and Hilbert's sixth problem

NASA Astrophysics Data System (ADS)

Accardi, Luigi

2018-04-01

With the birth of quantum mechanics, the two disciplines that Hilbert proposed to axiomatize, probability and mechanics, became entangled and a new probabilistic model arose in addition to the classical one. Thus, to meet Hilbert's challenge, an axiomatization should account deductively for the basic features of all three disciplines. This goal was achieved within the framework of quantum probability. The present paper surveys the quantum probabilistic axiomatization. This article is part of the themed issue `Hilbert's sixth problem'.

Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spaces

NASA Technical Reports Server (NTRS)

Ito, Kazufumi

1987-01-01

The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.

A kernel adaptive algorithm for quaternion-valued inputs.

PubMed

Paul, Thomas K; Ogunfunmi, Tokunbo

2015-10-01

The use of quaternion data can provide benefit in applications like robotics and image recognition, and particularly for performing transforms in 3-D space. Here, we describe a kernel adaptive algorithm for quaternions. A least mean square (LMS)-based method was used, resulting in the derivation of the quaternion kernel LMS (Quat-KLMS) algorithm. Deriving this algorithm required describing the idea of a quaternion reproducing kernel Hilbert space (RKHS), as well as kernel functions suitable with quaternions. A modified HR calculus for Hilbert spaces was used to find the gradient of cost functions defined on a quaternion RKHS. In addition, the use of widely linear (or augmented) filtering is proposed to improve performance. The benefit of the Quat-KLMS and widely linear forms in learning nonlinear transformations of quaternion data are illustrated with simulations.

Automorphic Forms and Mock Modular Forms in String Theory

NASA Astrophysics Data System (ADS)

Nazaroglu, Caner

We study a variety of modular invariant objects in relation to string theory. First, we focus on Jacobi forms over generic rank lattices and Siegel forms that appear in N = 2, D = 4 compactifications of heterotic string with Wilson lines. Constraints from low energy spectrum and modularity are employed to deduce the relevant supersymmetric partition functions entirely. This procedure is applied on models that lead to Jacobi forms of index 3, 4, 5 as well as Jacobi forms over root lattices A2 and A3. These computations are then checked against an explicit orbifold model which can be Higgsed to the models under question. Models with a single Wilson line are then studied in detail with their relation to paramodular group Gammam as T-duality group made explicit. These results on the heterotic string side are then turned into predictions for geometric invariants using TypeII - Heterotic duality. Secondly, we study theta functions for indenite signature lattices of generic signature. Building on results in literature for signature (n-1,1) and (n-2,2) lattices, we work out the properties of generalized error functions which we call r-tuple error functions. We then use these functions to build such indenite theta functions and describe their modular completions.

Direct Images, Fields of Hilbert Spaces, and Geometric Quantization

NASA Astrophysics Data System (ADS)

Lempert, László; Szőke, Róbert

2014-04-01

Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family H s of Hilbert spaces, and the question arises if the spaces H s are canonically isomorphic. Axelrod et al. (J. Diff. Geo. 33:787-902, 1991) and Hitchin (Commun. Math. Phys. 131:347-380, 1990) suggest viewing H s as fibers of a Hilbert bundle H, introduce a connection on H, and use parallel transport to identify different fibers. Here we explore to what extent this can be done. First we introduce the notion of smooth and analytic fields of Hilbert spaces, and prove that if an analytic field over a simply connected base is flat, then it corresponds to a Hermitian Hilbert bundle with a flat connection and path independent parallel transport. Second we address a general direct image problem in complex geometry: pushing forward a Hermitian holomorphic vector bundle along a non-proper map . We give criteria for the direct image to be a smooth field of Hilbert spaces. Third we consider quantizing an analytic Riemannian manifold M by endowing TM with the family of adapted Kähler structures from Lempert and Szőke (Bull. Lond. Math. Soc. 44:367-374, 2012). This leads to a direct image problem. When M is homogeneous, we prove the direct image is an analytic field of Hilbert spaces. For certain such M—but not all—the direct image is even flat; which means that in those cases quantization is unique.

Computation and visualization of geometric partial differential equations

NASA Astrophysics Data System (ADS)

Tiee, Christopher L.

The chief goal of this work is to explore a modern framework for the study and approximation of partial differential equations, recast common partial differential equations into this framework, and prove theorems about such equations and their approximations. A central motivation is to recognize and respect the essential geometric nature of such problems, and take it into consideration when approximating. The hope is that this process will lead to the discovery of more refined algorithms and processes and apply them to new problems. In the first part, we introduce our quantities of interest and reformulate traditional boundary value problems in the modern framework. We see how Hilbert complexes capture and abstract the most important properties of such boundary value problems, leading to generalizations of important classical results such as the Hodge decomposition theorem. They also provide the proper setting for numerical approximations. We also provide an abstract framework for evolution problems in these spaces: Bochner spaces. We next turn to approximation. We build layers of abstraction, progressing from functions, to differential forms, and finally, to Hilbert complexes. We explore finite element exterior calculus (FEEC), which allows us to approximate solutions involving differential forms, and analyze the approximation error. In the second part, we prove our central results. We first prove an extension of current error estimates for the elliptic problem in Hilbert complexes. This extension handles solutions with nonzero harmonic part. Next, we consider evolution problems in Hilbert complexes and prove abstract error estimates. We apply these estimates to the problem for Riemannian hypersurfaces in R. {n+1},generalizing current results for open subsets of R. {n}. Finally, we applysome of the concepts to a nonlinear problem, the Ricci flow on surfaces, and use tools from nonlinear analysis to help develop and analyze the equations. In the appendices, we detail some additional motivation and a source for further examples: canonical geometries that are realized as steady-state solutions to parabolic equations similar to that of Ricci flow. An eventual goal is to compute such solutions using the methods of the previous chapters.

A Hilbert Space Geometric Representation of Shared Awareness and Joint Decision Making

ERIC Educational Resources Information Center

Canan, Mustafa

2017-01-01

Two people in the same situation may ascribe very different meanings to their experiences. They will form different awareness, reacting differently to shared information. Various factors can give rise to this behavior. These factors include, but are not limited to, prior knowledge, training, biases, cultural factors, social factors, team vs.…

Nonstandard Methods in Lie Theory

ERIC Educational Resources Information Center

Goldbring, Isaac Martin

2009-01-01

In this thesis, we apply model theory to Lie theory and geometric group theory. These applications of model theory come via nonstandard analysis. In Lie theory, we use nonstandard methods to prove two results. First, we give a positive solution to the local form of Hilbert's Fifth Problem, which asks whether every locally euclidean local…

Detecting communities using asymptotical surprise

NASA Astrophysics Data System (ADS)

Traag, V. A.; Aldecoa, R.; Delvenne, J.-C.

2015-08-01

Nodes in real-world networks are repeatedly observed to form dense clusters, often referred to as communities. Methods to detect these groups of nodes usually maximize an objective function, which implicitly contains the definition of a community. We here analyze a recently proposed measure called surprise, which assesses the quality of the partition of a network into communities. In its current form, the formulation of surprise is rather difficult to analyze. We here therefore develop an accurate asymptotic approximation. This allows for the development of an efficient algorithm for optimizing surprise. Incidentally, this leads to a straightforward extension of surprise to weighted graphs. Additionally, the approximation makes it possible to analyze surprise more closely and compare it to other methods, especially modularity. We show that surprise is (nearly) unaffected by the well-known resolution limit, a particular problem for modularity. However, surprise may tend to overestimate the number of communities, whereas they may be underestimated by modularity. In short, surprise works well in the limit of many small communities, whereas modularity works better in the limit of few large communities. In this sense, surprise is more discriminative than modularity and may find communities where modularity fails to discern any structure.

Theory of the Decoherence Effect in Finite and Infinite Open Quantum Systems Using the Algebraic Approach

NASA Astrophysics Data System (ADS)

Blanchard, Philippe; Hellmich, Mario; Ługiewicz, Piotr; Olkiewicz, Robert

Quantum mechanics is the greatest revision of our conception of the character of the physical world since Newton. Consequently, David Hilbert was very interested in quantum mechanics. He and John von Neumann discussed it frequently during von Neumann's residence in Göttingen. He published in 1932 his book Mathematical Foundations of Quantum Mechanics. In Hilbert's opinion it was the first exposition of quantum mechanics in a mathematically rigorous way. The pioneers of quantum mechanics, Heisenberg and Dirac, neither had use for rigorous mathematics nor much interest in it. Conceptually, quantum theory as developed by Bohr and Heisenberg is based on the positivism of Mach as it describes only observable quantities. It first emerged as a result of experimental data in the form of statistical observations of quantum noise, the basic concept of quantum probability.

Vocational Training in Europe: Towards a Modular Form? Discussion Paper. CEDEFOP Panorama. First Edition.

ERIC Educational Resources Information Center

Sellin, Burkart

Discussion of whether and to what extent initial vocational training and adult education in European Community (EC) member countries can assume a modular form hinges on the issue of the module as an organizational principle. In such a context, modules are viewed not as closed teaching and learning units but rather as integral parts of a more…

Maass Forms and Quantum Modular Forms

NASA Astrophysics Data System (ADS)

Rolen, Larry

This thesis describes several new results in the theory of harmonic Maass forms and related objects. Maass forms have recently led to a flood of applications throughout number theory and combinatorics in recent years, especially following their development by the work of Bruinier and Funke the modern understanding Ramanujan's mock theta functions due to Zwegers. The first of three main theorems discussed in this thesis concerns the integrality properties of singular moduli. These are well-known to be algebraic integers, and they play a beautiful role in complex multiplication and explicit class field theory for imaginary quadratic fields. One can also study "singular moduli" for special non-holomorphic functions, which are algebraic but are not necessarily algebraic integers. Here we will explain the phenomenon of integrality properties and provide a sharp bound on denominators of symmetric functions in singular moduli. The second main theme of the thesis concerns Zagier's recent definition of a quantum modular form. Since their definition in 2010 by Zagier, quantum modular forms have been connected to numerous different topics such as strongly unimodal sequences, ranks, cranks, and asymptotics for mock theta functions. Motivated by Zagier's example of the quantum modularity of Kontsevich's "strange" function F(q), we revisit work of Andrews, Jimenez-Urroz, and Ono to construct a natural vector-valued quantum modular form whose components. The final chapter of this thesis is devoted to a study of asymptotics of mock theta functions near roots of unity. In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function, and he offered some alleged examples. The theory of mock theta functions has been brought to fruition using the framework of harmonic Maass forms, thanks to Zwegers. Despite this understanding, little attention has been given to Ramanujan's original definition. Here we prove that Ramanujan's examples do indeed satisfy his original definition.

Modular assembly for supporting, straining, and directing flow to a core in a nuclear reactor

DOEpatents

Pennell, William E.

1977-01-01

A reactor core support arrangement for supporting, straining, and providing fluid flow to the core and periphery of a nuclear reactor during normal operation. A plurality of removable inlet modular units are contained within permanent liners in the lower supporting plate of the reactor vessel lower internals. During normal operation (1) each inlet modular unit directs main coolant flow to a plurality of core assemblies, the latter being removably supported in receptacles in the upper portion of the modular unit and (2) each inlet modular unit may direct bypass flow to a low pressure annular region of the reactor vessel. Each inlet modular unit may include special fluid seals interposed between mating surfaces of the inlet modular units and the core assemblies and between the inlet modular units and the liners, to minimize leakage and achieve an hydraulic balance. Utilizing the hydraulic balance, the modular units are held in the liners and the assemblies are held in the modular unit receptacles by their own respective weight. Included as part of the permanent liners below the horizontal support plate are generally hexagonal axial debris barriers. The axial debris barriers collectively form a bottom boundary of a secondary high pressure plenum, the upper boundary of which is the bottom surface of the horizontal support plate. Peripheral liners include radial debris barriers which collectively form a barrier against debris entry radially. During normal operation primary coolant inlet openings in the liner, below the axial debris barriers, pass a large amount of coolant into the inlet modular units, and secondary coolant inlet openings in the portion of the liners within the secondary plenum pass a small amount of coolant into the inlet modular units. The secondary coolant inlet openings also provide alternative coolant inlet flow paths in the unlikely event of blockage of the primary inlet openings. The primary inlet openings have characteristics which limit the entry of debris and minimize the potential for debris entering the primary inlets blocking the secondary inlets from inside the modular unit.

Redefining the modular organization of the core Mediator complex.

PubMed

Wang, Xuejuan; Sun, Qianqian; Ding, Zhenrui; Ji, Jinhua; Wang, Jianye; Kong, Xiao; Yang, Jianghong; Cai, Gang

2014-07-01

The Mediator complex plays an essential role in the regulation of eukaryotic transcription. The Saccharomyces cerevisiae core Mediator comprises 21 subunits, which are organized into Head, Middle and Tail modules. Previously, the Head module was assigned to a distinct dense domain at the base, and the Middle and Tail modules were identified to form a tight structure above the Head module, which apparently contradicted findings from many biochemical and functional studies. Here, we compared the structures of the core Mediator and its subcomplexes, especially the first 3D structure of the Head + Middle modules, which permitted an unambiguous assignment of the three modules. Furthermore, nanogold labeling pinpointing four Mediator subunits from different modules conclusively validated the modular assignment, in which the Head and Middle modules fold back on one another and form the upper portion of the core Mediator, while the Tail module forms a distinct dense domain at the base. The new modular model of the core Mediator has reconciled the previous inconsistencies between the structurally and functionally defined Mediator modules. Collectively, these analyses completely redefine the modular organization of the core Mediator, which allow us to integrate the structural and functional information into a coherent mechanism for the Mediator's modularity and regulation in transcription initiation.

Redefining the modular organization of the core Mediator complex

PubMed Central

Wang, Xuejuan; Sun, Qianqian; Ding, Zhenrui; Ji, Jinhua; Wang, Jianye; Kong, Xiao; Yang, Jianghong; Cai, Gang

2014-01-01

The Mediator complex plays an essential role in the regulation of eukaryotic transcription. The Saccharomyces cerevisiae core Mediator comprises 21 subunits, which are organized into Head, Middle and Tail modules. Previously, the Head module was assigned to a distinct dense domain at the base, and the Middle and Tail modules were identified to form a tight structure above the Head module, which apparently contradicted findings from many biochemical and functional studies. Here, we compared the structures of the core Mediator and its subcomplexes, especially the first 3D structure of the Head + Middle modules, which permitted an unambiguous assignment of the three modules. Furthermore, nanogold labeling pinpointing four Mediator subunits from different modules conclusively validated the modular assignment, in which the Head and Middle modules fold back on one another and form the upper portion of the core Mediator, while the Tail module forms a distinct dense domain at the base. The new modular model of the core Mediator has reconciled the previous inconsistencies between the structurally and functionally defined Mediator modules. Collectively, these analyses completely redefine the modular organization of the core Mediator, which allow us to integrate the structural and functional information into a coherent mechanism for the Mediator's modularity and regulation in transcription initiation. PMID:24810298

Cohomologie des Groupes Localement Compacts et Produits Tensoriels Continus de Representations

ERIC Educational Resources Information Center

Guichardet, A.

1976-01-01

Contains few and sometimes incomplete proofs on continuous tensor products of Hilbert spaces and of group representations, and on the irreducibility of the latter. Theory of continuous tensor products of Hilbert Spaces is closely related to that of conditionally positive definite functions; it relies on the technique of symmetric Hilbert spaces,…

Product modular design incorporating preventive maintenance issues

NASA Astrophysics Data System (ADS)

Gao, Yicong; Feng, Yixiong; Tan, Jianrong

2016-03-01

Traditional modular design methods lead to product maintenance problems, because the module form of a system is created according to either the function requirements or the manufacturing considerations. For solving these problems, a new modular design method is proposed with the considerations of not only the traditional function related attributes, but also the maintenance related ones. First, modularity parameters and modularity scenarios for product modularity are defined. Then the reliability and economic assessment models of product modularity strategies are formulated with the introduction of the effective working age of modules. A mathematical model used to evaluate the difference among the modules of the product so that the optimal module of the product can be established. After that, a multi-objective optimization problem based on metrics for preventive maintenance interval different degrees and preventive maintenance economics is formulated for modular optimization. Multi-objective GA is utilized to rapidly approximate the Pareto set of optimal modularity strategy trade-offs between preventive maintenance cost and preventive maintenance interval difference degree. Finally, a coordinate CNC boring machine is adopted to depict the process of product modularity. In addition, two factorial design experiments based on the modularity parameters are constructed and analyzed. These experiments investigate the impacts of these parameters on the optimal modularity strategies and the structure of module. The research proposes a new modular design method, which may help to improve the maintainability of product in modular design.

A Descriptive Outline of a Modular Schedule, Flexible Scheduling Using the Data Processing Method. A Report from Virgin Valley High School, Mesquite, Nevada.

ERIC Educational Resources Information Center

Allan, Blaine W., Comp.

The procedures, forms, and philosophy of the computerized modular scheduling program developed at Virgin Valley High School are outlined. The modular concept is eveloped as a new approach to course structure with explanations, examples, and worksheets included. Examples of courses of study, input information for the data processing center, output…

Modular properties of 6d (DELL) systems

NASA Astrophysics Data System (ADS)

Aminov, G.; Mironov, A.; Morozov, A.

2017-11-01

If super-Yang-Mills theory possesses the exact conformal invariance, there is an additional modular invariance under the change of the complex bare charge [InlineMediaObject not available: see fulltext.]. The low-energy Seiberg-Witten prepotential ℱ( a), however, is not explicitly invariant, because the flat moduli also change a - → a D = ∂ℱ/∂ a. In result, the prepotential is not a modular form and depends also on the anomalous Eisenstein series E 2. This dependence is usually described by the universal MNW modular anomaly equation. We demonstrate that, in the 6 d SU( N) theory with two independent modular parameters τ and \\widehat{τ} , the modular anomaly equation changes, because the modular transform of τ is accompanied by an ( N -dependent!) shift of \\widehat{τ} and vice versa. This is a new peculiarity of double-elliptic systems, which deserves further investigation.

Brain modularity controls the critical behavior of spontaneous activity.

PubMed

Russo, R; Herrmann, H J; de Arcangelis, L

2014-03-13

The human brain exhibits a complex structure made of scale-free highly connected modules loosely interconnected by weaker links to form a small-world network. These features appear in healthy patients whereas neurological diseases often modify this structure. An important open question concerns the role of brain modularity in sustaining the critical behaviour of spontaneous activity. Here we analyse the neuronal activity of a model, successful in reproducing on non-modular networks the scaling behaviour observed in experimental data, on a modular network implementing the main statistical features measured in human brain. We show that on a modular network, regardless the strength of the synaptic connections or the modular size and number, activity is never fully scale-free. Neuronal avalanches can invade different modules which results in an activity depression, hindering further avalanche propagation. Critical behaviour is solely recovered if inter-module connections are added, modifying the modular into a more random structure.

Symbols on Formal Groups

NASA Astrophysics Data System (ADS)

Vostokov, S. V.

1982-04-01

The theory of a continuous Steinberg symbol in a local field is generalized to formal commutative groups. For Lubin-Tate groups, a universal symbol is constructed in explicit form, and it is shown that the module of values of an arbitrary symbol imbeds into the group of points of the formal group. By means of this theory of symbols a new approach is given to obtaining an explicit form for the Hilbert norm residue symbol on Lubin-Tate formal groups. Bibliography: 10 titles.

A Formal Theory for Modular ERDF Ontologies

NASA Astrophysics Data System (ADS)

Analyti, Anastasia; Antoniou, Grigoris; Damásio, Carlos Viegas

The success of the Semantic Web is impossible without any form of modularity, encapsulation, and access control. In an earlier paper, we extended RDF graphs with weak and strong negation, as well as derivation rules. The ERDF #n-stable model semantics of the extended RDF framework (ERDF) is defined, extending RDF(S) semantics. In this paper, we propose a framework for modular ERDF ontologies, called modular ERDF framework, which enables collaborative reasoning over a set of ERDF ontologies, while support for hidden knowledge is also provided. In particular, the modular ERDF stable model semantics of modular ERDF ontologies is defined, extending the ERDF #n-stable model semantics. Our proposed framework supports local semantics and different points of view, local closed-world and open-world assumptions, and scoped negation-as-failure. Several complexity results are provided.

Modular multiplication in GF(p) for public-key cryptography

NASA Astrophysics Data System (ADS)

Olszyna, Jakub

Modular multiplication forms the basis of modular exponentiation which is the core operation of the RSA cryptosystem. It is also present in many other cryptographic algorithms including those based on ECC and HECC. Hence, an efficient implementation of PKC relies on efficient implementation of modular multiplication. The paper presents a survey of most common algorithms for modular multiplication along with hardware architectures especially suitable for cryptographic applications in energy constrained environments. The motivation for studying low-power and areaefficient modular multiplication algorithms comes from enabling public-key security for ultra-low power devices that can perform under constrained environments like wireless sensor networks. Serial architectures for GF(p) are analyzed and presented. Finally proposed architectures are verified and compared according to the amount of power dissipated throughout the operation.

Hilbert's 'Foundations of Physics': Gravitation and electromagnetism within the axiomatic method

NASA Astrophysics Data System (ADS)

Brading, K. A.; Ryckman, T. A.

2008-01-01

In November and December 1915, Hilbert presented two communications to the Göttingen Academy of Sciences under the common title 'The Foundations of Physics'. Versions of each eventually appeared in the Nachrichten of the Academy. Hilbert's first communication has received significant reconsideration in recent years, following the discovery of printer's proofs of this paper, dated 6 December 1915. The focus has been primarily on the 'priority dispute' over the Einstein field equations. Our contention, in contrast, is that the discovery of the December proofs makes it possible to see the thematic linkage between the material that Hilbert cut from the published version of the first communication and the content of the second, as published in 1917. The latter has been largely either disregarded or misinterpreted, and our aim is to show that (a) Hilbert's two communications should be regarded as part of a wider research program within the overarching framework of 'the axiomatic method' (as Hilbert expressly stated was the case), and (b) the second communication is a fine and coherent piece of work within this framework, whose principal aim is to address an apparent tension between general invariance and causality (in the precise sense of Cauchy determination), pinpointed in Theorem I of the first communication. This is not the same problem as that found in Einstein's 'hole argument'-something that, we argue, never confused Hilbert.

Facile "modular assembly" for fast construction of a highly oriented crystalline MOF nanofilm.

PubMed

Xu, Gang; Yamada, Teppei; Otsubo, Kazuya; Sakaida, Shun; Kitagawa, Hiroshi

2012-10-10

The preparation of crystalline, ordered thin films of metal-organic frameworks (MOFs) will be a critical process for MOF-based nanodevices in the future. MOF thin films with perfect orientation and excellent crystallinity were formed with novel nanosheet-structured components, Cu-TCPP [TCPP = 5,10,15,20-tetrakis(4-carboxyphenyl)porphyrin], by a new "modular assembly" strategy. The modular assembly process involves two steps: a "modularization" step is used to synthesize highly crystalline "modules" with a nanosized structure that can be conveniently assembled into a thin film in the following "assembly" step. With this method, MOF thin films can easily be set up on different substrates at very high speed with controllable thickness. This new approach also enabled us to prepare highly oriented crystalline thin films of MOFs that cannot be prepared in thin-film form by traditional techniques.

The eigenstate thermalization hypothesis in constrained Hilbert spaces: A case study in non-Abelian anyon chains

NASA Astrophysics Data System (ADS)

Chandran, A.; Schulz, Marc D.; Burnell, F. J.

2016-12-01

Many phases of matter, including superconductors, fractional quantum Hall fluids, and spin liquids, are described by gauge theories with constrained Hilbert spaces. However, thermalization and the applicability of quantum statistical mechanics has primarily been studied in unconstrained Hilbert spaces. In this paper, we investigate whether constrained Hilbert spaces permit local thermalization. Specifically, we explore whether the eigenstate thermalization hypothesis (ETH) holds in a pinned Fibonacci anyon chain, which serves as a representative case study. We first establish that the constrained Hilbert space admits a notion of locality by showing that the influence of a measurement decays exponentially in space. This suggests that the constraints are no impediment to thermalization. We then provide numerical evidence that ETH holds for the diagonal and off-diagonal matrix elements of various local observables in a generic disorder-free nonintegrable model. We also find that certain nonlocal observables obey ETH.

A No-Go Theorem for the Continuum Limit of a Periodic Quantum Spin Chain

NASA Astrophysics Data System (ADS)

Jones, Vaughan F. R.

2018-01-01

We show that the Hilbert space formed from a block spin renormalization construction of a cyclic quantum spin chain (based on the Temperley-Lieb algebra) does not support a chiral conformal field theory whose Hamiltonian generates translation on the circle as a continuous limit of the rotations on the lattice.

Acoustical Applications of the HHT Method

NASA Technical Reports Server (NTRS)

Huang, Norden E.

2003-01-01

A document discusses applications of a method based on the Huang-Hilbert transform (HHT). The method was described, without the HHT name, in Analyzing Time Series Using EMD and Hilbert Spectra (GSC-13817), NASA Tech Briefs, Vol. 24, No. 10 (October 2000), page 63. To recapitulate: The method is especially suitable for analyzing time-series data that represent nonstationary and nonlinear physical phenomena. The method involves the empirical mode decomposition (EMD), in which a complicated signal is decomposed into a finite number of functions, called intrinsic mode functions (IMFs), that admit well-behaved Hilbert transforms. The HHT consists of the combination of EMD and Hilbert spectral analysis.

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.

Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Wu, Jianping; Geng, Xianguo

2017-12-01

The inverse scattering transform of the coupled modified Korteweg-de Vries equation is studied by the Riemann-Hilbert approach. In the direct scattering process, the spectral analysis of the Lax pair is performed, from which a Riemann-Hilbert problem is established for the equation. In the inverse scattering process, by solving Riemann-Hilbert problems corresponding to the reflectionless cases, three types of multi-soliton solutions are obtained. The multi-soliton classification is based on the zero structures of the Riemann-Hilbert problem. In addition, some figures are given to illustrate the soliton characteristics of the coupled modified Korteweg-de Vries equation.

Application of the Hilbert-Huang Transform to Financial Data

NASA Technical Reports Server (NTRS)

Huang, Norden

2005-01-01

A paper discusses the application of the Hilbert-Huang transform (HHT) method to time-series financial-market data. The method was described, variously without and with the HHT name, in several prior NASA Tech Briefs articles and supporting documents. To recapitulate: The method is especially suitable for analyzing time-series data that represent nonstationary and nonlinear phenomena including physical phenomena and, in the present case, financial-market processes. The method involves the empirical mode decomposition (EMD), in which a complicated signal is decomposed into a finite number of functions, called "intrinsic mode functions" (IMFs), that admit well-behaved Hilbert transforms. The HHT consists of the combination of EMD and Hilbert spectral analysis. The local energies and the instantaneous frequencies derived from the IMFs through Hilbert transforms can be used to construct an energy-frequency-time distribution, denoted a Hilbert spectrum. The instant paper begins with a discussion of prior approaches to quantification of market volatility, summarizes the HHT method, then describes the application of the method in performing time-frequency analysis of mortgage-market data from the years 1972 through 2000. Filtering by use of the EMD is shown to be useful for quantifying market volatility.

Clifford coherent state transforms on spheres

NASA Astrophysics Data System (ADS)

Dang, Pei; Mourão, José; Nunes, João P.; Qian, Tao

2018-01-01

We introduce a one-parameter family of transforms, U(m)t , t > 0, from the Hilbert space of Clifford algebra valued square integrable functions on the m-dimensional sphere, L2(Sm , dσm) ⊗Cm+1, to the Hilbert spaces, ML2(R m + 1 ∖ { 0 } , dμt) , of solutions of the Euclidean Dirac equation on R m + 1 ∖ { 0 } which are square integrable with respect to appropriate measures, dμt. We prove that these transforms are unitary isomorphisms of the Hilbert spaces and are extensions of the Segal-Bargman coherent state transform, U(1) :L2(S1 , dσ1) ⟶ HL2(C ∖ { 0 } , dμ) , to higher dimensional spheres in the context of Clifford analysis. In Clifford analysis it is natural to replace the analytic continuation from Sm to SCm as in (Hall, 1994; Stenzel, 1999; Hall and Mitchell, 2002) by the Cauchy-Kowalewski extension from Sm to R m + 1 ∖ { 0 } . One then obtains a unitary isomorphism from an L2-Hilbert space to a Hilbert space of solutions of the Dirac equation, that is to a Hilbert space of monogenic functions.

Brain Network Modularity Predicts Exercise-Related Executive Function Gains in Older Adults

PubMed Central

Baniqued, Pauline L.; Gallen, Courtney L.; Voss, Michelle W.; Burzynska, Agnieszka Z.; Wong, Chelsea N.; Cooke, Gillian E.; Duffy, Kristin; Fanning, Jason; Ehlers, Diane K.; Salerno, Elizabeth A.; Aguiñaga, Susan; McAuley, Edward; Kramer, Arthur F.; D'Esposito, Mark

2018-01-01

Recent work suggests that the brain can be conceptualized as a network comprised of groups of sub-networks or modules. The extent of segregation between modules can be quantified with a modularity metric, where networks with high modularity have dense connections within modules and sparser connections between modules. Previous work has shown that higher modularity predicts greater improvements after cognitive training in patients with traumatic brain injury and in healthy older and young adults. It is not known, however, whether modularity can also predict cognitive gains after a physical exercise intervention. Here, we quantified modularity in older adults (N = 128, mean age = 64.74) who underwent one of the following interventions for 6 months (NCT01472744 on ClinicalTrials.gov): (1) aerobic exercise in the form of brisk walking (Walk), (2) aerobic exercise in the form of brisk walking plus nutritional supplement (Walk+), (3) stretching, strengthening and stability (SSS), or (4) dance instruction. After the intervention, the Walk, Walk+ and SSS groups showed gains in cardiorespiratory fitness (CRF), with larger effects in both walking groups compared to the SSS and Dance groups. The Walk, Walk+ and SSS groups also improved in executive function (EF) as measured by reasoning, working memory, and task-switching tests. In the Walk, Walk+, and SSS groups that improved in EF, higher baseline modularity was positively related to EF gains, even after controlling for age, in-scanner motion and baseline EF. No relationship between modularity and EF gains was observed in the Dance group, which did not show training-related gains in CRF or EF control. These results are consistent with previous studies demonstrating that individuals with a more modular brain network organization are more responsive to cognitive training. These findings suggest that the predictive power of modularity may be generalizable across interventions aimed to enhance aspects of cognition and that, especially in low-performing individuals, global network properties can capture individual differences in neuroplasticity. PMID:29354050

Hybrid Techniques for Quantum Circuit Simulation

DTIC Science & Technology

2014-02-01

Detailed theorems and proofs describing these results are included in our published manuscript [10]. Embedding of stabilizer geometry in the Hilbert ...space. We also describe how the discrete embedding of stabilizer geometry in Hilbert space complicates several natural geometric tasks. As described...the Hilbert space in which they are embedded, and that they are arranged in a fairly uniform pattern. These factors suggest that, if one seeks a

Testing the Dimension of Hilbert Spaces

NASA Astrophysics Data System (ADS)

Brunner, Nicolas; Pironio, Stefano; Acin, Antonio; Gisin, Nicolas; Méthot, André Allan; Scarani, Valerio

2008-05-01

Given a set of correlations originating from measurements on a quantum state of unknown Hilbert space dimension, what is the minimal dimension d necessary to describe such correlations? We introduce the concept of dimension witness to put lower bounds on d. This work represents a first step in a broader research program aiming to characterize Hilbert space dimension in various contexts related to fundamental questions and quantum information applications.

H-SLAM: Rao-Blackwellized Particle Filter SLAM Using Hilbert Maps.

PubMed

Vallicrosa, Guillem; Ridao, Pere

2018-05-01

Occupancy Grid maps provide a probabilistic representation of space which is important for a variety of robotic applications like path planning and autonomous manipulation. In this paper, a SLAM (Simultaneous Localization and Mapping) framework capable of obtaining this representation online is presented. The H-SLAM (Hilbert Maps SLAM) is based on Hilbert Map representation and uses a Particle Filter to represent the robot state. Hilbert Maps offer a continuous probabilistic representation with a small memory footprint. We present a series of experimental results carried both in simulation and with real AUVs (Autonomous Underwater Vehicles). These results demonstrate that our approach is able to represent the environment more consistently while capable of running online.

Terahertz bandwidth photonic Hilbert transformers based on synthesized planar Bragg grating fabrication.

PubMed

Sima, Chaotan; Gates, J C; Holmes, C; Mennea, P L; Zervas, M N; Smith, P G R

2013-09-01

Terahertz bandwidth photonic Hilbert transformers are proposed and experimentally demonstrated. The integrated device is fabricated via a direct UV grating writing technique in a silica-on-silicon platform. The photonic Hilbert transformer operates at bandwidths of up to 2 THz (~16 nm) in the telecom band, a 10-fold greater bandwidth than any previously reported experimental approaches. Achieving this performance requires detailed knowledge of the system transfer function of the direct UV grating writing technique; this allows improved linearity and yields terahertz bandwidth Bragg gratings with improved spectral quality. By incorporating a flat-top reflector and Hilbert grating with a waveguide coupler, an ultrawideband all-optical single-sideband filter is demonstrated.

On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An abstract approximation framework for the solution of operator algebraic Riccati equations is developed. The approach taken is based on a formulation of the Riccati equation as an abstract nonlinear operator equation on the space of Hilbert-Schmidt operators. Hilbert-Schmidt norm convergence of solutions to generic finite dimensional Galerkin approximations to the Riccati equation to the solution of the original infinite dimensional problem is argued. The application of the general theory is illustrated via an operator Riccati equation arising in the linear-quadratic design of an optimal feedback control law for a 1-D heat/diffusion equation. Numerical results demonstrating the convergence of the associated Hilbert-Schmidt kernels are included.

Axial 3D region of interest reconstruction using weighted cone beam BPF/DBPF algorithm cascaded with adequately oriented orthogonal butterfly filtering

NASA Astrophysics Data System (ADS)

Tang, Shaojie; Tang, Xiangyang

2016-03-01

Axial cone beam (CB) computed tomography (CT) reconstruction is still the most desirable in clinical applications. As the potential candidates with analytic form for the task, the back projection-filtration (BPF) and the derivative backprojection filtered (DBPF) algorithms, in which Hilbert filtering is the common algorithmic feature, are originally derived for exact helical and axial reconstruction from CB and fan beam projection data, respectively. These two algorithms have been heuristically extended for axial CB reconstruction via adoption of virtual PI-line segments. Unfortunately, however, streak artifacts are induced along the Hilbert filtering direction, since these algorithms are no longer accurate on the virtual PI-line segments. We have proposed to cascade the extended BPF/DBPF algorithm with orthogonal butterfly filtering for image reconstruction (namely axial CB-BPP/DBPF cascaded with orthogonal butterfly filtering), in which the orientation-specific artifacts caused by post-BP Hilbert transform can be eliminated, at a possible expense of losing the BPF/DBPF's capability of dealing with projection data truncation. Our preliminary results have shown that this is not the case in practice. Hence, in this work, we carry out an algorithmic analysis and experimental study to investigate the performance of the axial CB-BPP/DBPF cascaded with adequately oriented orthogonal butterfly filtering for three-dimensional (3D) reconstruction in region of interest (ROI).

Possible treatment of the ghost states in the Lee-Wick standard model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shalaby, Abouzeid M.; Physics Department, Faculty of Science, Qassim University

2009-07-15

In this work, we employ the techniques used to cure the indefinite norm problem in pseudo-Hermitian Hamiltonians to show that the ghost states in a higher derivative scalar field theory are not real ghosts. For the model under investigation, an imaginary auxiliary field is introduced to have an equivalent non-Hermitian two-field scalar theory. We were able to calculate exactly the positive definite metric operator {eta} for the quantum mechanical as well as the quantum field versions of the theory. While the equivalent Hamiltonian is non-Hermitian in a Hilbert space characterized by the Dirac sense inner product, it is, however, amore » Hermitian in a Hilbert space endowed with the inner product . The main feature of the latter Hilbert space is that the propagator has the correct sign (no Lee-Wick fields). Moreover, the calculated metric operator diagonalizes the Hamiltonian in the two fields (no mixing). We found that the Hermiticity of the calculated metric operator to lead to the constrain M>2m for the two Higgs masses, in agreement with other calculations in the literature. Besides, our mass formulas coincide with those obtained in other works (obtained by a very different regime but with the existence of ghost states), which means that our positive normed Hamiltonian form preserves the mass spectra.« less

Dissipation and entropy production in open quantum systems

NASA Astrophysics Data System (ADS)

Majima, H.; Suzuki, A.

2010-11-01

A microscopic description of an open system is generally expressed by the Hamiltonian of the form: Htot = Hsys + Henviron + Hsys-environ. We developed a microscopic theory of entropy and derived a general formula, so-called "entropy-Hamiltonian relation" (EHR), that connects the entropy of the system to the interaction Hamiltonian represented by Hsys-environ for a nonequilibrium open quantum system. To derive the EHR formula, we mapped the open quantum system to the representation space of the Liouville-space formulation or thermo field dynamics (TFD), and thus worked on the representation space Script L := Script H otimes , where Script H denotes the ordinary Hilbert space while the tilde Hilbert space conjugates to Script H. We show that the natural transformation (mapping) of nonequilibrium open quantum systems is accomplished within the theoretical structure of TFD. By using the obtained EHR formula, we also derived the equation of motion for the distribution function of the system. We demonstrated that by knowing the microscopic description of the interaction, namely, the specific form of Hsys-environ on the representation space Script L, the EHR formulas enable us to evaluate the entropy of the system and to gain some information about entropy for nonequilibrium open quantum systems.

Hilbert's axiomatic method and Carnap's general axiomatics.

PubMed

Stöltzner, Michael

2015-10-01

This paper compares the axiomatic method of David Hilbert and his school with Rudolf Carnap's general axiomatics that was developed in the late 1920s, and that influenced his understanding of logic of science throughout the 1930s, when his logical pluralism developed. The distinct perspectives become visible most clearly in how Richard Baldus, along the lines of Hilbert, and Carnap and Friedrich Bachmann analyzed the axiom system of Hilbert's Foundations of Geometry—the paradigmatic example for the axiomatization of science. Whereas Hilbert's axiomatic method started from a local analysis of individual axiom systems in which the foundations of mathematics as a whole entered only when establishing the system's consistency, Carnap and his Vienna Circle colleague Hans Hahn instead advocated a global analysis of axiom systems in general. A primary goal was to evade, or formalize ex post, mathematicians' 'material' talk about axiom systems for such talk was held to be error-prone and susceptible to metaphysics. Copyright © 2015 Elsevier Ltd. All rights reserved.

The place of probability in Hilbert's axiomatization of physics, ca. 1900-1928

NASA Astrophysics Data System (ADS)

Verburgt, Lukas M.

2016-02-01

Although it has become a common place to refer to the 'sixth problem' of Hilbert's (1900) Paris lecture as the starting point for modern axiomatized probability theory, his own views on probability have received comparatively little explicit attention. The central aim of this paper is to provide a detailed account of this topic in light of the central observation that the development of Hilbert's project of the axiomatization of physics went hand-in-hand with a redefinition of the status of probability theory and the meaning of probability. Where Hilbert first regarded the theory as a mathematizable physical discipline and later approached it as a 'vague' mathematical application in physics, he eventually understood probability, first, as a feature of human thought and, then, as an implicitly defined concept without a fixed physical interpretation. It thus becomes possible to suggest that Hilbert came to question, from the early 1920s on, the very possibility of achieving the goal of the axiomatization of probability as described in the 'sixth problem' of 1900.

A combined approach for weak fault signature extraction of rolling element bearing using Hilbert envelop and zero frequency resonator

NASA Astrophysics Data System (ADS)

Kumar, Keshav; Shukla, Sumitra; Singh, Sachin Kumar

2018-04-01

Periodic impulses arise due to localised defects in rolling element bearing. At the early stage of defects, the weak impulses are immersed in strong machinery vibration. This paper proposes a combined approach based upon Hilbert envelop and zero frequency resonator for the detection of the weak periodic impulses. In the first step, the strength of impulses is increased by taking normalised Hilbert envelop of the signal. It also helps in better localization of these impulses on time axis. In the second step, Hilbert envelope of the signal is passed through the zero frequency resonator for the exact localization of the periodic impulses. Spectrum of the resonator output gives peak at the fault frequency. Simulated noisy signal with periodic impulses is used to explain the working of the algorithm. The proposed technique is verified with experimental data also. A comparison of the proposed method with Hilbert-Haung transform (HHT) based method is presented to establish the effectiveness of the proposed method.

Minimal Cohomological Model of a Scalar Field on a Riemannian Manifold

NASA Astrophysics Data System (ADS)

Arkhipov, V. V.

2018-04-01

Lagrangians of the field-theory model of a scalar field are considered as 4-forms on a Riemannian manifold. The model is constructed on the basis of the Hodge inner product, this latter being an analog of the scalar product of two functions. Including the basis fields in the action of the terms with tetrads makes it possible to reproduce the Klein-Gordon equation and the Maxwell equations, and also the Einstein-Hilbert action. We conjecture that the principle of construction of the Lagrangians as 4-forms can give a criterion restricting possible forms of the field-theory models.

Some Remarks on Space-Time Decompositions, and Degenerate Metrics, in General Relativity

NASA Astrophysics Data System (ADS)

Bengtsson, Ingemar

Space-time decomposition of the Hilbert-Palatini action, written in a form which admits degenerate metrics, is considered. Simple numerology shows why D = 3 and 4 are singled out as admitting a simple phase space. The canonical structure of the degenerate sector turns out to be awkward. However, the real degenerate metrics obtained as solutions are the same as those that occur in Ashtekar's formulation of complex general relativity. An exact solution of Ashtekar's equations, with degenerate metric, shows that the manifestly four-dimensional form of the action, and its 3 + 1 form, are not quite equivalent.

Vulnerability detection using data-flow graphs and SMT solvers

DTIC Science & Technology

2016-10-31

concerns. The framework is modular and pipelined to allow scalable analysis on distributed systems. Our vulnerability detection framework employs machine...Design We designed the framework to be modular to enable flexible reuse and extendibility. In its current form, our framework performs the following

Modular Hamiltonians on the null plane and the Markov property of the vacuum state

NASA Astrophysics Data System (ADS)

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo

2017-09-01

We compute the modular Hamiltonians of regions having the future horizon lying on a null plane. For a CFT this is equivalent to regions with a boundary of arbitrary shape lying on the null cone. These Hamiltonians have a local expression on the horizon formed by integrals of the stress tensor. We prove this result in two different ways, and show that the modular Hamiltonians of these regions form an infinite dimensional Lie algebra. The corresponding group of unitary transformations moves the fields on the null surface locally along the null generators with arbitrary null line dependent velocities, but act non-locally outside the null plane. We regain this result in greater generality using more abstract tools on the algebraic quantum field theory. Finally, we show that modular Hamiltonians on the null surface satisfy a Markov property that leads to the saturation of the strong sub-additive inequality for the entropies and to the strong super-additivity of the relative entropy.

Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vourdas, A.

2014-08-15

The orthocomplemented modular lattice of subspaces L[H(d)], of a quantum system with d-dimensional Hilbert space H(d), is considered. A generalized additivity relation which holds for Kolmogorov probabilities is violated by quantum probabilities in the full lattice L[H(d)] (it is only valid within the Boolean subalgebras of L[H(d)]). This suggests the use of more general (than Kolmogorov) probability theories, and here the Dempster-Shafer probability theory is adopted. An operator D(H{sub 1},H{sub 2}), which quantifies deviations from Kolmogorov probability theory is introduced, and it is shown to be intimately related to the commutator of the projectors P(H{sub 1}),P(H{sub 2}), to the subspacesmore » H{sub 1}, H{sub 2}. As an application, it is shown that the proof of the inequalities of Clauser, Horne, Shimony, and Holt for a system of two spin 1/2 particles is valid for Kolmogorov probabilities, but it is not valid for Dempster-Shafer probabilities. The violation of these inequalities in experiments supports the interpretation of quantum probabilities as Dempster-Shafer probabilities.« less

Scalar curvature in conformal geometry of Connes-Landi noncommutative manifolds

NASA Astrophysics Data System (ADS)

Liu, Yang

2017-11-01

We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on noncommutative two tori, the quantum part of the curvature consists of actions of the modular derivation through two local curvature functions. Explicit expressions for those functions are obtained for all even dimensions (greater than two). In dimension four, the one variable function shows striking similarity to the analytic functions of the characteristic classes appeared in the Atiyah-Singer local index formula, namely, it is roughly a product of the j-function (which defines the A ˆ -class of a manifold) and an exponential function (which defines the Chern character of a bundle). By performing two different computations for the variation of the Einstein-Hilbert action, we obtain deep internal relations between two local curvature functions. Straightforward verification for those relations gives a strong conceptual confirmation for the whole computational machinery we have developed so far, especially the Mathematica code hidden behind the paper.

Elliptic complexes over C∗-algebras of compact operators

NASA Astrophysics Data System (ADS)

Krýsl, Svatopluk

2016-03-01

For a C∗-algebra A of compact operators and a compact manifold M, we prove that the Hodge theory holds for A-elliptic complexes of pseudodifferential operators acting on smooth sections of finitely generated projective A-Hilbert bundles over M. For these C∗-algebras and manifolds, we get a topological isomorphism between the cohomology groups of an A-elliptic complex and the space of harmonic elements of the complex. Consequently, the cohomology groups appear to be finitely generated projective C∗-Hilbert modules and especially, Banach spaces. We also prove that in the category of Hilbert A-modules and continuous adjointable Hilbert A-module homomorphisms, the property of a complex of being self-adjoint parametrix possessing characterizes the complexes of Hodge type.

On the Hilbert-Huang Transform Theoretical Developments

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Blank, Karin; Flatley, Thomas; Huang, Norden E.; Patrick, David; Hestnes, Phyllis

2005-01-01

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as linearity, of being stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposition data, the HHT allows spectrum analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a near orthogonal adaptive basis, a basis that is derived from the data. The IMFs can be further analyzed for spectrum interpretation by the classical Hilbert Transform. A new engineering spectrum analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications post additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs near orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the developments of new HHT processing options, such as real-time and 2-D processing using Field Programmable Array (FPGA) computational resources, enhanced HHT synthesis, and broaden the scope of HHT applications for signal processing.

On Certain Theoretical Developments Underlying the Hilbert-Huang Transform

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Blank, Karin; Flatley, Thomas; Huang, Norden E.; Petrick, David; Hestness, Phyllis

2006-01-01

One of the main traditional tools used in scientific and engineering data spectral analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as being linear and stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectral analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposed data, the HHT allows spectral analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real-value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a nearly orthogonal derived from the data (adaptive) basis. The IMFs can be further analyzed for spectrum content by using the classical Hilbert Transform. A new engineering spectral analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications pose additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs nearly orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the development of new HHT processing options, such as real-time and 2-D processing using Field Programmable Gate Array (FPGA) computational resources,

FAST TRACK COMMUNICATION: General approach to \\mathfrak {SU}(n) quasi-distribution functions

NASA Astrophysics Data System (ADS)

Klimov, Andrei B.; de Guise, Hubert

2010-10-01

We propose an operational form for the kernel of a mapping between an operator acting in a Hilbert space of a quantum system with an \\mathfrak {SU}(n) symmetry group and its symbol in the corresponding classical phase space. For symmetric irreps of \\mathfrak {SU}(n) , this mapping is bijective. We briefly discuss complications that will occur in the general case.

Quantum decimation in Hilbert space: Coarse graining without structure

NASA Astrophysics Data System (ADS)

Singh, Ashmeet; Carroll, Sean M.

2018-03-01

We present a technique to coarse grain quantum states in a finite-dimensional Hilbert space. Our method is distinguished from other approaches by not relying on structures such as a preferred factorization of Hilbert space or a preferred set of operators (local or otherwise) in an associated algebra. Rather, we use the data corresponding to a given set of states, either specified independently or constructed from a single state evolving in time. Our technique is based on principle component analysis (PCA), and the resulting coarse-grained quantum states live in a lower-dimensional Hilbert space whose basis is defined using the underlying (isometric embedding) transformation of the set of fine-grained states we wish to coarse grain. Physically, the transformation can be interpreted to be an "entanglement coarse-graining" scheme that retains most of the global, useful entanglement structure of each state, while needing fewer degrees of freedom for its reconstruction. This scheme could be useful for efficiently describing collections of states whose number is much smaller than the dimension of Hilbert space, or a single state evolving over time.

Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics.

PubMed

Corry, Leo

2018-04-28

The sixth of Hilbert's famous 1900 list of 23 problems was a programmatic call for the axiomatization of the physical sciences. It was naturally and organically rooted at the core of Hilbert's conception of what axiomatization is all about. In fact, the axiomatic method which he applied at the turn of the twentieth century in his famous work on the foundations of geometry originated in a preoccupation with foundational questions related with empirical science in general. Indeed, far from a purely formal conception, Hilbert counted geometry among the sciences with strong empirical content, closely related to other branches of physics and deserving a treatment similar to that reserved for the latter. In this treatment, the axiomatization project was meant to play, in his view, a crucial role. Curiously, and contrary to a once-prevalent view, from all the problems in the list, the sixth is the only one that continually engaged Hilbet's efforts over a very long period of time, at least between 1894 and 1932.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics

NASA Astrophysics Data System (ADS)

Corry, Leo

2018-04-01

The sixth of Hilbert's famous 1900 list of 23 problems was a programmatic call for the axiomatization of the physical sciences. It was naturally and organically rooted at the core of Hilbert's conception of what axiomatization is all about. In fact, the axiomatic method which he applied at the turn of the twentieth century in his famous work on the foundations of geometry originated in a preoccupation with foundational questions related with empirical science in general. Indeed, far from a purely formal conception, Hilbert counted geometry among the sciences with strong empirical content, closely related to other branches of physics and deserving a treatment similar to that reserved for the latter. In this treatment, the axiomatization project was meant to play, in his view, a crucial role. Curiously, and contrary to a once-prevalent view, from all the problems in the list, the sixth is the only one that continually engaged Hilbet's efforts over a very long period of time, at least between 1894 and 1932. This article is part of the theme issue `Hilbert's sixth problem'.

Lattices, vertex algebras, and modular categories

NASA Astrophysics Data System (ADS)

van Ekeren, Jethro

2018-03-01

In this note we give an account of recent progress on the construction of holomorphic vertex algebras as cyclic orbifolds as well as related topics in lattices and modular categories. We present a novel computation of the Schur indicator of a lattice involution orbifold using finite Heisenberg groups and discriminant forms.

Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bagarello, F., E-mail: fabio.bagarello@unipa.it

In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite dimensional Hilbert spaces. This is useful, but quite restrictive since many physically relevant quantum systems live in infinite dimensional Hilbert spaces. In this paper we consider this situation, and we discuss some applications to well known models, introduced in the literature in recent years: the extended harmonic oscillator, the Swanson model and a generalized version of the Landau levels Hamiltonian. Not surprisingly we willmore » find new interesting features not previously found in finite dimensional Hilbert spaces, useful for a deeper comprehension of this kind of physical systems.« less

Singular value decomposition for the truncated Hilbert transform

NASA Astrophysics Data System (ADS)

Katsevich, A.

2010-11-01

Starting from a breakthrough result by Gelfand and Graev, inversion of the Hilbert transform became a very important tool for image reconstruction in tomography. In particular, their result is useful when the tomographic data are truncated and one deals with an interior problem. As was established recently, the interior problem admits a stable and unique solution when some a priori information about the object being scanned is available. The most common approach to solving the interior problem is based on converting it to the Hilbert transform and performing analytic continuation. Depending on what type of tomographic data are available, one gets different Hilbert inversion problems. In this paper, we consider two such problems and establish singular value decomposition for the operators involved. We also propose algorithms for performing analytic continuation.

An Efficient Multiparty Quantum Secret Sharing Protocol Based on Bell States in the High Dimension Hilbert Space

NASA Astrophysics Data System (ADS)

Gao, Gan; Wang, Li-Ping

2010-11-01

We propose a quantum secret sharing protocol, in which Bell states in the high dimension Hilbert space are employed. The biggest advantage of our protocol is the high source capacity. Compared with the previous secret sharing protocol, ours has the higher controlling efficiency. In addition, as decoy states in the high dimension Hilbert space are used, we needn’t destroy quantum entanglement for achieving the goal to check the channel security.

Experimentally feasible quantum-key-distribution scheme using qubit-like qudits and its comparison with existing qubit- and qudit-based protocols

NASA Astrophysics Data System (ADS)

Chau, H. F.; Wang, Qinan; Wong, Cardythy

2017-02-01

Recently, Chau [Phys. Rev. A 92, 062324 (2015), 10.1103/PhysRevA.92.062324] introduced an experimentally feasible qudit-based quantum-key-distribution (QKD) scheme. In that scheme, one bit of information is phase encoded in the prepared state in a 2n-dimensional Hilbert space in the form (|i > ±|j >) /√{2 } with n ≥2 . For each qudit prepared and measured in the same two-dimensional Hilbert subspace, one bit of raw secret key is obtained in the absence of transmission error. Here we show that by modifying the basis announcement procedure, the same experimental setup can generate n bits of raw key for each qudit prepared and measured in the same basis in the noiseless situation. The reason is that in addition to the phase information, each qudit also carries information on the Hilbert subspace used. The additional (n -1 ) bits of raw key comes from a clever utilization of this extra piece of information. We prove the unconditional security of this modified protocol and compare its performance with other existing provably secure qubit- and qudit-based protocols on market in the one-way classical communication setting. Interestingly, we find that for the case of n =2 , the secret key rate of this modified protocol using nondegenerate random quantum code to perform one-way entanglement distillation is equal to that of the six-state scheme.

On a canonical quantization of 3D Anti de Sitter pure gravity

NASA Astrophysics Data System (ADS)

Kim, Jihun; Porrati, Massimo

2015-10-01

We perform a canonical quantization of pure gravity on AdS 3 using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL(2,{R})× SL(2,{R}) . We first quantize the theory canonically on an asymptotically AdS space -which is topologically the real line times a Riemann surface with one connected boundary. Using the "constrain first" approach we reduce canonical quantization to quantization of orbits of the Virasoro group and Kähler quantization of Teichmüller space. After explicitly computing the Kähler form for the torus with one boundary component and after extending that result to higher genus, we recover known results, such as that wave functions of SL(2,{R}) Chern-Simons theory are conformal blocks. We find new restrictions on the Hilbert space of pure gravity by imposing invariance under large diffeomorphisms and normalizability of the wave function. The Hilbert space of pure gravity is shown to be the target space of Conformal Field Theories with continuous spectrum and a lower bound on operator dimensions. A projection defined by topology changing amplitudes in Euclidean gravity is proposed. It defines an invariant subspace that allows for a dual interpretation in terms of a Liouville CFT. Problems and features of the CFT dual are assessed and a new definition of the Hilbert space, exempt from those problems, is proposed in the case of highly-curved AdS 3.

Relative importance of modularity and other morphological attributes on different types of lithic point weapons: assessing functional variations.

PubMed

González-José, Rolando; Charlin, Judith

2012-01-01

The specific using of different prehistoric weapons is mainly determined by its physical properties, which provide a relative advantage or disadvantage to perform a given, particular function. Since these physical properties are integrated to accomplish that function, examining design variables and their pattern of integration or modularity is of interest to estimate the past function of a point. Here we analyze a composite sample of lithic points from southern Patagonia likely formed by arrows, thrown spears and hand-held points to test if they can be viewed as a two-module system formed by the blade and the stem, and to evaluate the degree in which shape, size, asymmetry, blade: stem length ratio, and tip angle explain the observed variance and differentiation among points supposedly aimed to accomplish different functions. To do so we performed a geometric morphometric analysis on 118 lithic points, departing from 24 two-dimensional landmark and semi landmarks placed on the point's contour. Klingenberg's covariational modularity tests were used to evaluate different modularity hypotheses, and a composite PCA including shape, size, asymmetry, blade: stem length ratio, and tip angle was used to estimate the importance of each attribute to explaining variation patterns. Results show that the blade and the stem can be seen as "near decomposable units" in the points integrating the studied sample. However, this modular pattern changes after removing the effects of reduction. Indeed, a resharpened point tends to show a tip/rest of the point modular pattern. The composite PCA analyses evidenced three different patterns of morphometric attributes compatible with arrows, thrown spears, and hand-held tools. Interestingly, when analyzed independently, these groups show differences in their modular organization. Our results indicate that stone tools can be approached as flexible designs, characterized by a composite set of interacting morphometric attributes, and evolving on a modular way.

Relative Importance of Modularity and Other Morphological Attributes on Different Types of Lithic Point Weapons: Assessing Functional Variations

PubMed Central

González-José, Rolando; Charlin, Judith

2012-01-01

The specific using of different prehistoric weapons is mainly determined by its physical properties, which provide a relative advantage or disadvantage to perform a given, particular function. Since these physical properties are integrated to accomplish that function, examining design variables and their pattern of integration or modularity is of interest to estimate the past function of a point. Here we analyze a composite sample of lithic points from southern Patagonia likely formed by arrows, thrown spears and hand-held points to test if they can be viewed as a two-module system formed by the blade and the stem, and to evaluate the degree in which shape, size, asymmetry, blade: stem length ratio, and tip angle explain the observed variance and differentiation among points supposedly aimed to accomplish different functions. To do so we performed a geometric morphometric analysis on 118 lithic points, departing from 24 two-dimensional landmark and semi landmarks placed on the point's contour. Klingenberg's covariational modularity tests were used to evaluate different modularity hypotheses, and a composite PCA including shape, size, asymmetry, blade: stem length ratio, and tip angle was used to estimate the importance of each attribute to explaining variation patterns. Results show that the blade and the stem can be seen as “near decomposable units” in the points integrating the studied sample. However, this modular pattern changes after removing the effects of reduction. Indeed, a resharpened point tends to show a tip/rest of the point modular pattern. The composite PCA analyses evidenced three different patterns of morphometric attributes compatible with arrows, thrown spears, and hand-held tools. Interestingly, when analyzed independently, these groups show differences in their modular organization. Our results indicate that stone tools can be approached as flexible designs, characterized by a composite set of interacting morphometric attributes, and evolving on a modular way. PMID:23094104

Hardware for Accelerating N-Modular Redundant Systems for High-Reliability Computing

NASA Technical Reports Server (NTRS)

Dobbs, Carl, Sr.

2012-01-01

A hardware unit has been designed that reduces the cost, in terms of performance and power consumption, for implementing N-modular redundancy (NMR) in a multiprocessor device. The innovation monitors transactions to memory, and calculates a form of sumcheck on-the-fly, thereby relieving the processors of calculating the sumcheck in software

Projective flatness in the quantisation of bosons and fermions

NASA Astrophysics Data System (ADS)

Wu, Siye

2015-07-01

We compare the quantisation of linear systems of bosons and fermions. We recall the appearance of projectively flat connection and results on parallel transport in the quantisation of bosons. We then discuss pre-quantisation and quantisation of fermions using the calculus of fermionic variables. We define a natural connection on the bundle of Hilbert spaces and show that it is projectively flat. This identifies, up to a phase, equivalent spinor representations constructed by various polarisations. We introduce the concept of metaplectic correction for fermions and show that the bundle of corrected Hilbert spaces is naturally flat. We then show that the parallel transport in the bundle of Hilbert spaces along a geodesic is a rescaled projection provided that the geodesic lies within the complement of a cut locus. Finally, we study the bundle of Hilbert spaces when there is a symmetry.

Improved specimen reconstruction by Hilbert phase contrast tomography.

PubMed

Barton, Bastian; Joos, Friederike; Schröder, Rasmus R

2008-11-01

The low signal-to-noise ratio (SNR) in images of unstained specimens recorded with conventional defocus phase contrast makes it difficult to interpret 3D volumes obtained by electron tomography (ET). The high defocus applied for conventional tilt series generates some phase contrast but leads to an incomplete transfer of object information. For tomography of biological weak-phase objects, optimal image contrast and subsequently an optimized SNR are essential for the reconstruction of details such as macromolecular assemblies at molecular resolution. The problem of low contrast can be partially solved by applying a Hilbert phase plate positioned in the back focal plane (BFP) of the objective lens while recording images in Gaussian focus. Images recorded with the Hilbert phase plate provide optimized positive phase contrast at low spatial frequencies, and the contrast transfer in principle extends to the information limit of the microscope. The antisymmetric Hilbert phase contrast (HPC) can be numerically converted into isotropic contrast, which is equivalent to the contrast obtained by a Zernike phase plate. Thus, in-focus HPC provides optimal structure factor information without limiting effects of the transfer function. In this article, we present the first electron tomograms of biological specimens reconstructed from Hilbert phase plate image series. We outline the technical implementation of the phase plate and demonstrate that the technique is routinely applicable for tomography. A comparison between conventional defocus tomograms and in-focus HPC volumes shows an enhanced SNR and an improved specimen visibility for in-focus Hilbert tomography.

Characterizing resonant component in speech: A different view of tracking fundamental frequency

NASA Astrophysics Data System (ADS)

Dong, Bin

2017-05-01

Inspired by the nonlinearity and nonstationarity and the modulations in speech, Hilbert-Huang Transform and cyclostationarity analysis are employed to investigate the speech resonance in vowel in sequence. Cyclostationarity analysis is not directly manipulated on the target vowel, but on its intrinsic mode functions one by one. Thanks to the equivalence between the fundamental frequency in speech and the cyclic frequency in cyclostationarity analysis, the modulation intensity distributions of the intrinsic mode functions provide much information for the estimation of the fundamental frequency. To highlight the relationship between frequency and time, the pseudo-Hilbert spectrum is proposed to replace the Hilbert spectrum here. After contrasting the pseudo-Hilbert spectra of and the modulation intensity distributions of the intrinsic mode functions, it finds that there is usually one intrinsic mode function which works as the fundamental component of the vowel. Furthermore, the fundamental frequency of the vowel can be determined by tracing the pseudo-Hilbert spectrum of its fundamental component along the time axis. The later method is more robust to estimate the fundamental frequency, when meeting nonlinear components. Two vowels [a] and [i], picked up from a speech database FAU Aibo Emotion Corpus, are applied to validate the above findings.

Computer implemented empirical mode decomposition method, apparatus and article of manufacture

NASA Technical Reports Server (NTRS)

Huang, Norden E. (Inventor)

1999-01-01

A computer implemented physical signal analysis method is invented. This method includes two essential steps and the associated presentation techniques of the results. All the steps exist only in a computer: there are no analytic expressions resulting from the method. The first step is a computer implemented Empirical Mode Decomposition to extract a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform. The final result is the Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum.

Quantum Computation of Fluid Dynamics

DTIC Science & Technology

1998-02-16

state of the quantum computer’s "memory". With N qubits, the quantum state IT) resides in an exponentially large Hilbert space with 2 N dimensions. A new...size of the Hilbert space in which the entanglement occurs. And to make matters worse, even if a quantum computer was constructed with a large number of...number of qubits "* 2 N is the size of the full Hilbert space "* 2 B is the size of the on-site submanifold, denoted 71 "* B is the size of the

Support vector machine based decision for mechanical fault condition monitoring in induction motor using an advanced Hilbert-Park transform.

PubMed

Ben Salem, Samira; Bacha, Khmais; Chaari, Abdelkader

2012-09-01

In this work we suggest an original fault signature based on an improved combination of Hilbert and Park transforms. Starting from this combination we can create two fault signatures: Hilbert modulus current space vector (HMCSV) and Hilbert phase current space vector (HPCSV). These two fault signatures are subsequently analysed using the classical fast Fourier transform (FFT). The effects of mechanical faults on the HMCSV and HPCSV spectrums are described, and the related frequencies are determined. The magnitudes of spectral components, relative to the studied faults (air-gap eccentricity and outer raceway ball bearing defect), are extracted in order to develop the input vector necessary for learning and testing the support vector machine with an aim of classifying automatically the various states of the induction motor. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Modular Cognitive-Behavioral Therapy for Childhood Anxiety Disorders. Guides to Individualized Evidence-Based Treatment Series

ERIC Educational Resources Information Center

Chorpita, Bruce F.

2006-01-01

This clinically wise and pragmatic book presents a systematic approach for treating any form of childhood anxiety using proven exposure-based techniques. What makes this rigorously tested modular treatment unique is that it is explicitly designed with flexibility and individualization in mind. Developed in a real-world, highly diverse community…

Hardening Effect Analysis by Modular Upper Bound and Finite Element Methods in Indentation of Aluminum, Steel, Titanium and Superalloys

PubMed Central

Bermudo, Carolina; Sevilla, Lorenzo; Martín, Francisco; Trujillo, Francisco Javier

2017-01-01

The application of incremental processes in the manufacturing industry is having a great development in recent years. The first stage of an Incremental Forming Process can be defined as an indentation. Because of this, the indentation process is starting to be widely studied, not only as a hardening test but also as a forming process. Thus, in this work, an analysis of the indentation process under the new Modular Upper Bound perspective has been performed. The modular implementation has several advantages, including the possibility of the introduction of different parameters to extend the study, such as the friction effect, the temperature or the hardening effect studied in this paper. The main objective of the present work is to analyze the three hardening models developed depending on the material characteristics. In order to support the validation of the hardening models, finite element analyses of diverse materials under an indentation are carried out. Results obtained from the Modular Upper Bound are in concordance with the results obtained from the numerical analyses. In addition, the numerical and analytical methods are in concordance with the results previously obtained in the experimental indentation of annealed aluminum A92030. Due to the introduction of the hardening factor, the new modular distribution is a suitable option for the analysis of indentation process. PMID:28772914

Model of brain activation predicts the neural collective influence map of the brain

PubMed Central

Morone, Flaviano; Roth, Kevin; Min, Byungjoon; Makse, Hernán A.

2017-01-01

Efficient complex systems have a modular structure, but modularity does not guarantee robustness, because efficiency also requires an ingenious interplay of the interacting modular components. The human brain is the elemental paradigm of an efficient robust modular system interconnected as a network of networks (NoN). Understanding the emergence of robustness in such modular architectures from the interconnections of its parts is a longstanding challenge that has concerned many scientists. Current models of dependencies in NoN inspired by the power grid express interactions among modules with fragile couplings that amplify even small shocks, thus preventing functionality. Therefore, we introduce a model of NoN to shape the pattern of brain activations to form a modular environment that is robust. The model predicts the map of neural collective influencers (NCIs) in the brain, through the optimization of the influence of the minimal set of essential nodes responsible for broadcasting information to the whole-brain NoN. Our results suggest intervention protocols to control brain activity by targeting influential neural nodes predicted by network theory. PMID:28351973

On the role of sparseness in the evolution of modularity in gene regulatory networks

PubMed Central

2018-01-01

Modularity is a widespread property in biological systems. It implies that interactions occur mainly within groups of system elements. A modular arrangement facilitates adjustment of one module without perturbing the rest of the system. Therefore, modularity of developmental mechanisms is a major factor for evolvability, the potential to produce beneficial variation from random genetic change. Understanding how modularity evolves in gene regulatory networks, that create the distinct gene activity patterns that characterize different parts of an organism, is key to developmental and evolutionary biology. One hypothesis for the evolution of modules suggests that interactions between some sets of genes become maladaptive when selection favours additional gene activity patterns. The removal of such interactions by selection would result in the formation of modules. A second hypothesis suggests that modularity evolves in response to sparseness, the scarcity of interactions within a system. Here I simulate the evolution of gene regulatory networks and analyse diverse experimentally sustained networks to study the relationship between sparseness and modularity. My results suggest that sparseness alone is neither sufficient nor necessary to explain modularity in gene regulatory networks. However, sparseness amplifies the effects of forms of selection that, like selection for additional gene activity patterns, already produce an increase in modularity. That evolution of new gene activity patterns is frequent across evolution also supports that it is a major factor in the evolution of modularity. That sparseness is widespread across gene regulatory networks indicates that it may have facilitated the evolution of modules in a wide variety of cases. PMID:29775459

On the role of sparseness in the evolution of modularity in gene regulatory networks.

PubMed

Espinosa-Soto, Carlos

2018-05-01

Modularity is a widespread property in biological systems. It implies that interactions occur mainly within groups of system elements. A modular arrangement facilitates adjustment of one module without perturbing the rest of the system. Therefore, modularity of developmental mechanisms is a major factor for evolvability, the potential to produce beneficial variation from random genetic change. Understanding how modularity evolves in gene regulatory networks, that create the distinct gene activity patterns that characterize different parts of an organism, is key to developmental and evolutionary biology. One hypothesis for the evolution of modules suggests that interactions between some sets of genes become maladaptive when selection favours additional gene activity patterns. The removal of such interactions by selection would result in the formation of modules. A second hypothesis suggests that modularity evolves in response to sparseness, the scarcity of interactions within a system. Here I simulate the evolution of gene regulatory networks and analyse diverse experimentally sustained networks to study the relationship between sparseness and modularity. My results suggest that sparseness alone is neither sufficient nor necessary to explain modularity in gene regulatory networks. However, sparseness amplifies the effects of forms of selection that, like selection for additional gene activity patterns, already produce an increase in modularity. That evolution of new gene activity patterns is frequent across evolution also supports that it is a major factor in the evolution of modularity. That sparseness is widespread across gene regulatory networks indicates that it may have facilitated the evolution of modules in a wide variety of cases.

Singularity formations for a surface wave model

NASA Astrophysics Data System (ADS)

Castro, Angel; Córdoba, Diego; Gancedo, Francisco

2010-11-01

In this paper we study the Burgers equation with a nonlocal term of the form Hu where H is the Hilbert transform. This system has been considered as a quadratic approximation for the dynamics of a free boundary of a vortex patch (see Biello and Hunter 2010 Commun. Pure Appl. Math. LXIII 0303-36 Marsden and Weinstein 1983 Physica D 7 305-23). We prove blowup in finite time for a large class of initial data with finite energy. Considering a more general nonlocal term, of the form ΛαHu for 0 < α < 1, finite time singularity formation is also shown.

Super-Quantum Mechanics in the Integral Form Formalism

NASA Astrophysics Data System (ADS)

Castellani, L.; Catenacci, R.; Grassi, P. A.

2018-05-01

We reformulate Super Quantum Mechanics in the context of integral forms. This framework allows to interpolate between different actions for the same theory, connected by different choices of Picture Changing Operators (PCO). In this way we retrieve component and superspace actions, and prove their equivalence. The PCO are closed integral forms, and can be interpreted as super Poincar\\'e duals of bosonic submanifolds embedded into a supermanifold.. We use them to construct Lagrangians that are top integral forms, and therefore can be integrated on the whole supermanifold. The $D=1, ~N=1$ and the $D=1,~ N=2$ cases are studied, in a flat and in a curved supermanifold. In this formalism we also consider coupling with gauge fields, Hilbert space of quantum states and observables.

The Riemann-Hilbert problem for nonsymmetric systems

NASA Astrophysics Data System (ADS)

Greenberg, W.; Zweifel, P. F.; Paveri-Fontana, S.

1991-12-01

A comparison of the Riemann-Hilbert problem and the Wiener-Hopf factorization problem arising in the solution of half-space singular integral equations is presented. Emphasis is on the factorization of functions lacking the reflection symmetry usual in transport theory.

NexusHaus: Solar Decathlon House

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garrison, Michael Lynn

The University of Texas at Austin and The Technical University of Munich 2015 Solar Decathlon house is called Nexushaus because it combines UT Austin and TUM students in an affordable modular residential green building in the context of Austin, Texas, based on shape forming principles found in nature that demonstrates transformative technologies in Zero Net Energy, Zero Net Water and Carbon Neutrality. To meet the needs of the competition, a portable modular design has been developed with an assembly that enables ease of installation and both quantitative and qualitative performance in the design. The prefabricated house sits lightly on themore » land and forms the superstructure for photovoltaic technologies, rainwater collection, aquaculture and permaculture gardening and indoor/outdoor living. The ultimate goal of Nexushaus is to serve as a potential prototype for a next-generation modular home that could be reproduced in mass in an assembly plant in Austin.« less

Diblock Copolymer Micelles and Supported Films with Noncovalently Incorporated Chromophores: A Modular Platform for Efficient Energy Transfer

DOE PAGES

Adams, Peter G.; Collins, Aaron M.; Sahin, Tuba; ...

2015-04-08

Here we report generation of modular, artificial light-harvesting assemblies where an amphiphilic diblock copolymer, poly(ethylene oxide)-block-poly(butadiene), serves as the framework for noncovalent organization of BODIPY-based energy donor and bacteriochlorin-based energy acceptor chromophores. The assemblies are adaptive and form well-defined micelles in aqueous solution and high-quality monolayer and bilayer films on solid supports, with the latter showing greater than 90% energy transfer efficiency. Ultimately, this study lays the groundwork for further development of modular, polymer-based materials for light harvesting and other photonic applications.

On the Computation of Optimal Designs for Certain Time Series Models with Applications to Optimal Quantile Selection for Location or Scale Parameter Estimation.

DTIC Science & Technology

1981-07-01

process is observed over all of (0,1], the reproducing kernel Hilbert space (RKHS) techniques developed by Parzen (1961a, 1961b) 2 may be used to construct...covariance kernel,R, for the process (1.1) is the reproducing kernel for a reproducing kernel Hilbert space (RKHS) which will be denoted as H(R) (c.f...2.6), it is known that (c.f. Eubank, Smith and Smith (1981a, 1981b)), i) H(R) is a Hilbert function space consisting of functions which satisfy for fEH

A Hilbert Space Representation of Generalized Observables and Measurement Processes in the ESR Model

NASA Astrophysics Data System (ADS)

Sozzo, Sandro; Garola, Claudio

2010-12-01

The extended semantic realism ( ESR) model recently worked out by one of the authors embodies the mathematical formalism of standard (Hilbert space) quantum mechanics in a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide here a Hilbert space representation of the generalized observables introduced by the ESR model that satisfy a simple physical condition, propose a generalization of the projection postulate, and suggest a possible mathematical description of the measurement process in terms of evolution of the compound system made up of the measured system and the measuring apparatus.

Empirical mode decomposition for analyzing acoustical signals

NASA Technical Reports Server (NTRS)

Huang, Norden E. (Inventor)

2005-01-01

The present invention discloses a computer implemented signal analysis method through the Hilbert-Huang Transformation (HHT) for analyzing acoustical signals, which are assumed to be nonlinear and nonstationary. The Empirical Decomposition Method (EMD) and the Hilbert Spectral Analysis (HSA) are used to obtain the HHT. Essentially, the acoustical signal will be decomposed into the Intrinsic Mode Function Components (IMFs). Once the invention decomposes the acoustic signal into its constituting components, all operations such as analyzing, identifying, and removing unwanted signals can be performed on these components. Upon transforming the IMFs into Hilbert spectrum, the acoustical signal may be compared with other acoustical signals.

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

NASA Technical Reports Server (NTRS)

Huang, Norden E. (Inventor)

2004-01-01

A computer implemented physical signal analysis method includes four basic steps and the associated presentation techniques of the results. The first step is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform which produces a Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum. The third step filters the physical signal by combining a subset of the IMFs. In the fourth step, a curve may be fitted to the filtered signal which may not have been possible with the original, unfiltered signal.

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

NASA Technical Reports Server (NTRS)

Huang, Norden E. (Inventor)

2002-01-01

A computer implemented physical signal analysis method includes four basic steps and the associated presentation techniques of the results. The first step is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform which produces a Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum. The third step filters the physical signal by combining a subset of the IMFs. In the fourth step, a curve may be fitted to the filtered signal which may not have been possible with the original, unfiltered signal.

Computer implemented empirical mode decomposition method apparatus, and article of manufacture utilizing curvature extrema

NASA Technical Reports Server (NTRS)

Shen, Zheng (Inventor); Huang, Norden Eh (Inventor)

2003-01-01

A computer implemented physical signal analysis method is includes two essential steps and the associated presentation techniques of the results. All the steps exist only in a computer: there are no analytic expressions resulting from the method. The first step is a computer implemented Empirical Mode Decomposition to extract a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals based on local extrema and curvature extrema. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform. The final result is the Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum.

Pressurized bellows flat contact heat exchanger interface

NASA Technical Reports Server (NTRS)

Voss, Fred E. (Inventor); Howell, Harold R. (Inventor); Winkler, Roger V. (Inventor)

1990-01-01

Disclosed is an interdigitated plate-type heat exchanger interface. The interface includes a modular interconnect to thermally connect a pair or pairs of plate-type heat exchangers to a second single or multiple plate-type heat exchanger. The modular interconnect comprises a series of parallel, plate-type heat exchangers arranged in pairs to form a slot therebetween. The plate-type heat exchangers of the second heat exchanger insert into the slots of the modular interconnect. Bellows are provided between the pairs of fins of the modular interconnect so that when the bellows are pressurized, they drive the plate-type heat exchangers of the modular interconnect toward one another, thus closing upon the second heat exchanger plates. Each end of the bellows has a part thereof a thin, membrane diaphragm which readily conforms to the contours of the heat exchanger plates of the modular interconnect when the bellows is pressurized. This ensures an even distribution of pressure on the heat exchangers of the modular interconnect thus creating substantially planar contact between the two heat exchangers. The effect of the interface of the present invention is to provide a dry connection between two heat exchangers whereby the rate of heat transfer can be varied by varying the pressure within the bellows.

Sculpting the Intrinsic Modular Organization of Spontaneous Brain Activity by Art.

PubMed

Lin, Chia-Shu; Liu, Yong; Huang, Wei-Yuan; Lu, Chia-Feng; Teng, Shin; Ju, Tzong-Ching; He, Yong; Wu, Yu-Te; Jiang, Tianzi; Hsieh, Jen-Chuen

2013-01-01

Artistic training is a complex learning that requires the meticulous orchestration of sophisticated polysensory, motor, cognitive, and emotional elements of mental capacity to harvest an aesthetic creation. In this study, we investigated the architecture of the resting-state functional connectivity networks from professional painters, dancers and pianists. Using a graph-based network analysis, we focused on the art-related changes of modular organization and functional hubs in the resting-state functional connectivity network. We report that the brain architecture of artists consists of a hierarchical modular organization where art-unique and artistic form-specific brain states collectively mirror the mind states of virtuosos. We show that even in the resting state, this type of extraordinary and long-lasting training can macroscopically imprint a neural network system of spontaneous activity in which the related brain regions become functionally and topologically modularized in both domain-general and domain-specific manners. The attuned modularity reflects a resilient plasticity nurtured by long-term experience.

Sculpting the Intrinsic Modular Organization of Spontaneous Brain Activity by Art

PubMed Central

Lin, Chia-Shu; Liu, Yong; Huang, Wei-Yuan; Lu, Chia-Feng; Teng, Shin; Ju, Tzong-Ching; He, Yong; Wu, Yu-Te; Jiang, Tianzi; Hsieh, Jen-Chuen

2013-01-01

Artistic training is a complex learning that requires the meticulous orchestration of sophisticated polysensory, motor, cognitive, and emotional elements of mental capacity to harvest an aesthetic creation. In this study, we investigated the architecture of the resting-state functional connectivity networks from professional painters, dancers and pianists. Using a graph-based network analysis, we focused on the art-related changes of modular organization and functional hubs in the resting-state functional connectivity network. We report that the brain architecture of artists consists of a hierarchical modular organization where art-unique and artistic form-specific brain states collectively mirror the mind states of virtuosos. We show that even in the resting state, this type of extraordinary and long-lasting training can macroscopically imprint a neural network system of spontaneous activity in which the related brain regions become functionally and topologically modularized in both domain-general and domain-specific manners. The attuned modularity reflects a resilient plasticity nurtured by long-term experience. PMID:23840527

Simultaneous targeting of prostate stem cell antigen and prostate-specific membrane antigen improves the killing of prostate cancer cells using a novel modular T cell-retargeting system.

PubMed

Arndt, Claudia; Feldmann, Anja; Koristka, Stefanie; Cartellieri, Marc; Dimmel, Maria; Ehninger, Armin; Ehninger, Gerhard; Bachmann, Michael

2014-09-01

Recently, we described a novel modular platform technology in which T cell-recruitment and tumor-targeting domains of conventional bispecific antibodies are split to independent components, a universal effector module (EM) and replaceable monospecific/monovalent target modules (TMs) that form highly efficient T cell-retargeting complexes. Theoretically, our unique strategy should allow us to simultaneously retarget T cells to different tumor antigens by combining the EM with two or more different monovalent/monospecific TMs or even with bivalent/bispecific TMs, thereby overcoming limitations of a monospecific treatment such as the selection of target-negative tumor escape variants. In order to advance our recently introduced prostate stem cell antigen (PSCA)-specific modular system for a dual-targeting of prostate cancer cells, two additional TMs were constructed: a monovalent/monospecific TM directed against the prostate-specific membrane antigen (PSMA) and a bivalent/bispecific TM (bsTM) with specificity for PSMA and PSCA. The functionality of the novel dual-targeting strategies was analyzed by performing T cell activation and chromium release assays. Similar to the PSCA-specific modular system, the novel PSMA-specific modular system mediates an efficient target-dependent and -specific tumor cell lysis at low E:T ratios and picomolar Ab concentrations. Moreover, by combination of the EM with either the bispecific TM directed to PSMA and PSCA or both monospecifc TMs directed to either PSCA or PSMA, dual-specific targeting complexes were formed which allowed us to kill potential escape variants expressing only one or the other target antigen. Overall, the novel modular system represents a promising tool for multiple tumor targeting. © 2014 Wiley Periodicals, Inc.

Congruences between modular forms: raising the level and dropping Euler factors.

PubMed

Diamond, F

1997-10-14

We discuss the relationship among certain generalizations of results of Hida, Ribet, and Wiles on congruences between modular forms. Hida's result accounts for congruences in terms of the value of an L-function, and Ribet's result is related to the behavior of the period that appears there. Wiles' theory leads to a class number formula relating the value of the L-function to the size of a Galois cohomology group. The behavior of the period is used to deduce that a formula at "nonminimal level" is obtained from one at "minimal level" by dropping Euler factors from the L-function.

High-speed spectral calibration by complex FIR filter in phase-sensitive optical coherence tomography.

PubMed

Kim, Sangmin; Raphael, Patrick D; Oghalai, John S; Applegate, Brian E

2016-04-01

Swept-laser sources offer a number of advantages for Phase-sensitive Optical Coherence Tomography (PhOCT). However, inter- and intra-sweep variability leads to calibration errors that adversely affect phase sensitivity. While there are several approaches to overcoming this problem, our preferred method is to simply calibrate every sweep of the laser. This approach offers high accuracy and phase stability at the expense of a substantial processing burden. In this approach, the Hilbert phase of the interferogram from a reference interferometer provides the instantaneous wavenumber of the laser, but is computationally expensive. Fortunately, the Hilbert transform may be approximated by a Finite Impulse-Response (FIR) filter. Here we explore the use of several FIR filter based Hilbert transforms for calibration, explicitly considering the impact of filter choice on phase sensitivity and OCT image quality. Our results indicate that the complex FIR filter approach is the most robust and accurate among those considered. It provides similar image quality and slightly better phase sensitivity than the traditional FFT-IFFT based Hilbert transform while consuming fewer resources in an FPGA implementation. We also explored utilizing the Hilbert magnitude of the reference interferogram to calculate an ideal window function for spectral amplitude calibration. The ideal window function is designed to carefully control sidelobes on the axial point spread function. We found that after a simple chromatic correction, calculating the window function using the complex FIR filter and the reference interferometer gave similar results to window functions calculated using a mirror sample and the FFT-IFFT Hilbert transform. Hence, the complex FIR filter can enable accurate and high-speed calibration of the magnitude and phase of spectral interferograms.

High-speed spectral calibration by complex FIR filter in phase-sensitive optical coherence tomography

PubMed Central

Kim, Sangmin; Raphael, Patrick D.; Oghalai, John S.; Applegate, Brian E.

2016-01-01

Swept-laser sources offer a number of advantages for Phase-sensitive Optical Coherence Tomography (PhOCT). However, inter- and intra-sweep variability leads to calibration errors that adversely affect phase sensitivity. While there are several approaches to overcoming this problem, our preferred method is to simply calibrate every sweep of the laser. This approach offers high accuracy and phase stability at the expense of a substantial processing burden. In this approach, the Hilbert phase of the interferogram from a reference interferometer provides the instantaneous wavenumber of the laser, but is computationally expensive. Fortunately, the Hilbert transform may be approximated by a Finite Impulse-Response (FIR) filter. Here we explore the use of several FIR filter based Hilbert transforms for calibration, explicitly considering the impact of filter choice on phase sensitivity and OCT image quality. Our results indicate that the complex FIR filter approach is the most robust and accurate among those considered. It provides similar image quality and slightly better phase sensitivity than the traditional FFT-IFFT based Hilbert transform while consuming fewer resources in an FPGA implementation. We also explored utilizing the Hilbert magnitude of the reference interferogram to calculate an ideal window function for spectral amplitude calibration. The ideal window function is designed to carefully control sidelobes on the axial point spread function. We found that after a simple chromatic correction, calculating the window function using the complex FIR filter and the reference interferometer gave similar results to window functions calculated using a mirror sample and the FFT-IFFT Hilbert transform. Hence, the complex FIR filter can enable accurate and high-speed calibration of the magnitude and phase of spectral interferograms. PMID:27446666

DOE Office of Scientific and Technical Information (OSTI.GOV)

Znojil, Miloslav

For many quantum models an apparent non-Hermiticity of observables just corresponds to their hidden Hermiticity in another, physical Hilbert space. For these models we show that the existence of observables which are manifestly time-dependent may require the use of a manifestly time-dependent representation of the physical Hilbert space of states.

Computational algebraic geometry of epidemic models

NASA Astrophysics Data System (ADS)

Rodríguez Vega, Martín.

2014-06-01

Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.

Applications of rigged Hilbert spaces in quantum mechanics and signal processing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Celeghini, E., E-mail: celeghini@fi.infn.it; Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, Paseo Belén 7, 47011 Valladolid; Gadella, M., E-mail: manuelgadella1@gmail.com

Simultaneous use of discrete and continuous bases in quantum systems is not possible in the context of Hilbert spaces, but only in the more general structure of rigged Hilbert spaces (RHS). In addition, the relevant operators in RHS (but not in Hilbert space) are a realization of elements of a Lie enveloping algebra and support representations of semigroups. We explicitly construct here basis dependent RHS of the line and half-line and relate them to the universal enveloping algebras of the Weyl-Heisenberg algebra and su(1, 1), respectively. The complete sub-structure of both RHS and of the operators acting on them ismore » obtained from their algebraic structures or from the related fractional Fourier transforms. This allows us to describe both quantum and signal processing states and their dynamics. Two relevant improvements are introduced: (i) new kinds of filters related to restrictions to subspaces and/or the elimination of high frequency fluctuations and (ii) an operatorial structure that, starting from fix objects, describes their time evolution.« less

Single and two-shot quantitative phase imaging using Hilbert-Huang Transform based fringe pattern analysis

NASA Astrophysics Data System (ADS)

Trusiak, Maciej; Micó, Vicente; Patorski, Krzysztof; García-Monreal, Javier; Sluzewski, Lukasz; Ferreira, Carlos

2016-08-01

In this contribution we propose two Hilbert-Huang Transform based algorithms for fast and accurate single-shot and two-shot quantitative phase imaging applicable in both on-axis and off-axis configurations. In the first scheme a single fringe pattern containing information about biological phase-sample under study is adaptively pre-filtered using empirical mode decomposition based approach. Further it is phase demodulated by the Hilbert Spiral Transform aided by the Principal Component Analysis for the local fringe orientation estimation. Orientation calculation enables closed fringes efficient analysis and can be avoided using arbitrary phase-shifted two-shot Gram-Schmidt Orthonormalization scheme aided by Hilbert-Huang Transform pre-filtering. This two-shot approach is a trade-off between single-frame and temporal phase shifting demodulation. Robustness of the proposed techniques is corroborated using experimental digital holographic microscopy studies of polystyrene micro-beads and red blood cells. Both algorithms compare favorably with the temporal phase shifting scheme which is used as a reference method.

Monopole operators and Hilbert series of Coulomb branches of 3 d = 4 gauge theories

NASA Astrophysics Data System (ADS)

Cremonesi, Stefano; Hanany, Amihay; Zaffaroni, Alberto

2014-01-01

This paper addresses a long standing problem - to identify the chiral ring and moduli space (i.e. as an algebraic variety) on the Coulomb branch of an = 4 superconformal field theory in 2+1 dimensions. Previous techniques involved a computation of the metric on the moduli space and/or mirror symmetry. These methods are limited to sufficiently small moduli spaces, with enough symmetry, or to Higgs branches of sufficiently small gauge theories. We introduce a simple formula for the Hilbert series of the Coulomb branch, which applies to any good or ugly three-dimensional = 4 gauge theory. The formula counts monopole operators which are dressed by classical operators, the Casimir invariants of the residual gauge group that is left unbroken by the magnetic flux. We apply our formula to several classes of gauge theories. Along the way we make various tests of mirror symmetry, successfully comparing the Hilbert series of the Coulomb branch with the Hilbert series of the Higgs branch of the mirror theory.

Full dyon excitation spectrum in extended Levin-Wen models

NASA Astrophysics Data System (ADS)

Hu, Yuting; Geer, Nathan; Wu, Yong-Shi

2018-05-01

In Levin-Wen (LW) models, a wide class of exactly solvable discrete models, for two-dimensional topological phases, it is relatively easy to describe only single-fluxon excitations, but not the charge and dyonic as well as many-fluxon excitations. To incorporate charged and dyonic excitations in (doubled) topological phases, an extension of the LW models is proposed in this paper. We first enlarge the Hilbert space with adding a tail on one of the edges of each trivalent vertex to describe the internal charge degrees of freedom at the vertex. Then, we study the full dyon spectrum of the extended LW models, including both quantum numbers and wave functions for dyonic quasiparticle excitations. The local operators associated with the dyonic excitations are shown to form the so-called tube algebra, whose representations (modules) form the quantum double (categoric center) of the input data (unitary fusion category). In physically relevant cases, the input data are from a finite or quantum group (with braiding R matrices), and we find that the elementary excitations (or dyon species), as well as any localized/isolated excited states, are characterized by three quantum numbers: charge, fluxon type, and twist. They provide a "complete basis" for many-body states in the enlarged Hilbert space. Concrete examples are presented and the relevance of our results to the electric-magnetic duality existing in the models is addressed.

Subcommunities and Their Mutual Relationships in a Transaction Network

NASA Astrophysics Data System (ADS)

Iino, T.; Iyetomi, H.

We investigate a Japanese transaction network consisting ofabout 800 thousand firms (nodes) and four million business relations (links) with focus on its modular structure. Communities detected by maximizing modularity often are dominated by firms with common features or behaviors in the network, such as characterized by regions or industry sectors. However, it is well known that the modularity optimization approach has a resolution limit problem, that is, it fails in identifying fine communities buried in large communities. To unfold such hidden structures, we apply the community detection to each of subnetworks formed by isolating those communities from the whole body. Subcommunities thus identified are composed of firms with finer regions, more specified sectors or business affiliations. Also we introduce a new idea of reduced modularity matrix to measure the strength of relations between (sub)communities.

Dirac’s magnetic monopole and the Kontsevich star product

NASA Astrophysics Data System (ADS)

Soloviev, M. A.

2018-03-01

We examine relationships between various quantization schemes for an electrically charged particle in the field of a magnetic monopole. Quantization maps are defined in invariant geometrical terms, appropriate to the case of nontrivial topology, and are constructed for two operator representations. In the first setting, the quantum operators act on the Hilbert space of sections of a nontrivial complex line bundle associated with the Hopf bundle, whereas the second approach uses instead a quaternionic Hilbert module of sections of a trivial quaternionic line bundle. We show that these two quantizations are naturally related by a bundle morphism and, as a consequence, induce the same phase-space star product. We obtain explicit expressions for the integral kernels of star-products corresponding to various operator orderings and calculate their asymptotic expansions up to the third order in the Planck constant \\hbar . We also show that the differential form of the magnetic Weyl product corresponding to the symmetric ordering agrees completely with the Kontsevich formula for deformation quantization of Poisson structures and can be represented by Kontsevich’s graphs.

Canonical field anticommutators in the extended gauged Rarita-Schwinger theory

NASA Astrophysics Data System (ADS)

Adler, Stephen L.; Henneaux, Marc; Pais, Pablo

2017-10-01

We reexamine canonical quantization of the gauged Rarita-Schwinger theory using the extended theory, incorporating a dimension 1/2 auxiliary spin-1/2 field Λ , in which there is an exact off-shell gauge invariance. In Λ =0 gauge, which reduces to the original unextended theory, our results agree with those found by Johnson and Sudarshan, and later verified by Velo and Zwanziger, which give a canonical Rarita-Schwinger field Dirac bracket that is singular for small gauge fields. In gauge covariant radiation gauge, the Dirac bracket of the Rarita-Schwinger fields is nonsingular, but does not correspond to a positive semidefinite anticommutator, and the Dirac bracket of the auxiliary fields has a singularity of the same form as found in the unextended theory. These results indicate that gauged Rarita-Schwinger theory is somewhat pathological, and cannot be canonically quantized within a conventional positive semidefinite metric Hilbert space. We leave open the questions of whether consistent quantizations can be achieved by using an indefinite metric Hilbert space, by path integral methods, or by appropriate couplings to conventional dimension 3/2 spin-1/2 fields.

Improving the signal subtle feature extraction performance based on dual improved fractal box dimension eigenvectors

NASA Astrophysics Data System (ADS)

Chen, Xiang; Li, Jingchao; Han, Hui; Ying, Yulong

2018-05-01

Because of the limitations of the traditional fractal box-counting dimension algorithm in subtle feature extraction of radiation source signals, a dual improved generalized fractal box-counting dimension eigenvector algorithm is proposed. First, the radiation source signal was preprocessed, and a Hilbert transform was performed to obtain the instantaneous amplitude of the signal. Then, the improved fractal box-counting dimension of the signal instantaneous amplitude was extracted as the first eigenvector. At the same time, the improved fractal box-counting dimension of the signal without the Hilbert transform was extracted as the second eigenvector. Finally, the dual improved fractal box-counting dimension eigenvectors formed the multi-dimensional eigenvectors as signal subtle features, which were used for radiation source signal recognition by the grey relation algorithm. The experimental results show that, compared with the traditional fractal box-counting dimension algorithm and the single improved fractal box-counting dimension algorithm, the proposed dual improved fractal box-counting dimension algorithm can better extract the signal subtle distribution characteristics under different reconstruction phase space, and has a better recognition effect with good real-time performance.

Hierarchical organization of brain functional networks during visual tasks.

PubMed

Zhuo, Zhao; Cai, Shi-Min; Fu, Zhong-Qian; Zhang, Jie

2011-09-01

The functional network of the brain is known to demonstrate modular structure over different hierarchical scales. In this paper, we systematically investigated the hierarchical modular organizations of the brain functional networks that are derived from the extent of phase synchronization among high-resolution EEG time series during a visual task. In particular, we compare the modular structure of the functional network from EEG channels with that of the anatomical parcellation of the brain cortex. Our results show that the modular architectures of brain functional networks correspond well to those from the anatomical structures over different levels of hierarchy. Most importantly, we find that the consistency between the modular structures of the functional network and the anatomical network becomes more pronounced in terms of vision, sensory, vision-temporal, motor cortices during the visual task, which implies that the strong modularity in these areas forms the functional basis for the visual task. The structure-function relationship further reveals that the phase synchronization of EEG time series in the same anatomical group is much stronger than that of EEG time series from different anatomical groups during the task and that the hierarchical organization of functional brain network may be a consequence of functional segmentation of the brain cortex.

The Application of Hilbert-Huang Transforms to Meteorological Datasets

NASA Technical Reports Server (NTRS)

Duffy, Dean G.

2003-01-01

Recently a new spectral technique as been developed for the analysis of aperiodic and nonlinear signals - the Hilbert-Huang transform. This paper shows how these transforms can be used to discover synoptic and climatic features: For sea level data, the transforms capture the oceanic tides as well as large, aperiodic river outflows. In the case of solar radiation, we observe variations in the diurnal and seasonal cycles. Finally, from barographic data, the Hilbert-Huang transform reveals the passage of extratropical cyclones, fronts, and troughs. Thus, this technique can flag significant weather events such its a flood or the passage of a squall line.

Optical Hilbert transform using fiber Bragg gratings

NASA Astrophysics Data System (ADS)

Ge, Jing; Wang, Chinhua; Zhu, Xiaojun

2010-11-01

In this paper, we demonstrate that a simple and practical phase-shifted fiber Bragg grating (PSFBG) operated in reflection can provide the required spectral response for implementing an all-optical Hilbert transformer (HT), including both integer and fractional orders. The PSFBG consists of two concatenated identical uniform FBGs with a phase shift between them. It can be proved that the phase shift of the FBG and the apodizing profile of the refractive index modulation determine the order of the transform. The device shows a good accuracy in calculating the Hilbert transform of the complex field of an arbitrary input optical waveforms when compared with the theoretical results.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kay, Randolph R; Campbell, David V; Shinde, Subhash L

A modular, scalable focal plane array is provided as an array of integrated circuit dice, wherein each die includes a given amount of modular pixel array circuitry. The array of dice effectively multiplies the amount of modular pixel array circuitry to produce a larger pixel array without increasing die size. Desired pixel pitch across the enlarged pixel array is preserved by forming die stacks with each pixel array circuitry die stacked on a separate die that contains the corresponding signal processing circuitry. Techniques for die stack interconnections and die stack placement are implemented to ensure that the desired pixel pitchmore » is preserved across the enlarged pixel array.« less

Molecular modularity and asymmetry of the molluscan mantle revealed by a gene expression atlas.

PubMed

Herlitze, Ines; Marie, Benjamin; Marin, Frédéric; Jackson, Daniel J

2018-06-01

Conchiferan molluscs construct a biocalcified shell that likely supported much of their evolutionary success. However, beyond broad proteomic and transcriptomic surveys of molluscan shells and the shell-forming mantle tissue, little is known of the spatial and ontogenetic regulation of shell fabrication. In addition, most efforts have been focused on species that deposit nacre, which is at odds with the majority of conchiferan species that fabricate shells using a crossed-lamellar microstructure, sensu lato. By combining proteomic and transcriptomic sequencing with in situ hybridization we have identified a suite of gene products associated with the production of the crossed-lamellar shell in Lymnaea stagnalis. With this spatial expression data we are able to generate novel hypotheses of how the adult mantle tissue coordinates the deposition of the calcified shell. These hypotheses include functional roles for unusual and otherwise difficult-to-study proteins such as those containing repetitive low-complexity domains. The spatial expression readouts of shell-forming genes also reveal cryptic patterns of asymmetry and modularity in the shell-forming cells of larvae and adult mantle tissue. This molecular modularity of the shell-forming mantle tissue hints at intimate associations between structure, function, and evolvability and may provide an elegant explanation for the evolutionary success of the second largest phylum among the Metazoa.

Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter.

PubMed

Zhuang, Leimeng; Khan, Muhammad Rezaul; Beeker, Willem; Leinse, Arne; Heideman, René; Roeloffzen, Chris

2012-11-19

We propose and demonstrate a novel wideband microwave photonic fractional Hilbert transformer implemented using a ring resonator-based optical all-pass filter. The full programmability of the ring resonator allows variable and arbitrary fractional order of the Hilbert transformer. The performance analysis in both frequency and time domain validates that the proposed implementation provides a good approximation to an ideal fractional Hilbert transformer. This is also experimentally verified by an electrical S₂₁ response characterization performed on a waveguide realization of a ring resonator. The waveguide-based structure allows the proposed Hilbert transformer to be integrated together with other building blocks on a photonic integrated circuit to create various system-level functionalities for on-chip microwave photonic signal processors. As an example, a circuit consisting of a splitter and a ring resonator has been realized which can perform on-chip phase control of microwave signals generated by means of optical heterodyning, and simultaneous generation of in-phase and quadrature microwave signals for a wide frequency range. For these functionalities, this simple and on-chip solution is considered to be practical, particularly when operating together with a dual-frequency laser. To our best knowledge, this is the first-time on-chip demonstration where ring resonators are employed to perform phase control functionalities for optical generation of microwave signals by means of optical heterodyning.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suchanecki, Z.; Antoniou, I.; Tasaki, S.

We consider the problem of rigging for the Koopman operators of the Renyi and the baker maps. We show that the rigged Hilbert space for the Renyi maps has some of the properties of a strict inductive limit and give a detailed description of the rigged Hilbert space for the baker maps. {copyright} {ital 1996 American Institute of Physics.}

Automatic loudness control in short-form content for broadcasting.

PubMed

Pires, Leandro da S; Vieira, Maurílio N; Yehia, Hani C

2017-03-01

During the early years of the International Telecommunication Union (ITU) loudness calculation standard for sound broadcasting [ITU-R (2006), Rec. BS Series, 1770], the need for additional loudness descriptors to evaluate short-form content, such as commercials and live inserts, was identified. This work proposes a loudness control scheme to prevent loudness jumps, which can bother audiences. It employs short-form content audio detection and dynamic range processing methods for the maximum loudness level criteria. Detection is achieved by combining principal component analysis for dimensionality reduction and support vector machines for binary classification. Subsequent processing is based on short-term loudness integrators and Hilbert transformers. The performance was assessed using quality classification metrics and demonstrated through a loudness control example.

Structure and composition of the courtship phenotype in the bird of paradise Parotia lawesii (Aves: Paradisaeidae).

PubMed

Scholes, Edwin

2008-01-01

Ethology is rooted in the idea that behavior is composed of discrete units and sub-units that can be compared among taxa in a phylogenetic framework. This means that behavior, like morphology and genes, is inherently modular. Yet, the concept of modularity is not well integrated into how we envision the behavioral components of phenotype. Understanding ethological modularity, and its implications for animal phenotype organization and evolution, requires that we construct interpretive schemes that permit us to examine it. In this study, I describe the structure and composition of a complex part of the behavioral phenotype of Parotia lawesii Ramsay, 1885--a bird of paradise (Aves: Paradisaeidae) from the forests of eastern New Guinea. I use archived voucher video clips, photographic ethograms, and phenotype ontology diagrams to describe the modular units comprising courtship at various levels of integration. Results show P. lawesii to have 15 courtship and mating behaviors (11 males, 4 females) hierarchically arranged within a complex seven-level structure. At the finest level examined, male displays are comprised of 49 modular sub-units (elements) differentially employed to form more complex modular units (phases and versions) at higher-levels of integration. With its emphasis on hierarchical modularity, this study provides an important conceptual framework for understanding courtship-related phenotypic complexity and provides a solid basis for comparative study of the genus Parotia.

Investigation on changes of modularity and robustness by edge-removal mutations in signaling networks.

PubMed

Truong, Cong-Doan; Kwon, Yung-Keun

2017-12-21

Biological networks consisting of molecular components and interactions are represented by a graph model. There have been some studies based on that model to analyze a relationship between structural characteristics and dynamical behaviors in signaling network. However, little attention has been paid to changes of modularity and robustness in mutant networks. In this paper, we investigated the changes of modularity and robustness by edge-removal mutations in three signaling networks. We first observed that both the modularity and robustness increased on average in the mutant network by the edge-removal mutations. However, the modularity change was negatively correlated with the robustness change. This implies that it is unlikely that both the modularity and the robustness values simultaneously increase by the edge-removal mutations. Another interesting finding is that the modularity change was positively correlated with the degree, the number of feedback loops, and the edge betweenness of the removed edges whereas the robustness change was negatively correlated with them. We note that these results were consistently observed in randomly structure networks. Additionally, we identified two groups of genes which are incident to the highly-modularity-increasing and the highly-robustness-decreasing edges with respect to the edge-removal mutations, respectively, and observed that they are likely to be central by forming a connected component of a considerably large size. The gene-ontology enrichment of each of these gene groups was significantly different from the rest of genes. Finally, we showed that the highly-robustness-decreasing edges can be promising edgetic drug-targets, which validates the usefulness of our analysis. Taken together, the analysis of changes of robustness and modularity against edge-removal mutations can be useful to unravel novel dynamical characteristics underlying in signaling networks.

Fox proteins are modular competency factors for facial cartilage and tooth specification.

PubMed

Xu, Pengfei; Balczerski, Bartosz; Ciozda, Amanda; Louie, Kristin; Oralova, Veronika; Huysseune, Ann; Crump, J Gage

2018-06-26

Facial form depends on the precise positioning of cartilage, bone, and tooth fields in the embryonic pharyngeal arches. How complex signaling information is integrated to specify these cell types remains a mystery. We find that modular expression of Forkhead domain transcription factors (Fox proteins) in the zebrafish face arises through integration of Hh, Fgf, Bmp, Edn1 and Jagged-Notch pathways. Whereas loss of C-class Fox proteins results in reduced upper facial cartilages, loss of F-class Fox proteins results in distal jaw truncations and absent midline cartilages and teeth. We show that Fox proteins are required for Sox9a to promote chondrogenic gene expression. Fox proteins are sufficient in neural crest-derived cells for cartilage development, and neural crest-specific misexpression of Fox proteins expands the cartilage domain but inhibits bone. These results support a modular role for Fox proteins in establishing the competency of progenitors to form cartilage and teeth in the face. © 2018. Published by The Company of Biologists Ltd.

Symmetric modular torsatron

DOEpatents

Rome, J.A.; Harris, J.H.

1984-01-01

A fusion reactor device is provided in which the magnetic fields for plasma confinement in a toroidal configuration is produced by a plurality of symmetrical modular coils arranged to form a symmetric modular torsatron referred to as a symmotron. Each of the identical modular coils is helically deformed and comprise one field period of the torsatron. Helical segments of each coil are connected by means of toroidally directed windbacks which may also provide part of the vertical field required for positioning the plasma. The stray fields of the windback segments may be compensated by toroidal coils. A variety of magnetic confinement flux surface configurations may be produced by proper modulation of the winding pitch of the helical segments of the coils, as in a conventional torsatron, winding the helix on a noncircular cross section and varying the poloidal and radial location of the windbacks and the compensating toroidal ring coils.

Generation of dark hollow beams by using a fractional radial Hilbert transform system

NASA Astrophysics Data System (ADS)

Xie, Qiansen; Zhao, Daomu

2007-07-01

The radial Hilbert transform has been extend to the fractional field, which could be called the fractional radial Hilbert transform (FRHT). Using edge-enhancement characteristics of this transform, we convert a Gaussian light beam into a variety of dark hollow beams (DHBs). Based on the fact that a hard-edged aperture can be expanded approximately as a finite sum of complex Gaussian functions, the analytical expression of a Gaussian beam passing through a FRHT system has been derived. As a numerical example, the properties of the DHBs with different fractional orders are illustrated graphically. The calculation results obtained by use of the analytical method and the integral method are also compared.

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Diffraction of Electromagnetic Waves on a Waveguide Joint

NASA Astrophysics Data System (ADS)

Malykh, Mikhail; Sevastianov, Leonid; Tyutyunnik, Anastasiya; Nikolaev, Nikolai

2018-02-01

In general, the investigation of the electromagnetic field in an inhomogeneous waveguide doesn't reduce to the study of two independent boundary value problems for the Helmholtz equation. We show how to rewrite the Helmholtz equations in the "Hamiltonian form" to express the connection between these two problems explicitly. The problem of finding monochromatic waves in an arbitrary waveguide is reduced to an infinite system of ordinary differential equations in a properly constructed Hilbert space. The calculations are performed in the computer algebra system Sage.

Modular invariant inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kobayashi, Tatsuo; Nitta, Daisuke; Urakawa, Yuko

2016-08-08

Modular invariance is a striking symmetry in string theory, which may keep stringy corrections under control. In this paper, we investigate a phenomenological consequence of the modular invariance, assuming that this symmetry is preserved as well as in a four dimensional (4D) low energy effective field theory. As a concrete setup, we consider a modulus field T whose contribution in the 4D effective field theory remains invariant under the modular transformation and study inflation drived by T. The modular invariance restricts a possible form of the scalar potenntial. As a result, large field models of inflation are hardly realized. Meanwhile,more » a small field model of inflation can be still accomodated in this restricted setup. The scalar potential traced during the slow-roll inflation mimics the hilltop potential V{sub ht}, but it also has a non-negligible deviation from V{sub ht}. Detecting the primordial gravitational waves predicted in this model is rather challenging. Yet, we argue that it may be still possible to falsify this model by combining the information in the reheating process which can be determined self-completely in this setup.« less

Modular forms, Schwarzian conditions, and symmetries of differential equations in physics

NASA Astrophysics Data System (ADS)

Abdelaziz, Y.; Maillard, J.-M.

2017-05-01

We give examples of infinite order rational transformations that leave linear differential equations covariant. These examples are non-trivial yet simple enough illustrations of exact representations of the renormalization group. We first illustrate covariance properties on order-two linear differential operators associated with identities relating the same {}_2F1 hypergeometric function with different rational pullbacks. These rational transformations are solutions of a differentially algebraic equation that already emerged in a paper by Casale on the Galoisian envelopes. We provide two new and more general results of the previous covariance by rational functions: a new Heun function example and a higher genus {}_2F1 hypergeometric function example. We then focus on identities relating the same {}_2F1 hypergeometric function with two different algebraic pullback transformations: such remarkable identities correspond to modular forms, the algebraic transformations being solution of another differentially algebraic Schwarzian equation that also emerged in Casale’s paper. Further, we show that the first differentially algebraic equation can be seen as a subcase of the last Schwarzian differential condition, the restriction corresponding to a factorization condition of some associated order-two linear differential operator. Finally, we also explore generalizations of these results, for instance, to {}_3F2 , hypergeometric functions, and show that one just reduces to the previous {}_2F1 cases through a Clausen identity. The question of the reduction of these Schwarzian conditions to modular correspondences remains an open question. In a _2F1 hypergeometric framework the Schwarzian condition encapsulates all the modular forms and modular equations of the theory of elliptic curves, but these two conditions are actually richer than elliptic curves or {}_2F1 hypergeometric functions, as can be seen on the Heun and higher genus example. This work is a strong incentive to develop more differentially algebraic symmetry analysis in physics.

The Riemann-Hilbert approach to the Helmholtz equation in a quarter-plane: Neumann, Robin and Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Its, Alexander; Its, Elizabeth

2018-04-01

We revisit the Helmholtz equation in a quarter-plane in the framework of the Riemann-Hilbert approach to linear boundary value problems suggested in late 1990s by A. Fokas. We show the role of the Sommerfeld radiation condition in Fokas' scheme.

Group-theoretical approach to the construction of bases in 2{sup n}-dimensional Hilbert space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garcia, A.; Romero, J. L.; Klimov, A. B., E-mail: klimov@cencar.udg.mx

2011-06-15

We propose a systematic procedure to construct all the possible bases with definite factorization structure in 2{sup n}-dimensional Hilbert space and discuss an algorithm for the determination of basis separability. The results are applied for classification of bases for an n-qubit system.

Observables and density matrices embedded in dual Hilbert spaces

NASA Astrophysics Data System (ADS)

Prosen, T.; Martignon, L.; Seligman, T. H.

2015-06-01

The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured that we deal with Hilbert spaces although the mathematical background was not entirely clear, particularly, when dealing with bosonic operators. This in turn caused some doubts about the correct way to combine bosonic and fermionic operators or, in other words, regular and Grassmann variables. In this paper we present a formal answer to the problems on a simple and very general basis. We illustrate the resulting construction by revisiting the Bargmann transform and finding the known connection between {{L}}2({{R}}) and the Bargmann-Hilbert space. We pursue this line of thinking one step further and discuss the representations of complex extensions of linear canonical transformations as isometries between dual Hilbert spaces. We then use the formalism to give an explicit formulation for Fock spaces involving both fermions and bosons thus solving the problem at the origin of our considerations.

Averaging of random walks and shift-invariant measures on a Hilbert space

NASA Astrophysics Data System (ADS)

Sakbaev, V. Zh.

2017-06-01

We study random walks in a Hilbert space H and representations using them of solutions of the Cauchy problem for differential equations whose initial conditions are numerical functions on H. We construct a finitely additive analogue of the Lebesgue measure: a nonnegative finitely additive measure λ that is defined on a minimal subset ring of an infinite-dimensional Hilbert space H containing all infinite-dimensional rectangles with absolutely converging products of the side lengths and is invariant under shifts and rotations in H. We define the Hilbert space H of equivalence classes of complex-valued functions on H that are square integrable with respect to a shift-invariant measure λ. Using averaging of the shift operator in H over random vectors in H with a distribution given by a one-parameter semigroup (with respect to convolution) of Gaussian measures on H, we define a one-parameter semigroup of contracting self-adjoint transformations on H, whose generator is called the diffusion operator. We obtain a representation of solutions of the Cauchy problem for the Schrödinger equation whose Hamiltonian is the diffusion operator.

Basis-neutral Hilbert-space analyzers

PubMed Central

Martin, Lane; Mardani, Davood; Kondakci, H. Esat; Larson, Walker D.; Shabahang, Soroush; Jahromi, Ali K.; Malhotra, Tanya; Vamivakas, A. Nick; Atia, George K.; Abouraddy, Ayman F.

2017-01-01

Interferometry is one of the central organizing principles of optics. Key to interferometry is the concept of optical delay, which facilitates spectral analysis in terms of time-harmonics. In contrast, when analyzing a beam in a Hilbert space spanned by spatial modes – a critical task for spatial-mode multiplexing and quantum communication – basis-specific principles are invoked that are altogether distinct from that of ‘delay’. Here, we extend the traditional concept of temporal delay to the spatial domain, thereby enabling the analysis of a beam in an arbitrary spatial-mode basis – exemplified using Hermite-Gaussian and radial Laguerre-Gaussian modes. Such generalized delays correspond to optical implementations of fractional transforms; for example, the fractional Hankel transform is the generalized delay associated with the space of Laguerre-Gaussian modes, and an interferometer incorporating such a ‘delay’ obtains modal weights in the associated Hilbert space. By implementing an inherently stable, reconfigurable spatial-light-modulator-based polarization-interferometer, we have constructed a ‘Hilbert-space analyzer’ capable of projecting optical beams onto any modal basis. PMID:28344331

Projective loop quantum gravity. I. State space

NASA Astrophysics Data System (ADS)

Lanéry, Suzanne; Thiemann, Thomas

2016-12-01

Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In a latter work by Okolów, the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels. If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that the projective approach allows for a more balanced treatment of the holonomy and flux variables, so it might pave the way for the development of more satisfactory coherent states.

Functional brain abnormalities in major depressive disorder using the Hilbert-Huang transform.

PubMed

Yu, Haibin; Li, Feng; Wu, Tong; Li, Rui; Yao, Li; Wang, Chuanyue; Wu, Xia

2018-02-09

Major depressive disorder is a common disease worldwide, which is characterized by significant and persistent depression. Non-invasive accessory diagnosis of depression can be performed by resting-state functional magnetic resonance imaging (rs-fMRI). However, the fMRI signal may not satisfy linearity and stationarity. The Hilbert-Huang transform (HHT) is an adaptive time-frequency localization analysis method suitable for nonlinear and non-stationary signals. The objective of this study was to apply the HHT to rs-fMRI to find the abnormal brain areas of patients with depression. A total of 35 patients with depression and 37 healthy controls were subjected to rs-fMRI. The HHT was performed to extract the Hilbert-weighted mean frequency of the rs-fMRI signals, and multivariate receiver operating characteristic analysis was applied to find the abnormal brain regions with high sensitivity and specificity. We observed differences in Hilbert-weighted mean frequency between the patients and healthy controls mainly in the right hippocampus, right parahippocampal gyrus, left amygdala, and left and right caudate nucleus. Subsequently, the above-mentioned regions were included in the results obtained from the compared region homogeneity and the fractional amplitude of low frequency fluctuation method. We found brain regions with differences in the Hilbert-weighted mean frequency, and examined their sensitivity and specificity, which suggested a potential neuroimaging biomarker to distinguish between patients with depression and healthy controls. We further clarified the pathophysiological abnormality of these regions for the population with major depressive disorder.

Unveiling signatures of interdecadal climate changes by Hilbert analysis

NASA Astrophysics Data System (ADS)

Zappalà, Dario; Barreiro, Marcelo; Masoller, Cristina

2017-04-01

A recent study demonstrated that, in a class of networks of oscillators, the optimal network reconstruction from dynamics is obtained when the similarity analysis is performed not on the original dynamical time series, but on transformed series obtained by Hilbert transform. [1] That motivated us to use Hilbert transform to study another kind of (in a broad sense) "oscillating" series, such as the series of temperature. Actually, we found that Hilbert analysis of SAT (Surface Air Temperature) time series uncovers meaningful information about climate and is therefore a promising tool for the study of other climatological variables. [2] In this work we analysed a large dataset of SAT series, performing Hilbert transform and further analysis with the goal of finding signs of climate change during the analysed period. We used the publicly available ERA-Interim dataset, containing reanalysis data. [3] In particular, we worked on daily SAT time series, from year 1979 to 2015, in 16380 points arranged over a regular grid on the Earth surface. From each SAT time series we calculate the anomaly series and also, by using the Hilbert transform, we calculate the instantaneous amplitude and instantaneous frequency series. Our first approach is to calculate the relative variation: the difference between the average value on the last 10 years and the average value on the first 10 years, divided by the average value over all the analysed period. We did this calculations on our transformed series: frequency and amplitude, both with average values and standard deviation values. Furthermore, to have a comparison with an already known analysis methods, we did these same calculations on the anomaly series. We plotted these results as maps, where the colour of each site indicates the value of its relative variation. Finally, to gain insight in the interpretation of our results over real SAT data, we generated synthetic sinusoidal series with various levels of additive noise. By applying Hilbert analysis to the synthetic data, we uncovered a clear trend between mean amplitude and mean frequency: as the noise level grows, the amplitude increases while the frequency decreases. Research funded in part by AGAUR (Generalitat de Catalunya), EU LINC project (Grant No. 289447) and Spanish MINECO (FIS2015-66503-C3-2-P).

Low Earth Orbital Mission Aboard the Space Test Experiments Platform (STEP-3)

NASA Technical Reports Server (NTRS)

Brinza, David E.

1992-01-01

A discussion of the Space Active Modular Materials Experiments (SAMMES) is presented in vugraph form. The discussion is divided into three sections: (1) a description of SAMMES; (2) a SAMMES/STEP-3 mission overview; and (3) SAMMES follow on efforts. The SAMMES/STEP-3 mission objectives are as follows: assess LEO space environmental effects on SDIO materials; quantify orbital and local environments; and demonstrate the modular experiment concept.

Holomorphic projections and Ramanujan’s mock theta functions

PubMed Central

Imamoğlu, Özlem; Raum, Martin; Richter, Olav K.

2014-01-01

We use spectral methods of automorphic forms to establish a holomorphic projection operator for tensor products of vector-valued harmonic weak Maass forms and vector-valued modular forms. We apply this operator to discover simple recursions for Fourier series coefficients of Ramanujan’s mock theta functions. PMID:24591582

An algorithm for the split-feasibility problems with application to the split-equality problem.

PubMed

Chuang, Chih-Sheng; Chen, Chi-Ming

2017-01-01

In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality problem in Hilbert spaces, and we give new algorithms for these problems. Finally, numerical results are given for our main results.

MURI: Optimal Quantum Dynamic Discrimination of Chemical and Biological Agents

DTIC Science & Technology

2008-06-12

multiparameter) Hilbert space for enhanced detection and classification: an application of receiver operating curve statistics to laser-based mass...Adaptive reshaping of objects in (multiparameter) Hilbert space for enhanced detection and classification: an application of receiver operating curve...Doctoral Associate Muhannad Zamari, Graduate Student Ilya Greenberg , Computer Consultant Getahun Menkir, Graduate Student Lalinda Palliyaguru, Graduate

Hilbert transform evaluation for electron-phonon self-energies

NASA Astrophysics Data System (ADS)

Bevilacqua, Giuseppe; Menichetti, Guido; Pastori Parravicini, Giuseppe

2016-01-01

The electron tunneling current through nanostructures is considered in the presence of the electron-phonon interactions. In the Keldysh nonequilibrium formalism, the lesser, greater, advanced and retarded self-energies components are expressed by means of appropriate Langreth rules. We discuss the key role played by the entailed Hilbert transforms, and provide an analytic way for their evaluation. Particular attention is given to the current-conserving lowest-order-expansion for the treament of the electron-phonon interaction; by means of an appropriate elaboration of the analytic properties and pole structure of the Green's functions and of the Fermi functions, we arrive at a surprising simple, elegant, fully analytic and easy-to-use expression of the Hilbert transforms and involved integrals in the energy domain.

Non-algebraic integrability of the Chew-Low reversible dynamical system of the Cremona type and the relation with the 7th Hilbert problem (non-resonant case)

NASA Astrophysics Data System (ADS)

Rerikh, K. V.

A smooth reversible dynamical system (SRDS) and a system of nonlinear functional equations, defined by a certain rational quadratic Cremona mapping and arising from the static model of the dispersion approach in the theory of strong interactions (the Chew-Low equations for p- wave πN- scattering) are considered. This SRDS is splitted into 1- and 2-dimensional ones. An explicit Cremona transformation that completely determines the exact solution of the two-dimensional system is found. This solution depends on an odd function satisfying a nonlinear autonomous 3-point functional equation. Non-algebraic integrability of SRDS under consideration is proved using the method of Poincaré normal forms and the Siegel theorem on biholomorphic linearization of a mapping at a non-resonant fixed point. The proof is based on the classical Feldman-Baker theorem on linear forms of logarithms of algebraic numbers, which, in turn, relies upon solving the 7th Hilbert problem by A.I. Gel'fond and T. Schneider and new powerful methods of A. Baker in the theory of transcendental numbers. The general theorem, following from the Feldman-Baker theorem, on applicability of the Siegel theorem to the set of the eigenvalues λ ɛ Cn of a mapping at a non-resonant fixed point which belong to the algebraic number field A is formulated and proved. The main results are presented in Theorems 1-3, 5, 7, 8 and Remarks 3, 7.

Modular health services: a single case study approach to the applicability of modularity to residential mental healthcare.

PubMed

Soffers, Rutger; Meijboom, Bert; van Zaanen, Jos; van der Feltz-Cornelis, Christina

2014-05-09

The Dutch mental healthcare sector has to decrease costs by reducing intramural capacity with one third by 2020 and treating more patients in outpatient care. This transition necessitates enabling patients to become as self-supporting as possible, by customising the residential care they receive to their needs for self-development. Theoretically, modularity might help mental healthcare institutions with this. Modularity entails the decomposition of a healthcare service in parts that can be mixed-and-matched in a variety of ways, and combined form a functional whole. It brings about easier and better configuration, increased transparency and more variety without increasing costs. this study aims to explore the applicability of the modularity concept to the residential care provided in Assisted Living Facilities (ALFs) of Dutch mental healthcare institutions. A single case study is carried out at the centre for psychosis in Etten-Leur, part of the GGz Breburg IMPACT care group. The design enables in-depth analysis of a case in a specific context. This is considered appropriate since theory concerning healthcare modularity is in an early stage of development. The present study can be considered a pilot case. Data were gathered by means of interviews, observations and documentary analysis. At the centre for psychosis, the majority of the residential care can be decomposed in modules, which can be grouped in service bundles and sub-bundles; the service customisation process is sufficiently fit to apply modular thinking; and interfaces for most of the categories are present. Hence, the prerequisites for modular residential care offerings are already largely fulfilled. For not yet fulfilled aspects of these prerequisites, remedies are available. The modularity concept seems applicable to the residential care offered by the ALF of the mental healthcare institution under study. For a successful implementation of modularity however, some steps should be taken by the ALF, such as developing a catalogue of modules and a method for the personnel to work with this catalogue in application of the modules. Whether implementation of modular residential care might facilitate the transition from intramural residential care to outpatient care should be the subject of future research.

Modular health services: a single case study approach to the applicability of modularity to residential mental healthcare

PubMed Central

2014-01-01

Background The Dutch mental healthcare sector has to decrease costs by reducing intramural capacity with one third by 2020 and treating more patients in outpatient care. This transition necessitates enabling patients to become as self-supporting as possible, by customising the residential care they receive to their needs for self-development. Theoretically, modularity might help mental healthcare institutions with this. Modularity entails the decomposition of a healthcare service in parts that can be mixed-and-matched in a variety of ways, and combined form a functional whole. It brings about easier and better configuration, increased transparency and more variety without increasing costs. Aim: this study aims to explore the applicability of the modularity concept to the residential care provided in Assisted Living Facilities (ALFs) of Dutch mental healthcare institutions. Methods A single case study is carried out at the centre for psychosis in Etten-Leur, part of the GGz Breburg IMPACT care group. The design enables in-depth analysis of a case in a specific context. This is considered appropriate since theory concerning healthcare modularity is in an early stage of development. The present study can be considered a pilot case. Data were gathered by means of interviews, observations and documentary analysis. Results At the centre for psychosis, the majority of the residential care can be decomposed in modules, which can be grouped in service bundles and sub-bundles; the service customisation process is sufficiently fit to apply modular thinking; and interfaces for most of the categories are present. Hence, the prerequisites for modular residential care offerings are already largely fulfilled. For not yet fulfilled aspects of these prerequisites, remedies are available. Conclusion The modularity concept seems applicable to the residential care offered by the ALF of the mental healthcare institution under study. For a successful implementation of modularity however, some steps should be taken by the ALF, such as developing a catalogue of modules and a method for the personnel to work with this catalogue in application of the modules. Whether implementation of modular residential care might facilitate the transition from intramural residential care to outpatient care should be the subject of future research. PMID:24886367

On the decomposition of modular multiplicative inverse operators via a new functional algorithm approach to Bachet’s-Bezout’s Lemma

NASA Astrophysics Data System (ADS)

Cortés–Vega, Luis A.

2017-12-01

In this paper, we consider modular multiplicative inverse operators (MMIO)’s of the form: J(m+n):(ℤ/(m+n)ℤ)*→ℤ/(m+n)ℤ, J(m+n)(a)=a-1. A general method to decompose {{\\mathscr{J}}}(m+n)(.) over group of units {({{Z}}/(m+n){{Z}})}* is derived. As result, an interesting decomposition law for these operators over {({{Z}}/(m+n){{Z}})}* is established. Numerical examples illustring the new results are given. This, complement some recent results obtained by the author for (MMIO)’s defined over group of units of the form {({{Z}}/\\varrho {{Z}})}* with ϱ = m × n > 2.

Wick Product for Commutation Relations Connected with Yang-Baxter Operators and New Constructions of Factors

NASA Astrophysics Data System (ADS)

Krsolarlak, Ilona

We analyze a certain class of von Neumann algebras generated by selfadjoint elements , for satisfying the general commutation relations: Such algebras can be continuously embedded into some closure of the set of finite linear combinations of vectors , where is an orthonormal basis of a Hilbert space . The operator which represents the vector is denoted by and called the ``Wick product'' of the operators . We describe explicitly the form of this product. Also, we estimate the operator norm of for . Finally we apply these two results and prove that under the assumption all the von Neumann algebras considered are II1 factors.

The eigenfrequency spectrum of linear magnetohydrodynamic perturbations in stationary equilibria: A variational principle

NASA Astrophysics Data System (ADS)

Andries, Jesse

2010-11-01

The frequencies of the normal modes of oscillation of linear magnetohydrodynamic perturbations of a stationary equilibrium are related to the stationary points of a quadratic functional over the Hilbert space of Lagrangian displacement vectors, which is subject to a constraint. In the absence of a background flow (or of a uniform flow), the relation reduces to the well-known Rayleigh-Ritz variational principle. In contrast to the existing variational principles for perturbations of stationary equilibria, the present treatment does neither impose additional symmetry restrictions on the equilibrium, nor does it involve the generalization to bilinear functionals instead of quadratic forms. This allows a more natural interpretation of the quadratic forms as energy functionals.

A Modular Set of Mixed Reality Simulators for Blind and Guided Procedures

DTIC Science & Technology

2017-08-01

Form Factor, Modular, DoD CVA Sim: Learning Outcome Study This between-groups study will compare performance scores on the CVA simulator to determine...simulation.health.ufl.edu/research/ra_sim.wmv. Preliminary data from a new study of the CVA simulator indicates that an integrated tutor may be non-inferior to a human...instructor, opening the possibility of self- study and self-debriefing which in turn facilitate competency-based, instead of time-based simulation

Feasibility of Nuclear Power on U.S. Military Installations. 2nd Revision

DTIC Science & Technology

2011-03-01

Small Modular Reactor , Military Installation Energy, Energy Assurance 16. SECURITY CLASSIFICATION OF: a. REPORT I b. ABSTRACT U c. THIS PAGE i; 17. LIMITATION OF ABSTRACT SAR 18. NUMBER OF PAGES 98 19a. NAME OF RESPONSIBLE PERSON Knowledge Center/Rhea Stone 19b. TELEPHONE NUMBER (Include area code) 703-824-2110 Standard Form 298 (Rev. 8/98) Prescribed bv ANSI Sid 239.18 Contents Preliminary note: Development and commercial deployment of small modular reactors

Dual Cross-Linked Biofunctional and Self-Healing Networks to Generate User-Defined Modular Gradient Hydrogel Constructs.

PubMed

Wei, Zhao; Lewis, Daniel M; Xu, Yu; Gerecht, Sharon

2017-08-01

Gradient hydrogels have been developed to mimic the spatiotemporal differences of multiple gradient cues in tissues. Current approaches used to generate such hydrogels are restricted to a single gradient shape and distribution. Here, a hydrogel is designed that includes two chemical cross-linking networks, biofunctional, and self-healing networks, enabling the customizable formation of modular gradient hydrogel construct with various gradient distributions and flexible shapes. The biofunctional networks are formed via Michael addition between the acrylates of oxidized acrylated hyaluronic acid (OAHA) and the dithiol of matrix metalloproteinase (MMP)-sensitive cross-linker and RGD peptides. The self-healing networks are formed via dynamic Schiff base reaction between N-carboxyethyl chitosan (CEC) and OAHA, which drives the modular gradient units to self-heal into an integral modular gradient hydrogel. The CEC-OAHA-MMP hydrogel exhibits excellent flowability at 37 °C under shear stress, enabling its injection to generate gradient distributions and shapes. Furthermore, encapsulated sarcoma cells respond to the gradient cues of RGD peptides and MMP-sensitive cross-linkers in the hydrogel. With these superior properties, the dual cross-linked CEC-OAHA-MMP hydrogel holds significant potential for generating customizable gradient hydrogel constructs, to study and guide cellular responses to their microenvironment such as in tumor mimicking, tissue engineering, and stem cell differentiation and morphogenesis. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Adaptive learning in complex reproducing kernel Hilbert spaces employing Wirtinger's subgradients.

PubMed

Bouboulis, Pantelis; Slavakis, Konstantinos; Theodoridis, Sergios

2012-03-01

This paper presents a wide framework for non-linear online supervised learning tasks in the context of complex valued signal processing. The (complex) input data are mapped into a complex reproducing kernel Hilbert space (RKHS), where the learning phase is taking place. Both pure complex kernels and real kernels (via the complexification trick) can be employed. Moreover, any convex, continuous and not necessarily differentiable function can be used to measure the loss between the output of the specific system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. In order to derive analytically the subgradients, the principles of the (recently developed) Wirtinger's calculus in complex RKHS are exploited. Furthermore, both linear and widely linear (in RKHS) estimation filters are considered. To cope with the problem of increasing memory requirements, which is present in almost all online schemes in RKHS, the sparsification scheme, based on projection onto closed balls, has been adopted. We demonstrate the effectiveness of the proposed framework in a non-linear channel identification task, a non-linear channel equalization problem and a quadrature phase shift keying equalization scheme, using both circular and non circular synthetic signal sources.

An assessment of envelope-based demodulation in case of proximity of carrier and modulation frequencies

NASA Astrophysics Data System (ADS)

Shahriar, Md Rifat; Borghesani, Pietro; Randall, R. B.; Tan, Andy C. C.

2017-11-01

Demodulation is a necessary step in the field of diagnostics to reveal faults whose signatures appear as an amplitude and/or frequency modulation. The Hilbert transform has conventionally been used for the calculation of the analytic signal required in the demodulation process. However, the carrier and modulation frequencies must meet the conditions set by the Bedrosian identity for the Hilbert transform to be applicable for demodulation. This condition, basically requiring the carrier frequency to be sufficiently higher than the frequency of the modulation harmonics, is usually satisfied in many traditional diagnostic applications (e.g. vibration analysis of gear and bearing faults) due to the order-of-magnitude ratio between the carrier and modulation frequency. However, the diversification of the diagnostic approaches and applications shows cases (e.g. electrical signature analysis-based diagnostics) where the carrier frequency is in close proximity to the modulation frequency, thus challenging the applicability of the Bedrosian theorem. This work presents an analytic study to quantify the error introduced by the Hilbert transform-based demodulation when the Bedrosian identity is not satisfied and proposes a mitigation strategy to combat the error. An experimental study is also carried out to verify the analytical results. The outcome of the error analysis sets a confidence limit on the estimated modulation (both shape and magnitude) achieved through the Hilbert transform-based demodulation in case of violated Bedrosian theorem. However, the proposed mitigation strategy is found effective in combating the demodulation error aroused in this scenario, thus extending applicability of the Hilbert transform-based demodulation.

Dynamic characterization of a damaged beam using empirical mode decomposition and Hilbert spectrum method

NASA Astrophysics Data System (ADS)

Chang, Chih-Chen; Poon, Chun-Wing

2004-07-01

Recently, the empirical mode decomposition (EMD) in combination with the Hilbert spectrum method has been proposed to identify the dynamic characteristics of linear structures. In this study, this EMD and Hilbert spectrum method is used to analyze the dynamic characteristics of a damaged reinforced concrete (RC) beam in the laboratory. The RC beam is 4m long with a cross section of 200mm X 250mm. The beam is sequentially subjected to a concentrated load of different magnitudes at the mid-span to produce different degrees of damage. An impact load is applied around the mid-span to excite the beam. Responses of the beam are recorded by four accelerometers. Results indicate that the EMD and Hilbert spectrum method can reveal the variation of the dynamic characteristics in the time domain. These results are also compared with those obtained using the Fourier analysis. In general, it is found that the two sets of results correlate quite well in terms of mode counts and frequency values. Some differences, however, can be seen in the damping values, which perhaps can be attributed to the linear assumption of the Fourier transform.

Rational Solutions of the Painlevé-II Equation Revisited

NASA Astrophysics Data System (ADS)

Miller, Peter D.; Sheng, Yue

2017-08-01

The rational solutions of the Painlevé-II equation appear in several applications and are known to have many remarkable algebraic and analytic properties. They also have several different representations, useful in different ways for establishing these properties. In particular, Riemann-Hilbert representations have proven to be useful for extracting the asymptotic behavior of the rational solutions in the limit of large degree (equivalently the large-parameter limit). We review the elementary properties of the rational Painlevé-II functions, and then we describe three different Riemann-Hilbert representations of them that have appeared in the literature: a representation by means of the isomonodromy theory of the Flaschka-Newell Lax pair, a second representation by means of the isomonodromy theory of the Jimbo-Miwa Lax pair, and a third representation found by Bertola and Bothner related to pseudo-orthogonal polynomials. We prove that the Flaschka-Newell and Bertola-Bothner Riemann-Hilbert representations of the rational Painlevé-II functions are explicitly connected to each other. Finally, we review recent results describing the asymptotic behavior of the rational Painlevé-II functions obtained from these Riemann-Hilbert representations by means of the steepest descent method.

Faults Diagnostics of Railway Axle Bearings Based on IMF’s Confidence Index Algorithm for Ensemble EMD

PubMed Central

Yi, Cai; Lin, Jianhui; Zhang, Weihua; Ding, Jianming

2015-01-01

As train loads and travel speeds have increased over time, railway axle bearings have become critical elements which require more efficient non-destructive inspection and fault diagnostics methods. This paper presents a novel and adaptive procedure based on ensemble empirical mode decomposition (EEMD) and Hilbert marginal spectrum for multi-fault diagnostics of axle bearings. EEMD overcomes the limitations that often hypothesize about data and computational efforts that restrict the application of signal processing techniques. The outputs of this adaptive approach are the intrinsic mode functions that are treated with the Hilbert transform in order to obtain the Hilbert instantaneous frequency spectrum and marginal spectrum. Anyhow, not all the IMFs obtained by the decomposition should be considered into Hilbert marginal spectrum. The IMFs’ confidence index arithmetic proposed in this paper is fully autonomous, overcoming the major limit of selection by user with experience, and allows the development of on-line tools. The effectiveness of the improvement is proven by the successful diagnosis of an axle bearing with a single fault or multiple composite faults, e.g., outer ring fault, cage fault and pin roller fault. PMID:25970256

Hilbert-Huang transform analysis of dynamic and earthquake motion recordings

USGS Publications Warehouse

Zhang, R.R.; Ma, S.; Safak, E.; Hartzell, S.

2003-01-01

This study examines the rationale of Hilbert-Huang transform (HHT) for analyzing dynamic and earthquake motion recordings in studies of seismology and engineering. In particular, this paper first provides the fundamentals of the HHT method, which consist of the empirical mode decomposition (EMD) and the Hilbert spectral analysis. It then uses the HHT to analyze recordings of hypothetical and real wave motion, the results of which are compared with the results obtained by the Fourier data processing technique. The analysis of the two recordings indicates that the HHT method is able to extract some motion characteristics useful in studies of seismology and engineering, which might not be exposed effectively and efficiently by Fourier data processing technique. Specifically, the study indicates that the decomposed components in EMD of HHT, namely, the intrinsic mode function (IMF) components, contain observable, physical information inherent to the original data. It also shows that the grouped IMF components, namely, the EMD-based low- and high-frequency components, can faithfully capture low-frequency pulse-like as well as high-frequency wave signals. Finally, the study illustrates that the HHT-based Hilbert spectra are able to reveal the temporal-frequency energy distribution for motion recordings precisely and clearly.

Modular assembly of thick multifunctional cardiac patches

PubMed Central

Fleischer, Sharon; Shapira, Assaf; Feiner, Ron; Dvir, Tal

2017-01-01

In cardiac tissue engineering cells are seeded within porous biomaterial scaffolds to create functional cardiac patches. Here, we report on a bottom-up approach to assemble a modular tissue consisting of multiple layers with distinct structures and functions. Albumin electrospun fiber scaffolds were laser-patterned to create microgrooves for engineering aligned cardiac tissues exhibiting anisotropic electrical signal propagation. Microchannels were patterned within the scaffolds and seeded with endothelial cells to form closed lumens. Moreover, cage-like structures were patterned within the scaffolds and accommodated poly(lactic-co-glycolic acid) (PLGA) microparticulate systems that controlled the release of VEGF, which promotes vascularization, or dexamethasone, an anti-inflammatory agent. The structure, morphology, and function of each layer were characterized, and the tissue layers were grown separately in their optimal conditions. Before transplantation the tissue and microparticulate layers were integrated by an ECM-based biological glue to form thick 3D cardiac patches. Finally, the patches were transplanted in rats, and their vascularization was assessed. Because of the simple modularity of this approach, we believe that it could be used in the future to assemble other multicellular, thick, 3D, functional tissues. PMID:28167795

Value at 2 of the L-function of an elliptic curve

NASA Astrophysics Data System (ADS)

Brunault, Francois

2006-02-01

We study the special value at 2 of L-functions of modular forms of weight 2 on congruence subgroups of the modular group. We prove an explicit version of Beilinson's theorem for the modular curve X_1(N). When N is prime, we deduce that the target space of Beilinson's regulator map is generated by the images of Milnor symbols associated to modular units of X_1(N). We also suggest a reformulation of Zagier's conjecture on L(E,2) for the jacobian J_1(N) of X_1(N), where E is an elliptic curve of conductor N. In this direction we define an analogue of the elliptic dilogarithm for any jacobian J : it is a function R_J from the complex points of J to a finite-dimensional vector space. In the case J=J_1(N), we establish a link between the aforementioned L-values and the function R_J evaluated at Q-rational points of the cuspidal subgroup of J.

Employing the Hilbert-Huang Transform to analyze observed natural complex signals: Calm wind meandering cases

NASA Astrophysics Data System (ADS)

Martins, Luis Gustavo Nogueira; Stefanello, Michel Baptistella; Degrazia, Gervásio Annes; Acevedo, Otávio Costa; Puhales, Franciano Scremin; Demarco, Giuliano; Mortarini, Luca; Anfossi, Domenico; Roberti, Débora Regina; Costa, Felipe Denardin; Maldaner, Silvana

2016-11-01

In this study we analyze natural complex signals employing the Hilbert-Huang spectral analysis. Specifically, low wind meandering meteorological data are decomposed into turbulent and non turbulent components. These non turbulent movements, responsible for the absence of a preferential direction of the horizontal wind, provoke negative lobes in the meandering autocorrelation functions. The meandering characteristic time scales (meandering periods) are determined from the spectral peak provided by the Hilbert-Huang marginal spectrum. The magnitudes of the temperature and horizontal wind meandering period obtained agree with the results found from the best fit of the heuristic meandering autocorrelation functions. Therefore, the new method represents a new procedure to evaluate meandering periods that does not employ mathematical expressions to represent observed meandering autocorrelation functions.

On Replacing "Quantum Thinking" with Counterfactual Reasoning

NASA Astrophysics Data System (ADS)

Narens, Louis

The probability theory used in quantum mechanics is currently being employed by psychologists to model the impact of context on decision. Its event space consists of closed subspaces of a Hilbert space, and its probability function sometimes violate the law of the finite additivity of probabilities. Results from the quantum mechanics literature indicate that such a "Hilbert space probability theory" cannot be extended in a useful way to standard, finitely additive, probability theory by the addition of new events with specific probabilities. This chapter presents a new kind of probability theory that shares many fundamental algebraic characteristics with Hilbert space probability theory but does extend to standard probability theory by adjoining new events with specific probabilities. The new probability theory arises from considerations about how psychological experiments are related through counterfactual reasoning.

Frequency hopping signal detection based on wavelet decomposition and Hilbert-Huang transform

NASA Astrophysics Data System (ADS)

Zheng, Yang; Chen, Xihao; Zhu, Rui

2017-07-01

Frequency hopping (FH) signal is widely adopted by military communications as a kind of low probability interception signal. Therefore, it is very important to research the FH signal detection algorithm. The existing detection algorithm of FH signals based on the time-frequency analysis cannot satisfy the time and frequency resolution requirement at the same time due to the influence of window function. In order to solve this problem, an algorithm based on wavelet decomposition and Hilbert-Huang transform (HHT) was proposed. The proposed algorithm removes the noise of the received signals by wavelet decomposition and detects the FH signals by Hilbert-Huang transform. Simulation results show the proposed algorithm takes into account both the time resolution and the frequency resolution. Correspondingly, the accuracy of FH signals detection can be improved.

Master Lovas-Andai and equivalent formulas verifying the 8/33 two-qubit Hilbert-Schmidt separability probability and companion rational-valued conjectures

NASA Astrophysics Data System (ADS)

Slater, Paul B.

2018-04-01

We begin by investigating relationships between two forms of Hilbert-Schmidt two-rebit and two-qubit "separability functions"—those recently advanced by Lovas and Andai (J Phys A Math Theor 50(29):295303, 2017), and those earlier presented by Slater (J Phys A 40(47):14279, 2007). In the Lovas-Andai framework, the independent variable ɛ \\in [0,1] is the ratio σ (V) of the singular values of the 2 × 2 matrix V=D_2^{1/2} D_1^{-1/2} formed from the two 2 × 2 diagonal blocks (D_1, D_2) of a 4 × 4 density matrix D= ||ρ _{ij}||. In the Slater setting, the independent variable μ is the diagonal-entry ratio √{ρ _{11} ρ _ {44}/ρ _ {22 ρ _ {33}}}—with, of central importance, μ =ɛ or μ =1/ɛ when both D_1 and D_2 are themselves diagonal. Lovas and Andai established that their two-rebit "separability function" \\tilde{χ }_1 (ɛ ) (≈ ɛ ) yields the previously conjectured Hilbert-Schmidt separability probability of 29/64. We are able, in the Slater framework (using cylindrical algebraic decompositions [CAD] to enforce positivity constraints), to reproduce this result. Further, we newly find its two-qubit, two-quater[nionic]-bit and "two-octo[nionic]-bit" counterparts, \\tilde{χ _2}(ɛ ) =1/3 ɛ ^2 ( 4-ɛ ^2) , \\tilde{χ _4}(ɛ ) =1/35 ɛ ^4 ( 15 ɛ ^4-64 ɛ ^2+84) and \\tilde{χ _8} (ɛ )= 1/1287ɛ ^8 ( 1155 ɛ ^8-7680 ɛ ^6+20160 ɛ ^4-25088 ɛ ^2+12740) . These immediately lead to predictions of Hilbert-Schmidt separability/PPT-probabilities of 8/33, 26/323 and 44482/4091349, in full agreement with those of the "concise formula" (Slater in J Phys A 46:445302, 2013), and, additionally, of a "specialized induced measure" formula. Then, we find a Lovas-Andai "master formula," \\tilde{χ _d}(ɛ )= ɛ ^d Γ (d+1)^3 _3\\tilde{F}_2( -{d/2,d/2,d;d/2+1,3 d/2+1;ɛ ^2) }/{Γ ( d/2+1) ^2}, encompassing both even and odd values of d. Remarkably, we are able to obtain the \\tilde{χ _d}(ɛ ) formulas, d=1,2,4, applicable to full (9-, 15-, 27-) dimensional sets of density matrices, by analyzing (6-, 9, 15-) dimensional sets, with not only diagonal D_1 and D_2, but also an additional pair of nullified entries. Nullification of a further pair still leads to X-matrices, for which a distinctly different, simple Dyson-index phenomenon is noted. C. Koutschan, then, using his HolonomicFunctions program, develops an order-4 recurrence satisfied by the predictions of the several formulas, establishing their equivalence. A two-qubit separability probability of 1-256/27 π ^2 is obtained based on the operator monotone function √{x}, with the use of \\tilde{χ _2}(ɛ ).

Structural-based designed modular capsomere comprising HA1 for low-cost poultry influenza vaccination.

PubMed

Waneesorn, Jarurin; Wibowo, Nani; Bingham, John; Middelberg, Anton P J; Lua, Linda H L

2018-05-24

Highly pathogenic avian influenza (HPAI) viruses cause a severe and lethal infection in domestic birds. The increasing number of HPAI outbreaks has demonstrated the lack of capabilities to control the rapid spread of avian influenza. Poultry vaccination has been shown to not only reduce the virus spread in animals but also reduce the virus transmission to humans, preventing potential pandemic development. However, existing vaccine technologies cannot respond to a new virus outbreak rapidly and at a cost and scale that is commercially viable for poultry vaccination. Here, we developed modular capsomere, subunits of virus-like particle, as a low-cost poultry influenza vaccine. Modified murine polyomavirus (MuPyV) VP1 capsomere was used to present structural-based influenza Hemagglutinin (HA1) antigen. Six constructs of modular capsomeres presenting three truncated versions of HA1 and two constructs of modular capsomeres presenting non-modified HA1 have been generated. These modular capsomeres were successfully produced in stable forms using Escherichia coli, without the need for protein refolding. Based on ELISA, this adjuvanted modular capsomere (CaptHA1-3C) induced strong antibody response (almost 10 5 endpoint titre) when administered into chickens, similar to titres obtained in the group administered with insect cell-based HA1 proteins. Chickens that received adjuvanted CaptHA1-3C followed by challenge with HPAI virus were fully protected. The results presented here indicate that this platform for bacterially-produced modular capsomere could potentially translate into a rapid-response and low-cost vaccine manufacturing technology suitable for poultry vaccination. Copyright © 2016 Elsevier Ltd. All rights reserved.

The Modeling and Control of Acoustic/Structure Interaction Problems via Piezoceramic Actuators: 2-D Numerical Examples

DTIC Science & Technology

1992-04-01

the voltage applied to the it" patch, K ’ is a parameter which depends on the geometry and piezoceramic...in the state space II L 2(fQ) x L2 (F0 ). Here L2(Q) is the quotient space of L2 over the constant functions. The use of the quotient space results...form of the problem, we also define the Hilbert space V = fti(Q) x H(F 0 ) where h!(Q) is the quotient space of Il’ over the constant functions

An abstract approach to evaporation models in rarefied gas dynamics

NASA Astrophysics Data System (ADS)

Greenberg, W.; van der Mee, C. V. M.

1984-03-01

Strong evaporation models involving 1D stationary problems with linear self-adjoint collision operators and solutions in abstract Hilbert spaces are investigated analytically. An efficient algorithm for locating the transition from existence to nonexistence of solutions is developed and applied to the 1D and 3D BGK model equations and the 3D BGK model in moment form, demonstrating the nonexistence of stationary evaporation states with supersonic drift velocities. Applications to similar models in electron and phonon transport, radiative transfer, and neutron transport are suggested.

Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators

NASA Astrophysics Data System (ADS)

Kokurin, M. Yu.

2010-11-01

A general scheme for improving approximate solutions to irregular nonlinear operator equations in Hilbert spaces is proposed and analyzed in the presence of errors. A modification of this scheme designed for equations with quadratic operators is also examined. The technique of universal linear approximations of irregular equations is combined with the projection onto finite-dimensional subspaces of a special form. It is shown that, for finite-dimensional quadratic problems, the proposed scheme provides information about the global geometric properties of the intersections of quadrics.

The spectral function of a singular differential operator of order 2m

NASA Astrophysics Data System (ADS)

Kozko, Artem I.; Pechentsov, Alexander S.

2010-12-01

We study the spectral function of a self-adjoint semibounded below differential operator on a Hilbert space L_2 \\lbrack 0,\\infty) and obtain the formulae for the spectral function of the operator (-1)^{m}y^{(2m)}(x) with general boundary conditions at the zero. In particular, for the boundary conditions y(0)=y'(0)=\\dots=y^{(m-1)}(0)=0 we find the explicit form of the spectral function \\Theta_{mB'}(x,x,\\lambda) on the diagonal x=y for \\lambda \\ge 0.

A convenient basis for the Izergin-Korepin model

NASA Astrophysics Data System (ADS)

Qiao, Yi; Zhang, Xin; Hao, Kun; Cao, Junpeng; Li, Guang-Liang; Yang, Wen-Li; Shi, Kangjie

2018-05-01

We propose a convenient orthogonal basis of the Hilbert space for the quantum spin chain associated with the A2(2) algebra (or the Izergin-Korepin model). It is shown that compared with the original basis the monodromy-matrix elements acting on this basis take relatively simple forms, which is quite similar as that for the quantum spin chain associated with An algebra in the so-called F-basis. As an application of our general results, we present the explicit recursive expressions of the Bethe states in this basis for the Izergin-Korepin model.

Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincaré symmetry

NASA Astrophysics Data System (ADS)

Moretti, Valter; Oppio, Marco

As earlier conjectured by several authors and much later established by Solèr (relying on partial results by Piron, Maeda-Maeda and other authors), from the lattice theory point of view, Quantum Mechanics may be formulated in real, complex or quaternionic Hilbert spaces only. Stückelberg provided some physical, but not mathematically rigorous, reasons for ruling out the real Hilbert space formulation, assuming that any formulation should encompass a statement of Heisenberg principle. Focusing on this issue from another — in our opinion, deeper — viewpoint, we argue that there is a general fundamental reason why elementary quantum systems are not described in real Hilbert spaces. It is their basic symmetry group. In the first part of the paper, we consider an elementary relativistic system within Wigner’s approach defined as a locally-faithful irreducible strongly-continuous unitary representation of the Poincaré group in a real Hilbert space. We prove that, if the squared-mass operator is non-negative, the system admits a natural, Poincaré invariant and unique up to sign, complex structure which commutes with the whole algebra of observables generated by the representation itself. This complex structure leads to a physically equivalent reformulation of the theory in a complex Hilbert space. Within this complex formulation, differently from what happens in the real one, all selfadjoint operators represent observables in accordance with Solèr’s thesis, and the standard quantum version of Noether theorem may be formulated. In the second part of this work, we focus on the physical hypotheses adopted to define a quantum elementary relativistic system relaxing them on the one hand, and making our model physically more general on the other hand. We use a physically more accurate notion of irreducibility regarding the algebra of observables only, we describe the symmetries in terms of automorphisms of the restricted lattice of elementary propositions of the quantum system and we adopt a notion of continuity referred to the states viewed as probability measures on the elementary propositions. Also in this case, the final result proves that there exists a unique (up to sign) Poincaré invariant complex structure making the theory complex and completely fitting into Solèr’s picture. This complex structure reveals a nice interplay of Poincaré symmetry and the classification of the commutant of irreducible real von Neumann algebras.

A Modular Set of Mixed Reality Simulators for blind and Guided Procedures

DTIC Science & Technology

2015-08-01

W81XWH-14-1-0113 – Year 1 Report University of Florida Page 1 of 12 AWARD NUMBER: W81XWH-14-1-0113 TITLE: A Modular Set of Mixed Reality...Simulators for “blind” and Guided Procedures PRINCIPAL INVESTIGATOR: Samsun Lampotang CONTRACTING ORGANIZATION: University of Florida Gainesville, FL...designated by other documentation. W81XWH-14-1-0113 – Year 1 Report University of Florida Page 2 of 12 REPORT DOCUMENTATION PAGE Form Approved OMB No

Learning in Modular Systems

DTIC Science & Technology

2010-05-07

important for deep modular systems is that taking a series of small update steps and stopping before convergence, so called early stopping, is a form of regu...larization around the initial parameters of the system . For example, the stochastic gradient descent 5 1 u + 1 v = 1 6‖x2‖q = ‖x‖22q 22 Chapter 2...Aside from the overall speed of the classifier, no quantitative performance analysis was given, and the role played by the features in the larger system

A multilevel control approach for a modular structured space platform

NASA Technical Reports Server (NTRS)

Chichester, F. D.; Borelli, M. T.

1981-01-01

A three axis mathematical representation of a modular assembled space platform consisting of interconnected discrete masses, including a deployable truss module, was derived for digital computer simulation. The platform attitude control system as developed to provide multilevel control utilizing the Gauss-Seidel second level formulation along with an extended form of linear quadratic regulator techniques. The objectives of the multilevel control are to decouple the space platform's spatial axes and to accommodate the modification of the platform's configuration for each of the decoupled axes.

Photonic Hilbert transformers based on laterally apodized integrated waveguide Bragg gratings on a SOI wafer.

PubMed

Bazargani, Hamed Pishvai; Burla, Maurizio; Chrostowski, Lukas; Azaña, José

2016-11-01

We experimentally demonstrate high-performance integer and fractional-order photonic Hilbert transformers based on laterally apodized Bragg gratings in a silicon-on-insulator technology platform. The sub-millimeter-long gratings have been fabricated using single-etch electron beam lithography, and the resulting HT devices offer operation bandwidths approaching the THz range, with time-bandwidth products between 10 and 20.

Heterotic reduction of Courant algebroid connections and Einstein-Hilbert actions

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Vysoký, Jan

2016-08-01

We discuss Levi-Civita connections on Courant algebroids. We define an appropriate generalization of the curvature tensor and compute the corresponding scalar curvatures in the exact and heterotic case, leading to generalized (bosonic) Einstein-Hilbert type of actions known from supergravity. In particular, we carefully analyze the process of the reduction for the generalized metric, connection, curvature tensor and the scalar curvature.

Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agaltsov, A. D., E-mail: agalets@gmail.com; Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr; IEPT RAS, 117997 Moscow

2014-10-15

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

Modular assembly of chimeric phi29 packaging RNAs that support DNA packaging.

PubMed

Fang, Yun; Shu, Dan; Xiao, Feng; Guo, Peixuan; Qin, Peter Z

2008-08-08

The bacteriophage phi29 DNA packaging motor is a protein/RNA complex that can produce strong force to condense the linear-double-stranded DNA genome into a pre-formed protein capsid. The RNA component, called the packaging RNA (pRNA), utilizes magnesium-dependent inter-molecular base-pairing interactions to form ring-shaped complexes. The pRNA is a class of non-coding RNA, interacting with phi29 motor proteins to enable DNA packaging. Here, we report a two-piece chimeric pRNA construct that is fully competent in interacting with partner pRNA to form ring-shaped complexes, in packaging DNA via the motor, and in assembling infectious phi29 virions in vitro. This is the first example of a fully functional pRNA assembled using two non-covalently interacting fragments. The results support the notion of modular pRNA architecture in the phi29 packaging motor.

Modular assembly of chimeric phi29 packaging RNAs that support DNA packaging

PubMed Central

Fang, Yun; Shu, Dan; Xiao, Feng; Guo, Peixuan; Qin, Peter Z.

2008-01-01

The bacteriophage phi29 DNA packaging motor is a protein/RNA complex that can produce strong force to condense the linear-double stranded DNA genome into a pre-formed protein capsid. The RNA component, called the packaging RNA (pRNA), utilizes magnesium-dependent intermolecular base-pairing interactions to form ring-shaped complexes. The pRNA is a class of non-coding RNA, interacting with phi29 motor proteins to enable DNA packaging. Here, we report a 2-piece chimeric pRNA construct that is fully competent in interacting with partner pRNA to form ring-shaped complexes, in packaging DNA via the motor, and in assembling infectious phi29 virions in vitro. This is the first example of a fully functional pRNA assembled using two non-covalently interacting fragments. The results support the notion of modular pRNA architecture in the phi29 packaging motor. PMID:18514064

Large dynamic range optical vector analyzer based on optical single-sideband modulation and Hilbert transform

NASA Astrophysics Data System (ADS)

Xue, Min; Pan, Shilong; Zhao, Yongjiu

2016-07-01

A large dynamic range optical vector analyzer (OVA) based on optical single-sideband modulation is proposed and demonstrated. By dividing the optical signal after optical device under test into two paths, reversing the phase of one swept sideband using a Hilbert transformer in one path, and detecting the two signals from the two paths with a balanced photodetector, the measurement errors induced by the residual -1st-order sideband and the high-order sidebands can be eliminated and the dynamic range of the measurement is increased. In a proof-of-concept experiment, the stimulated Brillouin scattering and a fiber Bragg grating are measured by OVAs with and without the Hilbert transform and balanced photodetection. Results show that about 40-dB improvement in the measurement dynamic range is realized by the proposed OVA.

An "unreasonable effectiveness" of Hilbert transform for the transition phase behavior in an Aharonov-Bohm two-path interferometer

NASA Astrophysics Data System (ADS)

Englman, R.

2016-08-01

The recent phase shift data of Takada et al. (Phys. Rev. Lett. 113 (2014) 126601) for a two level system are reconstructed from their current intensity curves by the method of Hilbert transform, for which the underlying Physics is the principle of causality. An introductory algebraic model illustrates pedagogically the working of the method and leads to newly derived relationships involving phenomenological parameters, in particular for the sign of the phase slope between the resonance peaks. While the parametrization of the experimental current intensity data in terms of a few model parameters shows only a qualitative agreement for the phase shift, due to the strong impact of small, detailed variations in the experimental intensity curve on the phase behavior, the numerical Hilbert transform yields a satisfactory reproduction of the phase.

Connes distance function on fuzzy sphere and the connection between geometry and statistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Devi, Yendrembam Chaoba, E-mail: chaoba@bose.res.in; Chakraborty, Biswajit, E-mail: biswajit@bose.res.in; Prajapat, Shivraj, E-mail: shraprajapat@gmail.com

An algorithm to compute Connes spectral distance, adaptable to the Hilbert-Schmidt operatorial formulation of non-commutative quantum mechanics, was developed earlier by introducing the appropriate spectral triple and used to compute infinitesimal distances in the Moyal plane, revealing a deep connection between geometry and statistics. In this paper, using the same algorithm, the Connes spectral distance has been calculated in the Hilbert-Schmidt operatorial formulation for the fuzzy sphere whose spatial coordinates satisfy the su(2) algebra. This has been computed for both the discrete and the Perelemov’s SU(2) coherent state. Here also, we get a connection between geometry and statistics which ismore » shown by computing the infinitesimal distance between mixed states on the quantum Hilbert space of a particular fuzzy sphere, indexed by n ∈ ℤ/2.« less

Semiclassical propagation: Hilbert space vs. Wigner representation

NASA Astrophysics Data System (ADS)

Gottwald, Fabian; Ivanov, Sergei D.

2018-03-01

A unified viewpoint on the van Vleck and Herman-Kluk propagators in Hilbert space and their recently developed counterparts in Wigner representation is presented. Based on this viewpoint, the Wigner Herman-Kluk propagator is conceptually the most general one. Nonetheless, the respective semiclassical expressions for expectation values in terms of the density matrix and the Wigner function are mathematically proven here to coincide. The only remaining difference is a mere technical flexibility of the Wigner version in choosing the Gaussians' width for the underlying coherent states beyond minimal uncertainty. This flexibility is investigated numerically on prototypical potentials and it turns out to provide neither qualitative nor quantitative improvements. Given the aforementioned generality, utilizing the Wigner representation for semiclassical propagation thus leads to the same performance as employing the respective most-developed (Hilbert-space) methods for the density matrix.

An Image Encryption Algorithm Utilizing Julia Sets and Hilbert Curves

PubMed Central

Sun, Yuanyuan; Chen, Lina; Xu, Rudan; Kong, Ruiqing

2014-01-01

Image encryption is an important and effective technique to protect image security. In this paper, a novel image encryption algorithm combining Julia sets and Hilbert curves is proposed. The algorithm utilizes Julia sets’ parameters to generate a random sequence as the initial keys and gets the final encryption keys by scrambling the initial keys through the Hilbert curve. The final cipher image is obtained by modulo arithmetic and diffuse operation. In this method, it needs only a few parameters for the key generation, which greatly reduces the storage space. Moreover, because of the Julia sets’ properties, such as infiniteness and chaotic characteristics, the keys have high sensitivity even to a tiny perturbation. The experimental results indicate that the algorithm has large key space, good statistical property, high sensitivity for the keys, and effective resistance to the chosen-plaintext attack. PMID:24404181

Semiconductor laser self-mixing micro-vibration measuring technology based on Hilbert transform

NASA Astrophysics Data System (ADS)

Tao, Yufeng; Wang, Ming; Xia, Wei

2016-06-01

A signal-processing synthesizing Wavelet transform and Hilbert transform is employed to measurement of uniform or non-uniform vibrations in self-mixing interferometer on semiconductor laser diode with quantum well. Background noise and fringe inclination are solved by decomposing effect, fringe counting is adopted to automatic determine decomposing level, a couple of exact quadrature signals are produced by Hilbert transform to extract vibration. The tempting potential of real-time measuring micro vibration with high accuracy and wide dynamic response bandwidth using proposed method is proven by both simulation and experiment. Advantages and error sources are presented as well. Main features of proposed semiconductor laser self-mixing interferometer are constant current supply, high resolution, simplest optical path and much higher tolerance to feedback level than existing self-mixing interferometers, which is competitive for non-contact vibration measurement.

A modular approach to creating large engineered cartilage surfaces.

PubMed

Ford, Audrey C; Chui, Wan Fung; Zeng, Anne Y; Nandy, Aditya; Liebenberg, Ellen; Carraro, Carlo; Kazakia, Galateia; Alliston, Tamara; O'Connell, Grace D

2018-01-23

Native articular cartilage has limited capacity to repair itself from focal defects or osteoarthritis. Tissue engineering has provided a promising biological treatment strategy that is currently being evaluated in clinical trials. However, current approaches in translating these techniques to developing large engineered tissues remains a significant challenge. In this study, we present a method for developing large-scale engineered cartilage surfaces through modular fabrication. Modular Engineered Tissue Surfaces (METS) uses the well-known, but largely under-utilized self-adhesion properties of de novo tissue to create large scaffolds with nutrient channels. Compressive mechanical properties were evaluated throughout METS specimens, and the tensile mechanical strength of the bonds between attached constructs was evaluated over time. Raman spectroscopy, biochemical assays, and histology were performed to investigate matrix distribution. Results showed that by Day 14, stable connections had formed between the constructs in the METS samples. By Day 21, bonds were robust enough to form a rigid sheet and continued to increase in size and strength over time. Compressive mechanical properties and glycosaminoglycan (GAG) content of METS and individual constructs increased significantly over time. The METS technique builds on established tissue engineering accomplishments of developing constructs with GAG composition and compressive properties approaching native cartilage. This study demonstrated that modular fabrication is a viable technique for creating large-scale engineered cartilage, which can be broadly applied to many tissue engineering applications and construct geometries. Copyright © 2017 Elsevier Ltd. All rights reserved.

Application of Huang-Hilbert Transforms to Geophysical Datasets

NASA Technical Reports Server (NTRS)

Duffy, Dean G.

2003-01-01

The Huang-Hilbert transform is a promising new method for analyzing nonstationary and nonlinear datasets. In this talk I will apply this technique to several important geophysical datasets. To understand the strengths and weaknesses of this method, multi- year, hourly datasets of the sea level heights and solar radiation will be analyzed. Then we will apply this transform to the analysis of gravity waves observed in a mesoscale observational net.

Efficient Asymptotic Preserving Deterministic methods for the Boltzmann Equation

DTIC Science & Technology

2011-04-01

history tracing back to Hilbert , Chapmann and Enskog (Cercignani, 1988) at the beginning of the last century. The mathematical difficulties related to the...accurate determin- istic computations of the stationary solutions, which may be treated by schemes aimed to capture the stationary state ( Greenberg and...Stokes model, can be considered using the Chapmann-Enskog and the Hilbert expansions. We refer to Levermore (1996) for a mathematical setting of the

The Einstein-Hilbert gravitation with minimum length

NASA Astrophysics Data System (ADS)

Louzada, H. L. C.

2018-05-01

We study the Einstein-Hilbert gravitation with the deformed Heisenberg algebra leading to the minimum length, with the intention to find and estimate the corrections in this theory, clarifying whether or not it is possible to obtain, by means of the minimum length, a theory, in D=4, which is causal, unitary and provides a massive graviton. Therefore, we will calculate and analyze the dispersion relationships of the considered theory.

Phage-bacteria infection networks: From nestedness to modularity

NASA Astrophysics Data System (ADS)

Flores, Cesar O.; Valverde, Sergi; Weitz, Joshua S.

2013-03-01

Bacteriophages (viruses that infect bacteria) are the most abundant biological life-forms on Earth. However, very little is known regarding the structure of phage-bacteria infections. In a recent study we re-evaluated 38 prior studies and demonstrated that phage-bacteria infection networks tend to be statistically nested in small scale communities (Flores et al 2011). Nestedness is consistent with a hierarchy of infection and resistance within phages and bacteria, respectively. However, we predicted that at large scales, phage-bacteria infection networks should be typified by a modular structure. We evaluate and confirm this hypothesis using the most extensive study of phage-bacteria infections (Moebus and Nattkemper 1981). In this study, cross-infections were evaluated between 215 marine phages and 286 marine bacteria. We develop a novel multi-scale network analysis and find that the Moebus and Nattkemper (1981) study, is highly modular (at the whole network scale), yet also exhibits nestedness and modularity at the within-module scale. We examine the role of geography in driving these modular patterns and find evidence that phage-bacteria interactions can exhibit strong similarity despite large distances between sites. CFG acknowledges the support of CONACyT Foundation. JSW holds a Career Award at the Scientific Interface from the Burroughs Wellcome Fund and acknowledges the support of the James S. McDonnell Foundation

Direct social perception and dual process theories of mindreading.

PubMed

Herschbach, Mitchell

2015-11-01

The direct social perception (DSP) thesis claims that we can directly perceive some mental states of other people. The direct perception of mental states has been formulated phenomenologically and psychologically, and typically restricted to the mental state types of intentions and emotions. I will compare DSP to another account of mindreading: dual process accounts that posit a fast, automatic "Type 1" form of mindreading and a slow, effortful "Type 2" form. I will here analyze whether dual process accounts' Type 1 mindreading serves as a rival to DSP or whether some Type 1 mindreading can be perceptual. I will focus on Apperly and Butterfill's dual process account of mindreading epistemic states such as perception, knowledge, and belief. This account posits a minimal form of Type 1 mindreading of belief-like states called registrations. I will argue that general dual process theories fit well with a modular view of perception that is considered a kind of Type 1 process. I will show that this modular view of perception challenges and has significant advantages over DSP's phenomenological and psychological theses. Finally, I will argue that if such a modular view of perception is accepted, there is significant reason for thinking Type 1 mindreading of belief-like states is perceptual in nature. This would mean extending the scope of DSP to at least one type of epistemic state. Copyright © 2015 Elsevier Inc. All rights reserved.

BKM Lie superalgebras from dyon spectra in Z N CHL orbifolds for composite N

NASA Astrophysics Data System (ADS)

Govindarajan, Suresh; Gopala Krishna, K.

2010-05-01

We show that the generating function of electrically charged 1/2 -BPS states in mathcal{N} = 4 supersymmetric CHL {mathbb{Z}_N} -orbifolds of the heterotic string on T 6 are given by multiplicative η-products. The η-products are determined by the cycle shape of the corresponding symplectic involution in the dual type II picture. This enables us to complete the construction of the genus-two Siegel modular forms due to David, Jatkar and Sen [arXiv:hep-th/0609109] for {mathbb{Z}_N} -orbifolds when N is non-prime. We study the {mathbb{Z}_4} CHL orbifold in detail and show that the associated Siegel modular forms, {Φ_3}left( mathbb{Z} right) and {widetildeΦ_3}left( mathbb{Z} right) , are given by the square of the product of three even genus-two theta constants. Extending work by us as well as Cheng and Dabholkar, we show that the ‘square roots’ of the two Siegel modular forms appear as the denominator formulae of two distinct Borcherds-Kac-Moody (BKM) Lie superalgebras. The BKM Lie superalgebra associated with the generating function of 1/4 -BPS states, i.e., {widetildeΦ_3}left( mathbb{Z} right) has a parabolic root system with a lightlike Weyl vector and the walls of its fundamental Weyl chamber are mapped to the walls of marginal stability of the 1/4 -BPS states.

Miniature modular microwave end-to-end receiver

NASA Technical Reports Server (NTRS)

Sukamto, Lin M. (Inventor); Cooley, Thomas W. (Inventor); Janssen, Michael A. (Inventor); Parks, Gary S. (Inventor)

1993-01-01

An end-to-end microwave receiver system contained in a single miniature hybrid package mounted on a single heatsink is presented. It includes an input end connected to a microwave receiver antenna and an output end which produces a digital count proportional to the amplitude of a signal of a selected microwave frequency band received at the antenna and corresponding to one of the water vapor absorption lines near frequencies of 20 GHz or 30 GHz. The hybrid package is on the order of several centimeters in length and a few centimeters in height and width. The package includes an L-shaped carrier having a base surface, a vertical wall extending up from the base surface and forming a corner therewith, and connection pins extending through the vertical wall. Modular blocks rest on the base surface against the vertical wall and support microwave monolithic integrated circuits on top surfaces thereof connected to the external connection pins. The modular blocks lie end-to-end on the base surface so as to be modularly removable by sliding along the base surface beneath the external connection pins away from the vertical wall.

MIDEX Advanced Modular and Distributed Spacecraft Avionics Architecture

NASA Technical Reports Server (NTRS)

Ruffa, John A.; Castell, Karen; Flatley, Thomas; Lin, Michael

1998-01-01

MIDEX (Medium Class Explorer) is the newest line in NASA's Explorer spacecraft development program. As part of the MIDEX charter, the MIDEX spacecraft development team has developed a new modular, distributed, and scaleable spacecraft architecture that pioneers new spaceflight technologies and implementation approaches, all designed to reduce overall spacecraft cost while increasing overall functional capability. This resultant "plug and play" system dramatically decreases the complexity and duration of spacecraft integration and test, providing a basic framework that supports spacecraft modularity and scalability for missions of varying size and complexity. Together, these subsystems form a modular, flexible avionics suite that can be modified and expanded to support low-end and very high-end mission requirements with a minimum of redesign, as well as allowing a smooth, continuous infusion of new technologies as they are developed without redesigning the system. This overall approach has the net benefit of allowing a greater portion of the overall mission budget to be allocated to mission science instead of a spacecraft bus. The MIDEX scaleable architecture is currently being manufactured and tested for use on the Microwave Anisotropy Probe (MAP), an inhouse program at GSFC.

Functional complexity emerging from anatomical constraints in the brain: the significance of network modularity and rich-clubs

NASA Astrophysics Data System (ADS)

Zamora-López, Gorka; Chen, Yuhan; Deco, Gustavo; Kringelbach, Morten L.; Zhou, Changsong

2016-12-01

The large-scale structural ingredients of the brain and neural connectomes have been identified in recent years. These are, similar to the features found in many other real networks: the arrangement of brain regions into modules and the presence of highly connected regions (hubs) forming rich-clubs. Here, we examine how modules and hubs shape the collective dynamics on networks and we find that both ingredients lead to the emergence of complex dynamics. Comparing the connectomes of C. elegans, cats, macaques and humans to surrogate networks in which either modules or hubs are destroyed, we find that functional complexity always decreases in the perturbed networks. A comparison between simulated and empirically obtained resting-state functional connectivity indicates that the human brain, at rest, lies in a dynamical state that reflects the largest complexity its anatomical connectome can host. Last, we generalise the topology of neural connectomes into a new hierarchical network model that successfully combines modular organisation with rich-club forming hubs. This is achieved by centralising the cross-modular connections through a preferential attachment rule. Our network model hosts more complex dynamics than other hierarchical models widely used as benchmarks.

Functional complexity emerging from anatomical constraints in the brain: the significance of network modularity and rich-clubs

PubMed Central

Zamora-López, Gorka; Chen, Yuhan; Deco, Gustavo; Kringelbach, Morten L.; Zhou, Changsong

2016-01-01

The large-scale structural ingredients of the brain and neural connectomes have been identified in recent years. These are, similar to the features found in many other real networks: the arrangement of brain regions into modules and the presence of highly connected regions (hubs) forming rich-clubs. Here, we examine how modules and hubs shape the collective dynamics on networks and we find that both ingredients lead to the emergence of complex dynamics. Comparing the connectomes of C. elegans, cats, macaques and humans to surrogate networks in which either modules or hubs are destroyed, we find that functional complexity always decreases in the perturbed networks. A comparison between simulated and empirically obtained resting-state functional connectivity indicates that the human brain, at rest, lies in a dynamical state that reflects the largest complexity its anatomical connectome can host. Last, we generalise the topology of neural connectomes into a new hierarchical network model that successfully combines modular organisation with rich-club forming hubs. This is achieved by centralising the cross-modular connections through a preferential attachment rule. Our network model hosts more complex dynamics than other hierarchical models widely used as benchmarks. PMID:27917958

A modular tooling set-up for incremental sheet forming (ISF) with subsequent stress-relief annealing under partial constraints

NASA Astrophysics Data System (ADS)

Maqbool, Fawad; Bambach, Markus

2017-10-01

Incremental sheet forming (ISF) is a manufacturing process most suitable for small-batch production of sheet metal parts. In ISF, a CNC-controlled tool moves over the sheet metal, following a specified contour to form a part of the desired geometry. This study focuses on one of the dominant process limitations associated with the ISF, i.e., the limited geometrical accuracy. In this regard, a case study is performed which shows that increased geometrical accuracy of the formed part can be achieved by a using stress-relief annealing before unclamping. To keep the tooling costs low, a modular die design consisting of a stiff metal frame and inserts made from inexpensive plastics (Sika®) were devised. After forming, the plastics inserts are removed. The metal frame supports the part during stress-relief annealing. Finite Element (FE) simulations of the manufacturing process are performed. Due to the residual stresses induced during the forming, the geometry of the formed part, from FE simulation and the actual manufacturing process, shows severe distortion upon unclamping the part. Stress relief annealing of the formed part under partial constraints exerted by the tool frame shows that a part with high geometrical accuracy can be obtained.

Geometry and experience: Einstein's 1921 paper and Hilbert's axiomatic system

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Gandt, Francois

2006-06-19

In his 1921 paper Geometrie und Erfahrung, Einstein decribes the new epistemological status of geometry, divorced from any intuitive or a priori content. He calls that 'axiomatics', following Hilbert's theoretical developments on axiomatic systems, which started with the stimulus given by a talk by Hermann Wiener in 1891 and progressed until the Foundations of geometry in 1899. Difficult questions arise: how is a theoretical system related to an intuitive empirical content?.

An Investigation of the Overlap Among Disinhibited Eating Behaviors in Children and Adolescents

DTIC Science & Technology

2013-09-01

findings suggest that emotional eating may be linked with aberrant eating patterns--excess overall energy intake and consumption of high- fat foods-that...overweight and have greater body fat mass than youth who reported no loss of control eating episodes (Ackard, Neumark-Sztainer, Story, & Perry, 2003; Field...reporting loss of control eating consumed more overall energy (Hilbert & Czaja, 2009; Hilbert, et al., 2010), especially from fat and carbohydrate

Inverse Problems and Imaging (Pitman Research Notes in Mathematics Series Number 245)

DTIC Science & Technology

1991-01-01

Multiparamcter spectral theory in Hilbert space functional differential cquations B D Sleeman F Kappel and W Schappacher 24 Mathematical modelling...techniques 49 Sequence spaces R Aris W 11 Ruckle 25 Singular points of smooth mappings 50 Recent contributions to nonlinear C G Gibson partial...of convergence in the central limit T Husain theorem 86 Hamilton-Jacobi equations in Hilbert spaces Peter Hall V Barbu and G Da Prato 63 Solution of

Homogenization via Sequential Projection to Nested Subspaces Spanned by Orthogonal Scaling and Wavelet Orthonormal Families of Functions

DTIC Science & Technology

2008-07-01

operators in Hilbert spaces. The homogenization procedure through successive multi- resolution projections is presented, followed by a numerical example of...is intended to be essentially self-contained. The mathematical ( Greenberg 1978; Gilbert 2006) and signal processing (Strang and Nguyen 1995...literature listed in the references. The ideas behind multi-resolution analysis unfold from the theory of linear operators in Hilbert spaces (Davis 1975

Experimental Test of Nonclassicality for a Single Particle

DTIC Science & Technology

2008-08-01

photon Greenberger -Horne-Zeilinger entanglement,” Nature 403, 515-519 (2000). 15. G. Brida, M. Genovese, C. Novero, and E. Predazzi, “New experimental...33, 34]) and its ability to show that some quantum states in a two dimensional Hilbert space cannot be classical. We note that because this is a...dimensional Hilbert space and a physical implementation of that test. Appendix A necessary requirement for a convincingly realizing the Alicki-Van Ryn’s

Using the Hilbert uniqueness method in a reconstruction algorithm for electrical impedance tomography.

PubMed

Dai, W W; Marsili, P M; Martinez, E; Morucci, J P

1994-05-01

This paper presents a new version of the layer stripping algorithm in the sense that it works essentially by repeatedly stripping away the outermost layer of the medium after having determined the conductivity value in this layer. In order to stabilize the ill posed boundary value problem related to each layer, we base our algorithm on the Hilbert uniqueness method (HUM) and implement it with the boundary element method (BEM).

Quantum Hilbert Hotel.

PubMed

Potoček, Václav; Miatto, Filippo M; Mirhosseini, Mohammad; Magaña-Loaiza, Omar S; Liapis, Andreas C; Oi, Daniel K L; Boyd, Robert W; Jeffers, John

2015-10-16

In 1924 David Hilbert conceived a paradoxical tale involving a hotel with an infinite number of rooms to illustrate some aspects of the mathematical notion of "infinity." In continuous-variable quantum mechanics we routinely make use of infinite state spaces: here we show that such a theoretical apparatus can accommodate an analog of Hilbert's hotel paradox. We devise a protocol that, mimicking what happens to the guests of the hotel, maps the amplitudes of an infinite eigenbasis to twice their original quantum number in a coherent and deterministic manner, producing infinitely many unoccupied levels in the process. We demonstrate the feasibility of the protocol by experimentally realizing it on the orbital angular momentum of a paraxial field. This new non-Gaussian operation may be exploited, for example, for enhancing the sensitivity of NOON states, for increasing the capacity of a channel, or for multiplexing multiple channels into a single one.

Cosmic transit and anisotropic models in f(R,T) gravity

NASA Astrophysics Data System (ADS)

Sahu, S. K.; Tripathy, S. K.; Sahoo, P. K.; Nath, A.

2017-06-01

Accelerating cosmological models are constructed in a modified gravity theory dubbed as $f(R,T)$ gravity at the backdrop of an anisotropic Bianchi type-III universe. $f(R,T)$ is a function of the Ricci scalar $R$ and the trace $T$ of the energy-momentum tensor and it replaces the Ricci scalar in the Einstein-Hilbert action of General Relativity. The models are constructed for two different ways of modification of the Einstein-Hilbert action. Exact solutions of the field equations are obtained by a novel method of integration. We have explored the behaviour of the cosmic transit from an decelerated phase of expansion to an accelerated phase to get the dynamical features of the universe. Within the formalism of the present work, it is found that, the modification of the Einstein-Hilbert action does not affect the scale factor. However the dynamics of the effective dark energy equation of state is significantly affected.

Spectral Automorphisms in Quantum Logics

NASA Astrophysics Data System (ADS)

Ivanov, Alexandru; Caragheorgheopol, Dan

2010-12-01

In quantum mechanics, the Hilbert space formalism might be physically justified in terms of some axioms based on the orthomodular lattice (OML) mathematical structure (Piron in Foundations of Quantum Physics, Benjamin, Reading, 1976). We intend to investigate the extent to which some fundamental physical facts can be described in the more general framework of OMLs, without the support of Hilbert space-specific tools. We consider the study of lattice automorphisms properties as a “substitute” for Hilbert space techniques in investigating the spectral properties of observables. This is why we introduce the notion of spectral automorphism of an OML. Properties of spectral automorphisms and of their spectra are studied. We prove that the presence of nontrivial spectral automorphisms allow us to distinguish between classical and nonclassical theories. We also prove, for finite dimensional OMLs, that for every spectral automorphism there is a basis of invariant atoms. This is an analogue of the spectral theorem for unitary operators having purely point spectrum.

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

NASA Astrophysics Data System (ADS)

Simon, R.; Mukunda, N.; Chaturvedi, S.; Srinivasan, V.

2008-11-01

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Liquid identification by Hilbert spectroscopy

NASA Astrophysics Data System (ADS)

Lyatti, M.; Divin, Y.; Poppe, U.; Urban, K.

2009-11-01

Fast and reliable identification of liquids is of great importance in, for example, security, biology and the beverage industry. An unambiguous identification of liquids can be made by electromagnetic measurements of their dielectric functions in the frequency range of their main dispersions, but this frequency range, from a few GHz to a few THz, is not covered by any conventional spectroscopy. We have developed a concept of liquid identification based on our new Hilbert spectroscopy and high- Tc Josephson junctions, which can operate at the intermediate range from microwaves to THz frequencies. A demonstration setup has been developed consisting of a polychromatic radiation source and a compact Hilbert spectrometer integrated in a Stirling cryocooler. Reflection polychromatic spectra of various bottled liquids have been measured at the spectral range of 15-300 GHz with total scanning time down to 0.2 s and identification of liquids has been demonstrated.

Independence and totalness of subspaces in phase space methods

NASA Astrophysics Data System (ADS)

Vourdas, A.

2018-04-01

The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the non-distributivity of the lattice of subspaces, there are various levels of independence, from pairwise independence up to (full) independence. Pairwise totalness, totalness and other intermediate concepts are also introduced, which roughly express that the subspaces overlap strongly among themselves, and they cover the full Hilbert space. A duality between independence and totalness, that involves orthocomplementation (logical NOT operation), is discussed. Another approach to independence is also studied, using Rota's formalism on independent partitions of the Hilbert space. This is used to define informational independence, which is proved to be equivalent to independence. As an application, the pentagram (used in discussions on contextuality) is analysed using these concepts.

Diurnal characteristics of turbulent intermittency in the Taklimakan Desert

NASA Astrophysics Data System (ADS)

Wei, Wei; Wang, Minzhong; Zhang, Hongsheng; He, Qing; Ali, Mamtimin; Wang, Yinjun

2017-12-01

A case study is performed to investigate the behavior of turbulent intermittency in the Taklimakan Desert using an intuitive, direct, and adaptive method, the arbitrary-order Hilbert spectral analysis (arbitrary-order HSA). Decomposed modes from the vertical wind speed series confirm the dyadic filter-bank essence of the empirical mode decomposition processes. Due to the larger eddies in the CBL, higher energy modes occur during the day. The second-order Hilbert spectra L2 (ω ) delineate the spectral gap separating fine-scale turbulence from large-scale motions. Both the values of kurtosis and the Hilbert-based scaling exponent ξ ( q ) reveal that the turbulence intermittency at night is much stronger than that during the day, and the stronger intermittency is associated with more stable stratification under clear-sky conditions. This study fills the gap in the characteristics of turbulence intermittency in the Taklimakan Desert area using a relatively new method.

Toward the Modularization of Decision Support Systems

NASA Astrophysics Data System (ADS)

Raskin, R. G.

2009-12-01

Decision support systems are typically developed entirely from scratch without the use of modular components. This “stovepiped” approach is inefficient and costly because it prevents a developer from leveraging the data, models, tools, and services of other developers. Even when a decision support component is made available, it is difficult to know what problem it solves, how it relates to other components, or even that the component exists, The Spatial Decision Support (SDS) Consortium was formed in 2008 to organize the body of knowledge in SDS within a common portal. The portal identifies the canonical steps in the decision process and enables decision support components to be registered, categorized, and searched. This presentation describes how a decision support system can be assembled from modular models, data, tools and services, based on the needs of the Earth science application.

Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous-variable systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adesso, Gerardo; CNR-INFM Coherentia , Naples; Grup d'Informacio Quantica, Universitat Autonoma de Barcelona, E-08193 Bellaterra

2007-08-15

Quantum mechanics imposes 'monogamy' constraints on the sharing of entanglement. We show that, despite these limitations, entanglement can be fully 'promiscuous', i.e., simultaneously present in unlimited two-body and many-body forms in states living in an infinite-dimensional Hilbert space. Monogamy just bounds the divergence rate of the various entanglement contributions. This is demonstrated in simple families of N-mode (N{>=}4) Gaussian states of light fields or atomic ensembles, which therefore enable infinitely more freedom in the distribution of information, as opposed to systems of individual qubits. Such a finding is of importance for the quantification, understanding, and potential exploitation of shared quantummore » correlations in continuous variable systems. We discuss how promiscuity gradually arises when considering simple families of discrete variable states, with increasing Hilbert space dimension towards the continuous variable limit. Such models are somehow analogous to Gaussian states with asymptotically diverging, but finite, squeezing. In this respect, we find that non-Gaussian states (which in general are more entangled than Gaussian states) exhibit also the interesting feature that their entanglement is more shareable: in the non-Gaussian multipartite arena, unlimited promiscuity can be already achieved among three entangled parties, while this is impossible for Gaussian, even infinitely squeezed states.« less

Terahertz Josephson spectral analysis and its applications

NASA Astrophysics Data System (ADS)

Snezhko, A. V.; Gundareva, I. I.; Lyatti, M. V.; Volkov, O. Y.; Pavlovskiy, V. V.; Poppe, U.; Divin, Y. Y.

2017-04-01

Principles of Hilbert-transform spectral analysis (HTSA) are presented and advantages of the technique in the terahertz (THz) frequency range are discussed. THz HTSA requires Josephson junctions with high values of characteristic voltages I c R n and dynamics described by a simple resistively shunted junction (RSJ) model. To meet these requirements, [001]- and [100]-tilt YBa2Cu3O7-x bicrystal junctions with deviations from the RSJ model less than 1% have been developed. Demonstrators of Hilbert-transform spectrum analyzers with various cryogenic environments, including integration into Stirling coolers, are described. Spectrum analyzers have been characterized in the spectral range from 50 GHz to 3 THz. Inside a power dynamic range of five orders, an instrumental function of the analyzers has been found to have a Lorentz form around a single frequency of 1.48 THz with a spectral resolution as low as 0.9 GHz. Spectra of THz radiation from optically pumped gas lasers and semiconductor frequency multipliers have been studied with these spectrum analyzers and the regimes of these radiation sources were optimized for a single-frequency operation. Future applications of HTSA will be related with quick and precise spectral characterization of new radiation sources and identification of substances in the THz frequency range.

Links between quantum physics and thought.

PubMed

Robson, Barry

2009-01-01

Quantum mechanics (QM) provides a variety of ideas that can assist in developing Artificial Intelligence for healthcare, and opens the possibility of developing a unified system of Best Practice for inference that will embrace both QM and classical inference. Of particular interest is inference in the hyperbolic-complex plane, the counterpart of the normal i-complex plane of basic QM. There are two reasons. First, QM appears to rotate from i-complex Hilbert space to hyperbolic-complex descriptions when observations are made on wave functions as particles, yielding classical results, and classical laws of probability manipulation (e.g. the law of composition of probabilities) then hold, whereas in the i-complex plane they do not. Second, i-complex Hilbert space is not the whole story in physics. Hyperbolic complex planes arise in extension from the Dirac-Clifford calculus to particle physics, in relativistic correction thereby, and in regard to spinors and twisters. Generalization of these forms resemble grammatical constructions and promote the idea that probability-weighted algebraic elements can be used to hold dimensions of syntactic and semantic meaning. It is also starting to look as though when a solution is reached by an inference system in the hyperbolic-complex, the hyperbolic-imaginary values disappear, while conversely hyperbolic-imaginary values are associated with the un-queried state of a system and goal seeking behavior.

Topics in spectral methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1985-01-01

After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

Dynamics in the Decompositions Approach to Quantum Mechanics

NASA Astrophysics Data System (ADS)

Harding, John

2017-12-01

In Harding (Trans. Amer. Math. Soc. 348(5), 1839-1862 1996) it was shown that the direct product decompositions of any non-empty set, group, vector space, and topological space X form an orthomodular poset Fact X. This is the basis for a line of study in foundational quantum mechanics replacing Hilbert spaces with other types of structures. Here we develop dynamics and an abstract version of a time independent Schrödinger's equation in the setting of decompositions by considering representations of the group of real numbers in the automorphism group of the orthomodular poset Fact X of decompositions.

String inspired brane world cosmology.

PubMed

Germani, Cristiano; Sopuerta, Carlos F

2002-06-10

We consider brane world scenarios including the leading correction to the Einstein-Hilbert action suggested by superstring theory, the Gauss-Bonnet term. We obtain and study the complete set of equations governing the cosmological dynamics. We find they have the same form as those in Randall-Sundrum scenarios but with time-varying four-dimensional gravitational and cosmological constants. By studying the bulk geometry we show that this variation is produced by bulk curvature terms parametrized by the mass of a black hole. Finally, we show there is a coupling between these curvature terms and matter that can be relevant for early universe cosmology.

Universal Local Symmetries and Nonsuperposition in Classical Mechanics

NASA Astrophysics Data System (ADS)

Gozzi, Ennio; Pagani, Carlo

2010-10-01

In the Hilbert space formulation of classical mechanics, pioneered by Koopman and von Neumann, there are potentially more observables than in the standard approach to classical mechanics. In this Letter, we show that actually many of those extra observables are not invariant under a set of universal local symmetries which appear once the Koopman and von Neumann formulation is extended to include the evolution of differential forms. Because of their noninvariance, those extra observables have to be removed. This removal makes the superposition of states in the Koopman and von Neumann formulation, and as a consequence also in classical mechanics, impossible.

Simple derivation of the Lindblad equation

NASA Astrophysics Data System (ADS)

Pearle, Philip

2012-07-01

The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is ‘simple’ in that all it uses is the expression of a Hermitian matrix in terms of its orthonormal eigenvectors and real eigenvalues. Thus, it is appropriate for students who have learned the algebra of quantum theory. Where helpful, arguments are first given in a two-dimensional Hilbert space.

Modular, Adaptive, Reconfigurable Systems: Technology for Sustainable, Reliable, Effective, and Affordable Space Exploration

NASA Technical Reports Server (NTRS)

Esper, Jaime

2004-01-01

In order to execute the Vision for Space Exploration, we must find ways to reduce cost, system complexity, design, build, and test times, and at the same time increase flexibility to satisfy multiple functions. Modular, Adaptive, Reconfigurable System (MARS) technologies promise to set the stage for the delivery of system elements that form the building blocks of increasingly ambitious missions involving humans and robots. Today, space systems are largely specialized and built on a case-by-case basis. The notion of modularity however, is nothing new to NASA. The 1970's saw the development of the Multi-Mission Modular spacecraft (MMS). From 1980 to 1992 at least six satellites were built under this paradigm, and included such Goddard Space Flight Center missions as SSM, EUVE, UARS, and Landsat 4 and 5. Earlier versions consisted of standard subsystem "module" or "box" components that could be replaced within a structure based on predefined form factors. Although the primary motivation for MMS was faster/cheaper integration and test, standardization of interfaces, and ease of incorporating new subsystem technology, it lacked the technology maturity and programmatic "upgrade infrastructure" needed to satisfy varied mission requirements, and ultimately it lacked user buy-in. Consequently, it never evolved and was phased out. Such concepts as the Rapid Spacecraft Development Office (RSDO) with its regularly updated catalogue of prequalified busses became the preferred method for acquiring satellites. Notwithstanding, over the past 30 years since MMS inception, technology has advanced considerably and now modularity can be extended beyond the traditional MMS module or box to cover levels of integration, from the chip, card, box, subsystem, to the space system and to the system-of-systems. This paper will present the MARS architecture, cast within the historical context of MMS. Its application will be highlighted by comparing a state-of-the-art point design vs. a MARS-enabled lunar mission, as a representative robotic case design.

Modular, Adaptive, Reconfigurable Systems: Technology for Sustainable, Reliable, Effective, and Affordable Space Exploration

NASA Astrophysics Data System (ADS)

Esper, Jaime

2005-02-01

In order to execute the Vision for Space Exploration, we must find ways to reduce cost, system complexity, design, build, and test times, and at the same time increase flexibility to satisfy multiple functions. Modular, Adaptive, Reconfigurable System (MARS) technologies promise to set the stage for the delivery of system elements that form the building blocks of increasingly ambitious missions involving humans and robots. Today, space systems are largely specialized and built on a case-by-case basis. The notion of modularity however, is nothing new to NASA. The 1970's saw the development of the Multi-Mission Modular spacecraft (MMS). From 1980 to 1992 at least six satellites were built under this paradigm, and included such Goddard Space Flight Center missions as SSM, EUVE, UARS, and Landsat 4 and 5. Earlier versions consisted of standard subsystem ``module'' or ``box'' components that could be replaced within a structure based on predefined form factors. Although the primary motivation for MMS was faster/cheaper integration and test, standardization of interfaces, and ease of incorporating new subsystem technology, it lacked the technology maturity and programmatic ``upgrade infrastructure'' needed to satisfy varied mission requirements, and ultimately it lacked user buy-in. Consequently, it never evolved and was phased out. Such concepts as the Rapid Spacecraft Development Office (RSDO) with its regularly updated catalogue of pre-qualified busses became the preferred method for acquiring satellites. Notwithstanding, over the past 30 years since MMS inception, technology has advanced considerably and now modularity can be extended beyond the traditional MMS module or box to cover levels of integration, from the chip, card, box, subsystem, to the space system and to the system-of-systems. This paper will present the MARS architecture, cast within the historical context of MMS. Its application will be highlighted by comparing a state-of-the-art point design vs. a MARS-enabled lunar mission, as a representative robotic case design.

Critical 2-D Percolation: Crossing Probabilities, Modular Forms and Factorization

NASA Astrophysics Data System (ADS)

Kleban, Peter

2007-03-01

We first consider crossing probabilities in critical 2-D percolation in rectangular geometries, derived via conformal field theory. These quantities are shown to exhibit interesting modular behavior [1], although the physical meaning of modular transformations in this context is not clear. We show that in many cases these functions are completely characterized by very simple transformation properties. In particular, Cardy's function for the percolation crossing probability (including the conformal dimension 1/3), follows from a simple modular argument. We next consider the probability of crossing between various points for percolation in the upper half-plane. For two points, with the point x an edge of the system, the probability is P(x,z)= k 1y^5/48 φ(x,z)^1/3 where φ is the potential at z of a 2-D dipole located at x, and k is a non-universal constant. For three points, one finds the exact and universal factorization [2,3] P(x1,x2,z)= C ; √P(x1,z)P(x2,z)P(x1,x2) with C= 8 √2; &5/2circ;3^3/4 ; γ(1/3)^9/2. These results are calculated by use of conformal field theory. Computer simulations verify them very precisely. Furthermore, simulations show that the same factorization holds asymptotically, with the same value of C, when one or both of the points xi are moved from the edge into the bulk.1.) Peter Kleban and Don Zagier, Crossing probabilities and modular forms, J. Stat. Phys. 113, 431-454 (2003) [arXiv: math-ph/0209023].2.) Peter Kleban, Jacob J. H. Simmons, and Robert M. Ziff, Anchored critical percolation clusters and 2-d electrostatics, Phys. Rev. Letters 97,115702 (2006) [arXiv: cond-mat/0605120].3.) Jacob J. H. Simmons and Peter Kleban, in preparation.

A rigorous approach to the formulation of extended Born-Oppenheimer equation for a three-state system

NASA Astrophysics Data System (ADS)

Sarkar, Biplab; Adhikari, Satrajit

If a coupled three-state electronic manifold forms a sub-Hilbert space, it is possible to express the non-adiabatic coupling (NAC) elements in terms of adiabatic-diabatic transformation (ADT) angles. Consequently, we demonstrate: (a) Those explicit forms of the NAC terms satisfy the Curl conditions with non-zero Divergences; (b) The formulation of extended Born-Oppenheimer (EBO) equation for any three-state BO system is possible only when there exists coordinate independent ratio of the gradients for each pair of ADT angles leading to zero Curls at and around the conical intersection(s). With these analytic advancements, we formulate a rigorous EBO equation and explore its validity as well as necessity with respect to the approximate one (Sarkar and Adhikari, J Chem Phys 2006, 124, 074101) by performing numerical calculations on two different models constructed with different chosen forms of the NAC elements.

Modeling and Control of Large Flexible Structures.

DTIC Science & Technology

1984-07-31

59 4.5 Spectral factorization using the Hilbert transform 62 4.6 Gain computations 64 4.7 Software development and control system performance 66 Part...in the Hilbert space - L2(S) with the natural inner product, ,>. In many cases A O has a discrete spectrum with associated 2 eigenfunctions which...Davis and Barry 1977) ( Greenberg , MacCamy Nisel and 1968). The natural boundary~.; ’? , : conditions for (17) are in terms of s(zt) at s-O and 1

Multirate Integration Properties of Waveform Relaxation with Applications to Circuit Simulation and Parallel Computation

DTIC Science & Technology

1985-11-18

Greenberg and K. Sakallah at Digital Equipment Corporation, and C-F. Chen, L Nagel, and P. ,. Subrahmanyam at AT&T Bell Laboratories, both for providing...Circuit Theory McGraw-Hill, 1969. [37] R. Courant and D. Hilbert , Partial Differential Equations, Vol. 2 of Methods of Mathematical Physics...McGraw-Hill, N.Y., 1965. Page 161 [44) R. Courant and D. Hilbert , Partial Differential Equations, Vol. 2 of Methods of Mathematical Physics

Filter distortion effects on telemetry signal-to-noise ratio

NASA Technical Reports Server (NTRS)

Sadr, R.; Hurd, W.

1987-01-01

The effect of filtering on the Signal-to-Noise Ratio (SNR) of a coherently demodulated band-limited signal is determined in the presence of worse-case amplitude ripple. The problem is formulated mathematically as an optimization problem in the L2-Hilbert space. The form of the worst-cast amplitude ripple is specified, and the degradation in the SNR is derived in a closed form expression. It is shown that when the maximum passband amplitude ripple is 2 delta (peak to peak), the SNR is degraded by at most (1 - delta squared), even when the ripple is unknown or uncompensated. For example, an SNR loss of less than 0.01 dB due to amplitude ripple can be assured by keeping the amplitude ripple to under 0.42 dB.

Fredholm-Volterra Integral Equation with a Generalized Singular Kernel and its Numerical Solutions

NASA Astrophysics Data System (ADS)

El-Kalla, I. L.; Al-Bugami, A. M.

2010-11-01

In this paper, the existence and uniqueness of solution of the Fredholm-Volterra integral equation (F-VIE), with a generalized singular kernel, are discussed and proved in the spaceL2(Ω)×C(0,T). The Fredholm integral term (FIT) is considered in position while the Volterra integral term (VIT) is considered in time. Using a numerical technique we have a system of Fredholm integral equations (SFIEs). This system of integral equations can be reduced to a linear algebraic system (LAS) of equations by using two different methods. These methods are: Toeplitz matrix method and Product Nyström method. A numerical examples are considered when the generalized kernel takes the following forms: Carleman function, logarithmic form, Cauchy kernel, and Hilbert kernel.

Development of an optical character recognition pipeline for handwritten form fields from an electronic health record.

PubMed

Rasmussen, Luke V; Peissig, Peggy L; McCarty, Catherine A; Starren, Justin

2012-06-01

Although the penetration of electronic health records is increasing rapidly, much of the historical medical record is only available in handwritten notes and forms, which require labor-intensive, human chart abstraction for some clinical research. The few previous studies on automated extraction of data from these handwritten notes have focused on monolithic, custom-developed recognition systems or third-party systems that require proprietary forms. We present an optical character recognition processing pipeline, which leverages the capabilities of existing third-party optical character recognition engines, and provides the flexibility offered by a modular custom-developed system. The system was configured and run on a selected set of form fields extracted from a corpus of handwritten ophthalmology forms. The processing pipeline allowed multiple configurations to be run, with the optimal configuration consisting of the Nuance and LEADTOOLS engines running in parallel with a positive predictive value of 94.6% and a sensitivity of 13.5%. While limitations exist, preliminary experience from this project yielded insights on the generalizability and applicability of integrating multiple, inexpensive general-purpose third-party optical character recognition engines in a modular pipeline.

Development of an optical character recognition pipeline for handwritten form fields from an electronic health record

PubMed Central

Peissig, Peggy L; McCarty, Catherine A; Starren, Justin

2011-01-01

Background Although the penetration of electronic health records is increasing rapidly, much of the historical medical record is only available in handwritten notes and forms, which require labor-intensive, human chart abstraction for some clinical research. The few previous studies on automated extraction of data from these handwritten notes have focused on monolithic, custom-developed recognition systems or third-party systems that require proprietary forms. Methods We present an optical character recognition processing pipeline, which leverages the capabilities of existing third-party optical character recognition engines, and provides the flexibility offered by a modular custom-developed system. The system was configured and run on a selected set of form fields extracted from a corpus of handwritten ophthalmology forms. Observations The processing pipeline allowed multiple configurations to be run, with the optimal configuration consisting of the Nuance and LEADTOOLS engines running in parallel with a positive predictive value of 94.6% and a sensitivity of 13.5%. Discussion While limitations exist, preliminary experience from this project yielded insights on the generalizability and applicability of integrating multiple, inexpensive general-purpose third-party optical character recognition engines in a modular pipeline. PMID:21890871

Ectoparasites and endoparasites of fish form networks with different structures.

PubMed

Bellay, S; DE Oliveira, E F; Almeida-Neto, M; Mello, M A R; Takemoto, R M; Luque, J L

2015-06-01

Hosts and parasites interact with each other in a variety of ways, and this diversity of interactions is reflected in the networks they form. To test for differences in interaction patterns of ecto- and endoparasites we analysed subnetworks formed by each kind of parasites and their host fish species in fish-parasite networks for 22 localities. We assessed the proportion of parasite species per host species, the relationship between parasite fauna composition and host taxonomy, connectance, nestedness and modularity of each subnetwork (n = 44). Furthermore, we evaluated the similarity in host species composition among modules in ecto- and endoparasite subnetworks. We found several differences between subnetworks of fish ecto- and endoparasites. The association with a higher number of host species observed among endoparasites resulted in higher connectance and nestedness, and lower values of modularity in their subnetworks than in those of ectoparasites. Taxonomically related host species tended to share ecto- or endoparasites with the same interaction intensity, but the species composition of hosts tended to differ between modules formed by ecto- and endoparasites. Our results suggest that different evolutionary and ecological processes are responsible for organizing the networks formed by ecto- and endoparasites and fish.

Coarse graining of entanglement classes in 2 ×m ×n systems

NASA Astrophysics Data System (ADS)

Hebenstreit, M.; Gachechiladze, M.; Gühne, O.; Kraus, B.

2018-03-01

We consider three-partite pure states in the Hilbert space C2⊗Cm⊗Cn and investigate to which states a given state can be locally transformed with a nonvanishing probability. Whenever the initial and final states are elements of the same Hilbert space, the problem can be solved via the characterization of the entanglement classes which are determined via stochastic local operations and classical communication (SLOCC). In the particular case considered here, the matrix pencil theory can be utilized to address this point. In general, there are infinitely many SLOCC classes. However, when considering transformations from higher to lower dimensional Hilbert spaces, an additional hierarchy among the classes can be found. This hierarchy of SLOCC classes coarse grains SLOCC classes which can be reached from a common resource state of higher dimension. We first show that a generic set of states in C2⊗Cm⊗Cn for n =m is the union of infinitely many SLOCC classes, which can be parameterized by m -3 parameters. However, for n ≠m there exists a single SLOCC class which is generic. Using this result, we then show that there is a full-measure set of states in C2⊗Cm⊗Cn such that any state within this set can be transformed locally to a full measure set of states in any lower dimensional Hilbert space. We also investigate resource states, which can be transformed to any state (not excluding any zero-measure set) in the smaller dimensional Hilbert space. We explicitly derive a state in C2⊗Cm⊗C2 m -2 which is the optimal common resource of all states in C2⊗Cm⊗Cm . We also show that for any n <2 m it is impossible to reach all states in C2⊗Cm⊗Cn ˜ whenever n ˜>m .

Improving 3d Spatial Queries Search: Newfangled Technique of Space Filling Curves in 3d City Modeling

NASA Astrophysics Data System (ADS)

Uznir, U.; Anton, F.; Suhaibah, A.; Rahman, A. A.; Mioc, D.

2013-09-01

The advantages of three dimensional (3D) city models can be seen in various applications including photogrammetry, urban and regional planning, computer games, etc.. They expand the visualization and analysis capabilities of Geographic Information Systems on cities, and they can be developed using web standards. However, these 3D city models consume much more storage compared to two dimensional (2D) spatial data. They involve extra geometrical and topological information together with semantic data. Without a proper spatial data clustering method and its corresponding spatial data access method, retrieving portions of and especially searching these 3D city models, will not be done optimally. Even though current developments are based on an open data model allotted by the Open Geospatial Consortium (OGC) called CityGML, its XML-based structure makes it challenging to cluster the 3D urban objects. In this research, we propose an opponent data constellation technique of space-filling curves (3D Hilbert curves) for 3D city model data representation. Unlike previous methods, that try to project 3D or n-dimensional data down to 2D or 3D using Principal Component Analysis (PCA) or Hilbert mappings, in this research, we extend the Hilbert space-filling curve to one higher dimension for 3D city model data implementations. The query performance was tested using a CityGML dataset of 1,000 building blocks and the results are presented in this paper. The advantages of implementing space-filling curves in 3D city modeling will improve data retrieval time by means of optimized 3D adjacency, nearest neighbor information and 3D indexing. The Hilbert mapping, which maps a subinterval of the [0, 1] interval to the corresponding portion of the d-dimensional Hilbert's curve, preserves the Lebesgue measure and is Lipschitz continuous. Depending on the applications, several alternatives are possible in order to cluster spatial data together in the third dimension compared to its clustering in 2D.

Differentiable representations of finite dimensional Lie groups in rigged Hilbert spaces

NASA Astrophysics Data System (ADS)

Wickramasekara, Sujeewa

The inceptive motivation for introducing rigged Hilbert spaces (RHS) in quantum physics in the mid 1960's was to provide the already well established Dirac formalism with a proper mathematical context. It has since become clear, however, that this mathematical framework is lissome enough to accommodate a class of solutions to the dynamical equations of quantum physics that includes some which are not possible in the normative Hilbert space theory. Among the additional solutions, in particular, are those which describe aspects of scattering and decay phenomena that have eluded the orthodox quantum physics. In this light, the RHS formulation seems to provide a mathematical rubric under which various phenomenological observations and calculational techniques, commonly known in the study of resonance scattering and decay as ``effective theories'' (e.g., the Wigner- Weisskopf method), receive a unified theoretical foundation. These observations lead to the inference that a theory founded upon the RHS mathematics may prove to be of better utility and value in understanding quantum physical phenomena. This dissertation primarily aims to contribute to the general formalism of the RHS theory of quantum mechanics by undertaking a study of differentiable representations of finite dimensional Lie groups. In particular, it is shown that a finite dimensional operator Lie algebra G in a rigged Hilbert space can be always integrated, provided one parameter integrability holds true for the elements of any basis for G . This result differs from and extends the well known integration theorem of E. Nelson and the subsequent works of others on unitary representations in that it does not require any assumptions on the existence of analytic vectors. Also presented here is a construction of a particular rigged Hilbert space of Hardy class functions that appears useful in formulating a relativistic version of the RHS theory of resonances and decay. As a contexture for the construction, a synopsis of the new relativistic theory is presented.

Modularity and hierarchical organization of action programs in children's acquisition of graphic skills.

PubMed

Manoel, Edison de J; Dantas, Luiz; Gimenez, Roberto; de Oliveira, Dalton Lustosa

2011-10-01

The organization of actions is based on modules in memory as a result of practice, easing the demand of performing more complex actions. If this modularization occurs, the elements of the module must remain invariant in new tasks. To test this hypothesis, 35 children, age 10 yr., practiced a graphic criterion task on a digital tablet and completed a complex graphic task enclosing the previous one. Total movement and pause times to draw the figure indicated skill acquisition. A module was identified by the variability of relative timing, pause time, and sequencing. Total movement to perform the criterion task did not increase significantly when it was embedded in the more complex task. Modularity was evidenced by the stability of relative timing and pause time and sequencing. The spatial position of new elements did not perturb the module, so the grammar of action may still have been forming.

100-kA vacuum current breaker of a modular design

NASA Astrophysics Data System (ADS)

Ivanov, V. P.; Vozdvijenskii, V. A.; Jagnov, V. A.; Solodovnikov, S. G.; Mazulin, A. V.; Ryjkov, V. M.

1994-05-01

Direct current breaker of a modular design is developed for the strong field tokamak power supply system. The power supply system comprises four 800 MW alternative current generators with 4 GJ flywheels, thyristor rectifiers providing inductive stores pumping by a current up to 100 kA for 1 - 4 sec. To form current pulses of various shapes in the tokamak windings current breakers are used with either pneumatic or explosive drive, at a current switching synchronously of not worse than 100 mks. Current breakers of these types require that the current conducting elements be replaced after each shot. For recent years vacuum arc quenching chambers with an axial magnetic field are successfully employed as repetitive performance current breakers, basically for currents up to 40 kA. In the report some results of researches of a vacuum switch modular are presented which we used as prototype switch for currents of the order of 100 kA.

Space Station

NASA Image and Video Library

1972-01-01

This is an artist's concept of a modular space station. In 1970 the Marshall Space Flight Center arnounced the completion of a study concerning a modular space station that could be launched by the planned-for reusable Space Shuttle. The study envisioned a space station composed of cylindrical sections 14 feet in diameter and of varying lengths joined to form any one of a number of possible shapes. The sections were restricted to 14 feet in diameter and 58 feet in length to be consistent with a shuttle cargo bay size of 15 by 60 feet. Center officials said that the first elements of the space station could be in orbit by about 1978 and could be manned by three or six men. This would be an interim space station with sections that could be added later to form a full 12-man station by the early 1980s.

Animal social networks as substrate for cultural behavioural diversity.

PubMed

Whitehead, Hal; Lusseau, David

2012-02-07

We used individual-based stochastic models to examine how social structure influences the diversity of socially learned behaviour within a non-human population. For continuous behavioural variables we modelled three forms of dyadic social learning, averaging the behavioural value of the two individuals, random transfer of information from one individual to the other, and directional transfer from the individual with highest behavioural value to the other. Learning had potential error. We also examined the transfer of categorical behaviour between individuals with random directionality and two forms of error, the adoption of a randomly chosen existing behavioural category or the innovation of a new type of behaviour. In populations without social structuring the diversity of culturally transmitted behaviour increased with learning error and population size. When the populations were structured socially either by making individuals members of permanent social units or by giving them overlapping ranges, behavioural diversity increased with network modularity under all scenarios, although the proportional increase varied considerably between continuous and categorical behaviour, with transmission mechanism, and population size. Although functions of the form e(c)¹(m)⁻(c)² + (c)³(Log(N)) predicted the mean increase in diversity with modularity (m) and population size (N), behavioural diversity could be highly unpredictable both between simulations with the same set of parameters, and within runs. Errors in social learning and social structuring generally promote behavioural diversity. Consequently, social learning may be considered to produce culture in populations whose social structure is sufficiently modular. Copyright © 2011 Elsevier Ltd. All rights reserved.

Separability and Entanglement in the Hilbert Space Reference Frames Related Through the Generic Unitary Transform for Four Level System

NASA Astrophysics Data System (ADS)

Man'ko, V. I.; Markovich, L. A.

2018-02-01

Quantum correlations in the state of four-level atom are investigated by using generic unitary transforms of the classical (diagonal) density matrix. Partial cases of pure state, X-state, Werner state are studied in details. The geometrical meaning of unitary Hilbert reference-frame rotations generating entanglement in the initially separable state is discussed. Characteristics of the entanglement in terms of concurrence, entropy and negativity are obtained as functions of the unitary matrix rotating the reference frame.

The Ostrovsky-Vakhnenko equation by a Riemann-Hilbert approach

NASA Astrophysics Data System (ADS)

Boutet de Monvel, Anne; Shepelsky, Dmitry

2015-01-01

We present an inverse scattering transform (IST) approach for the (differentiated) Ostrovsky-Vakhnenko equation This equation can also be viewed as the short wave model for the Degasperis-Procesi (sDP) equation. Our IST approach is based on an associated Riemann-Hilbert problem, which allows us to give a representation for the classical (smooth) solution, to get the principal term of its long time asymptotics, and also to describe loop soliton solutions. Dedicated to Johannes Sjöstrand with gratitude and admiration.

Transactions of the Army Conference on Applied Mathematics and Computing (2nd) Held at Washington, DC on 22-25 May 1984

DTIC Science & Technology

1985-02-01

0 Here Q denotes the midplane of the plate ?assumed to be a Lipschitzian) with a smooth boundary ", and H (Q) and H (Q) are the Hilbert spaces of...using a reproducing kernel Hilbert space approach, Weinert [8,9] et al, developed a structural correspondence between spline interpolation and linear...597 A Mesh Moving Technique for Time Dependent Partial Differential Equations in Two Space Dimensions David C. Arney and Joseph

Global Bifurcation of Periodic Solutions with Symmetry,

DTIC Science & Technology

1987-07-01

C4-family of sectorial operators on a real Hilbert (2.32.a) space X, with dense domain D(A(A)) which is independent of A E E, and with compact...Vanl, theorem 2.5.91. If .F and E’ are both Hilbert spaces with orthogonal action of r, we may drop the assumption that 1 is compact. Just take...some meandering. Let us define a limit for any sequence Si of subsets of some metric space . Following Whyburn [Why], we define lir sup Si {z: z

Weak Solution Classes for Parabolic Integro-Differential Equations

DTIC Science & Technology

1982-09-01

different existence argument for solutions of (I). It is partly based on a method that was used in (2) and (6] to treat a Hilbert - space version of (I) and...xx Differential Equations 35 (1980), 200-231. 121 V. Barbut Integro-Oifferential Squatton. in Hilbert Spaces. Ann. St. Univ. *Al. 1. Cuaxa 19 (1973... Greenberg : O,% the Existence, Uniqueness, and stability of the Equation 00 Xtt - 3(XX)X) AX *x . J Math. Anal. Appl. 25 (1969), S75-591. (131 7

Effect of Hilbert space truncation on Anderson localization

NASA Astrophysics Data System (ADS)

Krishna, Akshay; Bhatt, R. N.

2018-05-01

The 1D Anderson model possesses a completely localized spectrum of eigenstates for all values of the disorder. We consider the effect of projecting the Hamiltonian to a truncated Hilbert space, destroying time-reversal symmetry. We analyze the ensuing eigenstates using different measures such as inverse participation ratio and sample-averaged moments of the position operator. In addition, we examine amplitude fluctuations in detail to detect the possibility of multifractal behavior (characteristic of mobility edges) that may arise as a result of the truncation procedure.

A Lower Bound for the Norm of the Solution of a Nonlinear Volterra Equation in One-Dimensional Viscoelasticity.

DTIC Science & Technology

1980-12-09

34, Symp. on Non-well-posed Problems and Logarithmic Convexity (Lecture Notes on Math. #316), pp. 31-5h, Springer, 1973. 3. Greenberg , J.M., MacCamy, R.C...34Continuous Data Dependence for an Abstract Volterra Integro- Differential Equation in Hilbert Space with Applications to Viscoelasticity", Annali Scuola... Hilbert Space", to appear in the J. Applicable Analysis. 8. Slemrod, M., "Instability of Steady Shearing Flows in a Nonlinear Viscoelastic Fluid", Arch

New gravitational solutions via a Riemann-Hilbert approach

NASA Astrophysics Data System (ADS)

Cardoso, G. L.; Serra, J. C.

2018-03-01

We consider the Riemann-Hilbert factorization approach to solving the field equations of dimensionally reduced gravity theories. First we prove that functions belonging to a certain class possess a canonical factorization due to properties of the underlying spectral curve. Then we use this result, together with appropriate matricial decompositions, to study the canonical factorization of non-meromorphic monodromy matrices that describe deformations of seed monodromy matrices associated with known solutions. This results in new solutions, with unusual features, to the field equations.

Hilbert-Schmidt Measure of Pairwise Quantum Discord for Three-Qubit X States

NASA Astrophysics Data System (ADS)

Daoud, M.; Laamara, R. Ahl; Seddik, S.

2015-10-01

The Hilbert-Schmidt distance between a mixed three-qubit state and its closest state is used to quantify the amount of pairwise quantum correlations in a tripartite system. Analytical expressions of geometric quantum discord are derived. A particular attention is devoted to two special classes of three-qubit X states. They include three-qubit states of W, GHZ and Bell type. We also discuss the monogamy property of geometric quantum discord in some mixed three-qubit systems.

Reconfigurable Computing Concepts for Space Missions: Universal Modular Spares

NASA Technical Reports Server (NTRS)

Patrick, M. Clinton

2007-01-01

Computing hardware for control, data collection, and other purposes will prove many times over crucial resources in NASA's upcoming space missions. Ability to provide these resources within mission payload requirements, with the hardiness to operate for extended periods under potentially harsh conditions in off-World environments, is daunting enough without considering the possibility of doing so with conventional electronics. This paper examines some ideas and options, and proposes some initial approaches, for logical design of reconfigurable computing resources offering true modularity, universal compatibility, and unprecedented flexibility to service all forms and needs of mission infrastructure.

Modular power converter having fluid cooled support

DOEpatents

Beihoff, Bruce C.; Radosevich, Lawrence D.; Meyer, Andreas A.; Gollhardt, Neil; Kannenberg, Daniel G.

2005-09-06

A support may receive one or more power electronic circuits. The support may aid in removing heat from the circuits through fluid circulating through the support. The support, in conjunction with other packaging features may form a shield from both external EMI/RFI and from interference generated by operation of the power electronic circuits. Features may be provided to permit and enhance connection of the circuitry to external circuitry, such as improved terminal configurations. Modular units may be assembled that may be coupled to electronic circuitry via plug-in arrangements or through interface with a backplane or similar mounting and interconnecting structures.

Modular power converter having fluid cooled support

DOEpatents

Beihoff, Bruce C.; Radosevich, Lawrence D.; Meyer, Andreas A.; Gollhardt, Neil; Kannenberg, Daniel G.

2005-12-06

A support may receive one or more power electronic circuits. The support may aid in removing heat from the circuits through fluid circulating through the support. The support, in conjunction with other packaging features may form a shield from both external EMI/RFI and from interference generated by operation of the power electronic circuits. Features may be provided to permit and enhance connection of the circuitry to external circuitry, such as improved terminal configurations. Modular units may be assembled that may be coupled to electronic circuitry via plug-in arrangements or through interface with a backplane or similar mounting and interconnecting structures.

Triple products of Eisenstein series

NASA Astrophysics Data System (ADS)

Venkatesh, Anil

In this thesis, we construct a Massey triple product on the Deligne cohomology of the modular curve with coefficients in symmetric powers of the standard representation of the modular group. This result is obtained by constructing a Massey triple product on the extension groups in the category of admissible variations of mixed Hodge structure over the modular curve, which induces the desired construction on Deligne cohomology. The result extends Brown's construction of the cup product on Deligne cohomology to a higher cohomological product. Massey triple products on Deligne cohomology have been previously investigated by Deninger, who considered Deligne cohomology with trivial real coefficients. By working over the reals, Deninger was able to compute cohomology exclusively with differential forms. In this work, Deligne cohomology is studied over the rationals, which introduces an obstruction to applying Deninger's results. The obstruction arises from the fact that the integration map from the de Rham complex to the Eilenberg-MacLane complex of the modular group is not an algebra homomorphism. We compute the correction terms of the integration map as regularized iterated integrals of Eisenstein series, and show that these integrals arise in the cup product and Massey triple product on Deligne cohomology.

Modular microfluidic systems using reversibly attached PDMS fluid control modules

NASA Astrophysics Data System (ADS)

Skafte-Pedersen, Peder; Sip, Christopher G.; Folch, Albert; Dufva, Martin

2013-05-01

The use of soft lithography-based poly(dimethylsiloxane) (PDMS) valve systems is the dominating approach for high-density microscale fluidic control. Integrated systems enable complex flow control and large-scale integration, but lack modularity. In contrast, modular systems are attractive alternatives to integration because they can be tailored for different applications piecewise and without redesigning every element of the system. We present a method for reversibly coupling hard materials to soft lithography defined systems through self-aligning O-ring features thereby enabling easy interfacing of complex-valve-based systems with simpler detachable units. Using this scheme, we demonstrate the seamless interfacing of a PDMS-based fluid control module with hard polymer chips. In our system, 32 self-aligning O-ring features protruding from the PDMS fluid control module form chip-to-control module interconnections which are sealed by tightening four screws. The interconnection method is robust and supports complex fluidic operations in the reversibly attached passive chip. In addition, we developed a double-sided molding method for fabricating PDMS devices with integrated through-holes. The versatile system facilitates a wide range of applications due to the modular approach, where application specific passive chips can be readily attached to the flow control module.

A modular projection autostereoscopic system for stereo cinema

NASA Astrophysics Data System (ADS)

Elkhov, Victor A.; Kondratiev, Nikolai V.; Ovechkis, Yuri N.; Pautova, Larisa V.

2009-02-01

The lenticular raster system for 3D movies non-glasses show designed by NIKFI demonstrated commercially in Moscow in the 40'st of the last century. Essential lack of this method was narrow individual viewing zone as only two images on the film used. To solve this problem, we propose to use digital video projective system with modular principle of its design. Increase of the general number of the pixels forming the stereo image is reached by using of more than one projector. The modular projection autostereoscopic system for demonstration of the 3D movies includes diffuser screen; lenticular plate located in front of the screen; projective system consisted from several projectors and the block of parallax panoramogram fragments creator. By means of this block the parallax panoramogram is broken into fragments which quantity corresponds to number of projectors. For the large dimension lenticular screen making rectangular fragments of inclined raster were joined in a uniform leaf. To obtain the needed focal distance of the screen lenses we used immersion - aqueous solution of glycerin. The immersion also let essentially decrease visibility of fragments joints. An experimental prototype of the modular projection autostereoscopic system was created to validate proposed system.

Full-field optical coherence tomography image restoration based on Hilbert transformation

NASA Astrophysics Data System (ADS)

Na, Jihoon; Choi, Woo June; Choi, Eun Seo; Ryu, Seon Young; Lee, Byeong Ha

2007-02-01

We propose the envelope detection method that is based on Hilbert transform for image restoration in full-filed optical coherence tomography (FF-OCT). The FF-OCT system presenting a high-axial resolution of 0.9 μm was implemented with a Kohler illuminator based on Linnik interferometer configuration. A 250 W customized quartz tungsten halogen lamp was used as a broadband light source and a CCD camera was used as a 2-dimentional detector array. The proposed image restoration method for FF-OCT requires only single phase-shifting. By using both the original and the phase-shifted images, we could remove the offset and the background signals from the interference fringe images. The desired coherent envelope image was obtained by applying Hilbert transform. With the proposed image restoration method, we demonstrate en-face imaging performance of the implemented FF-OCT system by presenting a tilted mirror surface, an integrated circuit chip, and a piece of onion epithelium.

Exact Fan-Beam Reconstruction With Arbitrary Object Translations and Truncated Projections

NASA Astrophysics Data System (ADS)

Hoskovec, Jan; Clackdoyle, Rolf; Desbat, Laurent; Rit, Simon

2016-06-01

This article proposes a new method for reconstructing two-dimensional (2D) computed tomography (CT) images from truncated and motion contaminated sinograms. The type of motion considered here is a sequence of rigid translations which are assumed to be known. The algorithm first identifies the sufficiency of angular coverage in each 2D point of the CT image to calculate the Hilbert transform from the local “virtual” trajectory which accounts for the motion and the truncation. By taking advantage of data redundancy in the full circular scan, our method expands the reconstructible region beyond the one obtained with chord-based methods. The proposed direct reconstruction algorithm is based on the Differentiated Back-Projection with Hilbert filtering (DBP-H). The motion is taken into account during backprojection which is the first step of our direct reconstruction, before taking the derivatives and inverting the finite Hilbert transform. The algorithm has been tested in a proof-of-concept study on Shepp-Logan phantom simulations with several motion cases and detector sizes.

Bulk entanglement gravity without a boundary: Towards finding Einstein's equation in Hilbert space

NASA Astrophysics Data System (ADS)

Cao, ChunJun; Carroll, Sean M.

2018-04-01

We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's "entanglement equilibrium" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.

Renormalization group scale-setting from the action—a road to modified gravity theories

NASA Astrophysics Data System (ADS)

Domazet, Silvije; Štefančić, Hrvoje

2012-12-01

The renormalization group (RG) corrected gravitational action in Einstein-Hilbert and other truncations is considered. The running scale of the RG is treated as a scalar field at the level of the action and determined in a scale-setting procedure recently introduced by Koch and Ramirez for the Einstein-Hilbert truncation. The scale-setting procedure is elaborated for other truncations of the gravitational action and applied to several phenomenologically interesting cases. It is shown how the logarithmic dependence of the Newton's coupling on the RG scale leads to exponentially suppressed effective cosmological constant and how the scale-setting in particular RG-corrected gravitational theories yields the effective f(R) modified gravity theories with negative powers of the Ricci scalar R. The scale-setting at the level of the action at the non-Gaussian fixed point in Einstein-Hilbert and more general truncations is shown to lead to universal effective action quadratic in the Ricci tensor.

Image Intensifier Modules For Use With Commercially Available Solid State Cameras

NASA Astrophysics Data System (ADS)

Murphy, Howard; Tyler, Al; Lake, Donald W.

1989-04-01

A modular approach to design has contributed greatly to the success of the family of machine vision video equipment produced by EG&G Reticon during the past several years. Internal modularity allows high-performance area (matrix) and line scan cameras to be assembled with two or three electronic subassemblies with very low labor costs, and permits camera control and interface circuitry to be realized by assemblages of various modules suiting the needs of specific applications. Product modularity benefits equipment users in several ways. Modular matrix and line scan cameras are available in identical enclosures (Fig. 1), which allows enclosure components to be purchased in volume for economies of scale and allows field replacement or exchange of cameras within a customer-designed system to be easily accomplished. The cameras are optically aligned (boresighted) at final test; modularity permits optical adjustments to be made with the same precise test equipment for all camera varieties. The modular cameras contain two, or sometimes three, hybrid microelectronic packages (Fig. 2). These rugged and reliable "submodules" perform all of the electronic operations internal to the camera except for the job of image acquisition performed by the monolithic image sensor. Heat produced by electrical power dissipation in the electronic modules is conducted through low resistance paths to the camera case by the metal plates, which results in a thermally efficient and environmentally tolerant camera with low manufacturing costs. A modular approach has also been followed in design of the camera control, video processor, and computer interface accessory called the Formatter (Fig. 3). This unit can be attached directly onto either a line scan or matrix modular camera to form a self-contained units, or connected via a cable to retain the advantages inherent to a small, light weight, and rugged image sensing component. Available modules permit the bus-structured Formatter to be configured as required by a specific camera application. Modular line and matrix scan cameras incorporating sensors with fiber optic faceplates (Fig 4) are also available. These units retain the advantages of interchangeability, simple construction, ruggedness, and optical precision offered by the more common lens input units. Fiber optic faceplate cameras are used for a wide variety of applications. A common usage involves mating of the Reticon-supplied camera to a customer-supplied intensifier tube for low light level and/or short exposure time situations.

A new multi-scale method to reveal hierarchical modular structures in biological networks.

PubMed

Jiao, Qing-Ju; Huang, Yan; Shen, Hong-Bin

2016-11-15

Biological networks are effective tools for studying molecular interactions. Modular structure, in which genes or proteins may tend to be associated with functional modules or protein complexes, is a remarkable feature of biological networks. Mining modular structure from biological networks enables us to focus on a set of potentially important nodes, which provides a reliable guide to future biological experiments. The first fundamental challenge in mining modular structure from biological networks is that the quality of the observed network data is usually low owing to noise and incompleteness in the obtained networks. The second problem that poses a challenge to existing approaches to the mining of modular structure is that the organization of both functional modules and protein complexes in networks is far more complicated than was ever thought. For instance, the sizes of different modules vary considerably from each other and they often form multi-scale hierarchical structures. To solve these problems, we propose a new multi-scale protocol for mining modular structure (named ISIMB) driven by a node similarity metric, which works in an iteratively converged space to reduce the effects of the low data quality of the observed network data. The multi-scale node similarity metric couples both the local and the global topology of the network with a resolution regulator. By varying this resolution regulator to give different weightings to the local and global terms in the metric, the ISIMB method is able to fit the shape of modules and to detect them on different scales. Experiments on protein-protein interaction and genetic interaction networks show that our method can not only mine functional modules and protein complexes successfully, but can also predict functional modules from specific to general and reveal the hierarchical organization of protein complexes.

Integrated modular teaching in dermatology for undergraduate students: A novel approach

PubMed Central

Karthikeyan, Kaliaperumal; Kumar, Annapurna

2014-01-01

Context: Undergraduate teaching in dermatology comprises didactic lectures and clinical classes. Integrated modular teaching is a novel approach, which integrates basic sciences with dermatology in the form of a module. Further the module also incorporates various teaching modalities, which facilitate active participation from students and promotes learning. The pre- and post-test values showed the effectiveness of the integrated module. The students feedback was encouraging. Aims: The aim of this study was to determine the acceptance and opinion of undergraduate students regarding integrated modular teaching as a new teaching aid in dermatology. Settings and Design: This was a descriptive study. Varied teaching methodologies involving multiple disciplines were undertaken in six major undergraduate topics in dermatology for seventh and eighth semester students. Materials and Methods: A total of six modules were conducted over a period of 12 months for students of seventh and eighth semesters. The topics for the various modules were sexually transmitted diseases, acquired immunodeficiency syndrome, oral ulcers, leprosy, connective tissue disorders and psoriasis. Faculty members from different disciplines participated. Pre- and post-test were conducted before and after the modules respectively to gauge the effectiveness of the modules. Results: It was found that almost every student had a better score on the posttest as compared to the pretest. General feedback obtained from the students showed that all of them felt that modular teaching was a more interesting and useful teaching learning experience than conventional teaching. Conclusions: Integrated modular teaching can be an effective adjunct in imparting theoretical and practical knowledge to the students. Further, various teaching methodologies can be used in integrated modules effectively with active student participation. Thus integrated modular teaching addresses two important issues in medical education, namely integration and active student participation. PMID:25165641

On a wing and a prayer: an assessment of modularized crew resource management training for health care professionals.

PubMed

Clay-Williams, Robyn; Greenfield, David; Stone, Judy; Braithwaite, Jeffrey

2014-01-01

Evidence suggests that Crew Resource Management (CRM), a form of team training, is beneficial. In CRM training, participants learn individual portable team skills such as communication and decision making through group discussion and activities. However, the usual 1-day course format is not always compatible with health care organizational routines. A modular training format, while theoretically sound, is untested for interprofessional team training. The aim of this study was to explore the potential for modularized CRM training to be delivered to a group of interprofessional learners. Modularized CRM training, consisting of two 2-hour workshops, was delivered to health care workers in an Australian tertiary hospital. Kirkpatrick's evaluation model provided a framework for the study. Baseline attitude surveys were conducted prior to each workshop. Participants completed a written questionnaire at the end of each workshop that examined their motivations, reactions to the training, and learner demographics. An additional survey, administered 6 weeks post training, captured self-assessed behavior data. Twenty-three individuals from a range of professions and clinical streams participated. One in 5 participants (22%) reported that they translated teamwork skills to the workplace. While positive about the workshop format and content, many respondents identified personal, team, and organizational barriers to the application of the workshop techniques. CRM training when delivered in a modular format has positive outcomes. Following the training, some respondents overcame workplace barriers to attempt to change negative workplace behavior. This progress provides cautious optimism for the potential for modular CRM training to benefit groups of interprofessional health staff. © 2014 The Alliance for Continuing Education in the Health Professions, the Society for Academic Continuing Medical Education, and the Council on Continuing Medical Education, Association for Hospital Medical Education.

Integrated modular teaching in dermatology for undergraduate students: A novel approach.

PubMed

Karthikeyan, Kaliaperumal; Kumar, Annapurna

2014-07-01

Undergraduate teaching in dermatology comprises didactic lectures and clinical classes. Integrated modular teaching is a novel approach, which integrates basic sciences with dermatology in the form of a module. Further the module also incorporates various teaching modalities, which facilitate active participation from students and promotes learning. The pre- and post-test values showed the effectiveness of the integrated module. The students feedback was encouraging. The aim of this study was to determine the acceptance and opinion of undergraduate students regarding integrated modular teaching as a new teaching aid in dermatology. This was a descriptive study. Varied teaching methodologies involving multiple disciplines were undertaken in six major undergraduate topics in dermatology for seventh and eighth semester students. A total of six modules were conducted over a period of 12 months for students of seventh and eighth semesters. The topics for the various modules were sexually transmitted diseases, acquired immunodeficiency syndrome, oral ulcers, leprosy, connective tissue disorders and psoriasis. Faculty members from different disciplines participated. Pre- and post-test were conducted before and after the modules respectively to gauge the effectiveness of the modules. It was found that almost every student had a better score on the posttest as compared to the pretest. General feedback obtained from the students showed that all of them felt that modular teaching was a more interesting and useful teaching learning experience than conventional teaching. Integrated modular teaching can be an effective adjunct in imparting theoretical and practical knowledge to the students. Further, various teaching methodologies can be used in integrated modules effectively with active student participation. Thus integrated modular teaching addresses two important issues in medical education, namely integration and active student participation.

Lightweight composites for modular panelized construction

NASA Astrophysics Data System (ADS)

Vaidya, Amol S.

Rapid advances in construction materials technology have enabled civil engineers to achieve impressive gains in the safety, economy, and functionality of structures built to serve the common needs of society. Modular building systems is a fast-growing modern, form of construction gaining recognition for its increased efficiency and ability to apply modern technology to the needs of the market place. In the modular construction technique, a single structural panel can perform a number of functions such as providing thermal insulation, vibration damping, and structural strength. These multifunctional panels can be prefabricated in a manufacturing facility and then transferred to the construction site. A system that uses prefabricated panels for construction is called a "panelized construction system". This study focuses on the development of pre-cast, lightweight, multifunctional sandwich composite panels to be used for panelized construction. Two thermoplastic composite panels are proposed in this study, namely Composite Structural Insulated Panels (CSIPs) for exterior walls, floors and roofs, and Open Core Sandwich composite for multifunctional interior walls of a structure. Special manufacturing techniques are developed for manufacturing these panels. The structural behavior of these panels is analyzed based on various building design codes. Detailed descriptions of the design, cost analysis, manufacturing, finite element modeling and structural testing of these proposed panels are included in this study in the of form five peer-reviewed journal articles. The structural testing of the proposed panels involved in this study included flexural testing, axial compression testing, and low and high velocity impact testing. Based on the current study, the proposed CSIP wall and floor panels were found satisfactory, based on building design codes ASCE-7-05 and ACI-318-05. Joining techniques are proposed in this study for connecting the precast panels on the construction site. Keywords: Modular panelized construction, sandwich composites, composite structural insulated panels (CSIPs).

Ocean thermal plant

NASA Technical Reports Server (NTRS)

Owens, L. J. (Inventor)

1978-01-01

A floating energy converter is described which uses large volumes of sea water to produce electrical power. In this plant, a fluid working medium is pumped to an evaporator where is is heated by a flow of warm surface sea water. The fluid in liquid form boils to a pressurized gas vapor which is routed to drive a turbine that, in turn, drives a generator for producing electricity. The gas vapor then enters a condenser immersed in cold sea water pumped from lower depths, condenses to its original liquid form, and then pumped to the evaporator to repeat the cycle. Modular components can be readily interchanged on the ocean thermal unit and inlet pipes for the sea water are provided with means for maintaining the pipes in alignment with the oncoming current. The modular construction allows for the testing of various components to provide a more rapid optimization of a standardized plant.

Modular electronics packaging system

NASA Technical Reports Server (NTRS)

Hunter, Don J. (Inventor)

2001-01-01

A modular electronics packaging system includes multiple packaging slices that are mounted horizontally to a base structure. The slices interlock to provide added structural support. Each packaging slice includes a rigid and thermally conductive housing having four side walls that together form a cavity to house an electronic circuit. The chamber is enclosed on one end by an end wall, or web, that isolates the electronic circuit from a circuit in an adjacent packaging slice. The web also provides a thermal path between the electronic circuit and the base structure. Each slice also includes a mounting bracket that connects the packaging slice to the base structure. Four guide pins protrude from the slice into four corresponding receptacles in an adjacent slice. A locking element, such as a set screw, protrudes into each receptacle and interlocks with the corresponding guide pin. A conduit is formed in the slice to allow electrical connection to the electronic circuit.

Dying dyons don't count

NASA Astrophysics Data System (ADS)

Cheng, Miranda C. N.; Verlinde, Erik P.

2007-09-01

The dyonic 1/4-BPS states in 4D string theory with Script N = 4 spacetime supersymmetry are counted by a Siegel modular form. The pole structure of the modular form leads to a contour dependence in the counting formula obscuring its duality invariance. We exhibit the relation between this ambiguity and the (dis-)appearance of bound states of 1/2-BPS configurations. Using this insight we propose a precise moduli-dependent contour prescription for the counting formula. We then show that the degeneracies are duality-invariant and are correctly adjusted at the walls of marginal stability to account for the (dis-)appearance of the two-centered bound states. Especially, for large black holes none of these bound states exists at the attractor point and none of these ambiguous poles contributes to the counting formula. Using this fact we also propose a second, moduli-independent contour which counts the ``immortal dyons" that are stable everywhere.

Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and the KPI equation

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Polivanov, M. C.

1992-11-01

The resolvent operator of the linear problem is determined as the full Green function continued in the complex domain in two variables. An analog of the known Hilbert identity is derived. We demonstrate the role of this identity in the study of two-dimensional scattering. Considering the nonstationary Schrödinger equation as an example, we show that all types of solutions of the linear problems, as well as spectral data known in the literature, are given as specific values of this unique function — the resolvent function. A new form of the inverse problem is formulated.

Functors of White Noise Associated to Characters of the Infinite Symmetric Group

NASA Astrophysics Data System (ADS)

Bożejko, Marek; Guţă, Mădălin

The characters of the infinite symmetric group are extended to multiplicative positive definite functions on pair partitions by using an explicit representation due to Veršik and Kerov. The von Neumann algebra generated by the fields with f in an infinite dimensional real Hilbert space is infinite and the vacuum vector is not separating. For a family depending on an integer N< - 1 an ``exclusion principle'' is found allowing at most ``identical particles'' on the same state: The algebras are type factors. Functors of white noise are constructed and proved to be non-equivalent for different values of N.

dRGT theory of massive gravity from spontaneous symmetry breaking

NASA Astrophysics Data System (ADS)

Torabian, Mahdi

2018-05-01

In this note we propose a topological action for a Poincare times diffeomorphism invariant gauge theory. We show that there is Higgs phase where the gauge symmetry is spontaneous broken to a diagonal Lorentz subgroup and gives the Einstein-Hilbert action plus the dRGT potential terms. In this vacuum, there are five (three from Goldstone modes) propagating degrees of freedom which form polarizations of a massive spin 2 particle, an extra healthy heavy scalar (Higgs) mode and no Boulware-Deser ghost mode. We further show that the action can be derived in a limit from a topological de Sitter invariant gauge theory in 4 dimensions.

Numerical method for solving the nonlinear four-point boundary value problems

NASA Astrophysics Data System (ADS)

Lin, Yingzhen; Lin, Jinnan

2010-12-01

In this paper, a new reproducing kernel space is constructed skillfully in order to solve a class of nonlinear four-point boundary value problems. The exact solution of the linear problem can be expressed in the form of series and the approximate solution of the nonlinear problem is given by the iterative formula. Compared with known investigations, the advantages of our method are that the representation of exact solution is obtained in a new reproducing kernel Hilbert space and accuracy of numerical computation is higher. Meanwhile we present the convergent theorem, complexity analysis and error estimation. The performance of the new method is illustrated with several numerical examples.

Area law violations and quantum phase transitions in modified Motzkin walk spin chains

NASA Astrophysics Data System (ADS)

Sugino, Fumihiko; Padmanabhan, Pramod

2018-01-01

Area law violations for entanglement entropy in the form of a square root have recently been studied for one-dimensional frustration-free quantum systems based on the Motzkin walks and their variations. Here we consider a Motzkin walk with a different Hilbert space on each step of the walk spanned by the elements of a symmetric inverse semigroup with the direction of each step governed by its algebraic structure. This change alters the number of paths allowed in the Motzkin walk and introduces a ground state degeneracy that is sensitive to boundary perturbations. We study the frustration-free spin chains based on three symmetric inverse semigroups, \

"Above the Slough of Despond": Weylean invariantism and quantum physics

NASA Astrophysics Data System (ADS)

Toader, Iulian D.

2018-02-01

The pursuit of scientific objectivity turned physical theories into systems of symbols or, as Weyl also put it sometimes, into symbolic constructions. What characterizes such constructions, at least in part, is a certain type of Begriffsbildung, according to which scientific concepts are freely created by the mind, i.e., implicitly defined via fundamental theoretical postulates (Toader, 2013). This idea, inspired by Hilbert, together with an approach to understanding influenced by Husserl, led Weyl to a form of skepticism about science, according to which if objectivity could be attained, understanding would thereby be sacrificed; and if understanding were to be pursued, this would render objectivity unattainable (Toader, 2011).

Building blocks of a fish head: Developmental and variational modularity in a complex system.

PubMed

Lehoux, Caroline; Cloutier, Richard

2015-11-01

Evolution of the vertebrate skull is developmentally constrained by the interactions among its anatomical systems, such as the dermatocranium and the sensory system. The interaction between the dermal bones and lateral line canals has been debated for decades but their morphological integration has never been tested. An ontogenetic series of 97 juvenile and adult Amia calva (Actinopterygii) was used to describe the patterning and modularity of sensory lateral line canals and their integration with supporting cranial bones. Developmental modules were tested for the otic canal and supratemporal commissure by computing correlations in the branching sequence of groups of pores. Landmarks were digitized on 25 specimens to test a priori hypotheses of variational and developmental modularity at the level of canals and dermal bones. Branching sequence suggests a specific patterning supported by significant positive correlations in the sequence of appearance of branches between bilateral sides. Differences in patterning between the otic canal and the supratemporal commissure and tests of modularity with geometric morphometrics suggest that both canals form distinct modules. The integration between bones and canals was insufficient to detect a module. However, both components were not independent. Groups of pores tended to disappear without affecting other groups of pores suggesting that they are quasi-independent units acting as modules. This study provides evidence of a hierarchical organization for the modular sensory system that could explain variation of pattern of canals among species and their association with dermal bones. © 2015 Wiley Periodicals, Inc.

Business Case Analysis Of Small Modular Reactors (SMR) For DOD Assured Power

DTIC Science & Technology

2017-12-01

Smith Second Reader: Thomas L. Albright THIS PAGE INTENTIONALLY LEFT BLANK i REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 Public...SECURITY CLASSIFICATION OF ABSTRACT Unclassified 20. LIMITATION OF ABSTRACT UU NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89...attack (EMP) represents one of the most devastating forms of attack on the power grid. Because the North American grid is made up of three major

Structure parameters in rotating Couette-Poiseuille channel flow

NASA Technical Reports Server (NTRS)

Knightly, George H.; Sather, D.

1986-01-01

It is well-known that a number of steady state problems in fluid mechanics involving systems of nonlinear partial differential equations can be reduced to the problem of solving a single operator equation of the form: v + lambda Av + lambda B(v) = 0, v is the summation of H, lambda is the summation of one-dimensional Euclid space, where H is an appropriate (real or complex) Hilbert space. Here lambda is a typical load parameter, e.g., the Reynolds number, A is a linear operator, and B is a quadratic operator generated by a bilinear form. In this setting many bifurcation and stability results for problems were obtained. A rotating Couette-Poiseuille channel flow was studied, and it showed that, in general, the superposition of a Poiseuille flow on a rotating Couette channel flow is destabilizing.

SIC-POVMS and MUBS: Geometrical Relationships in Prime Dimension

NASA Astrophysics Data System (ADS)

Appleby, D. M.

2009-03-01

The paper concerns Weyl-Heisenberg covariant SIC-POVMs (symmetric informationally complete positive operator valued measures) and full sets of MUBs (mutually unbiased bases) in prime dimension. When represented as vectors in generalized Bloch space a SIC-POVM forms a d2-1 dimensional regular simplex (d being the Hilbert space dimension). By contrast, the generalized Bloch vectors representing a full set of MUBs form d+1 mutually orthogonal d-1 dimensional regular simplices. In this paper we show that, in the Weyl-Heisenberg case, there are some simple geometrical relationships between the single SIC-POVM simplex and the d+1 MUB simplices. We go on to give geometrical interpretations of the minimum uncertainty states introduced by Wootters and Sussman, and by Appleby, Dang and Fuchs, and of the fiduciality condition given by Appleby, Dang and Fuchs.

A lattice approach to spinorial quantum gravity

NASA Technical Reports Server (NTRS)

Renteln, Paul; Smolin, Lee

1989-01-01

A new lattice regularization of quantum general relativity based on Ashtekar's reformulation of Hamiltonian general relativity is presented. In this form, quantum states of the gravitational field are represented within the physical Hilbert space of a Kogut-Susskind lattice gauge theory. The gauge field of the theory is a complexified SU(2) connection which is the gravitational connection for left-handed spinor fields. The physical states of the gravitational field are those which are annihilated by additional constraints which correspond to the four constraints of general relativity. Lattice versions of these constraints are constructed. Those corresponding to the three-dimensional diffeomorphism generators move states associated with Wilson loops around on the lattice. The lattice Hamiltonian constraint has a simple form, and a correspondingly simple interpretation: it is an operator which cuts and joins Wilson loops at points of intersection.

Isomonodromy for the Degenerate Fifth Painlevé Equation

NASA Astrophysics Data System (ADS)

Acosta-Humánez, Primitivo B.; van der Put, Marius; Top, Jaap

2017-05-01

This is a sequel to papers by the last two authors making the Riemann-Hilbert correspondence and isomonodromy explicit. For the degenerate fifth Painlevé equation, the moduli spaces for connections and for monodromy are explicitly computed. It is proven that the extended Riemann-Hilbert morphism is an isomorphism. As a consequence these equations have the Painlevé property and the Okamoto-Painlevé space is identified with a moduli space of connections. Using MAPLE computations, one obtains formulas for the degenerate fifth Painlevé equation, for the Bäcklund transformations.

Near-complete teleportation of a superposed coherent state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheong, Yong Wook; Kim, Hyunjae; Lee, Hai-Woong

2004-09-01

The four Bell-type entangled coherent states, {alpha}>-{alpha}>{+-}-{alpha}>{alpha}> and {alpha}>{alpha}>{+-}-{alpha}>-{alpha}>, can be discriminated with a high probability using only linear optical means, as long as {alpha} is not too small. Based on this observation, we propose a simple scheme to almost completely teleport a superposed coherent state. The nonunitary transformation that is required to complete the teleportation can be achieved by embedding the receiver's field state in a larger Hilbert space consisting of the field and a single atom and performing a unitary transformation on this Hilbert space00.

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet

NASA Astrophysics Data System (ADS)

Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E.; Sols, Fernando; Carr, Lincoln D.

2018-06-01

We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet.

PubMed

Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E; Sols, Fernando; Carr, Lincoln D

2018-06-08

We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.

Proceedings of the MIT Student Workshop on VLSI and Parallel Systems Held in Dedham, Massachusetts on 21 July 1992

DTIC Science & Technology

1992-07-01

don’t multiplez the host References wtres, then neither does E., ® El. By repeated application of Theorem 1, using a leveled [1] D. S. Greenberg and S. N...1900, David Hilbert proposed twenty-three problems covering all areas of mathematics that guided the field for decades. These problems served a driving...session was to propose several grand challenge problems, similar in spirit to those of Hilbert [W1: [A] problem should be difficult in order to entice us

Majorana fermions and orthogonal complex structures

NASA Astrophysics Data System (ADS)

Calderón-García, J. S.; Reyes-Lega, A. F.

2018-05-01

Ground states of quadratic Hamiltonians for fermionic systems can be characterized in terms of orthogonal complex structures. The standard way in which such Hamiltonians are diagonalized makes use of a certain “doubling” of the Hilbert space. In this work, we show that this redundancy in the Hilbert space can be completely lifted if the relevant orthogonal structure is taken into account. Such an approach allows for a treatment of Majorana fermions which is both physically and mathematically transparent. Furthermore, an explicit connection between orthogonal complex structures and the topological ℤ2-invariant is given.

Unbounded Violations of Bipartite Bell Inequalities via Operator Space Theory

NASA Astrophysics Data System (ADS)

Junge, M.; Palazuelos, C.; Pérez-García, D.; Villanueva, I.; Wolf, M. M.

2010-12-01

In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order {Ω left(sqrt{n}/log^2n right)} when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator space theory and, in particular, the very recent noncommutative L p embedding theory. As a consequence of this result, we obtain better Hilbert space dimension witnesses and quantum violations of Bell inequalities with better resistance to noise.

Dynamical structure of pure Lovelock gravity

NASA Astrophysics Data System (ADS)

Dadhich, Naresh; Durka, Remigiusz; Merino, Nelson; Miskovic, Olivera

2016-03-01

We study the dynamical structure of pure Lovelock gravity in spacetime dimensions higher than four using the Hamiltonian formalism. The action consists of a cosmological constant and a single higher-order polynomial in the Riemann tensor. Similarly to the Einstein-Hilbert action, it possesses a unique constant curvature vacuum and charged black hole solutions. We analyze physical degrees of freedom and local symmetries in this theory. In contrast to the Einstein-Hilbert case, the number of degrees of freedom depends on the background and can vary from zero to the maximal value carried by the Lovelock theory.

A New View of Earthquake Ground Motion Data: The Hilbert Spectral Analysis

NASA Technical Reports Server (NTRS)

Huang, Norden; Busalacchi, Antonio J. (Technical Monitor)

2000-01-01

A brief description of the newly developed Empirical Mode Decomposition (ENID) and Hilbert Spectral Analysis (HSA) method will be given. The decomposition is adaptive and can be applied to both nonlinear and nonstationary data. Example of the method applied to a sample earthquake record will be given. The results indicate those low frequency components, totally missed by the Fourier analysis, are clearly identified by the new method. Comparisons with Wavelet and window Fourier analysis show the new method offers much better temporal and frequency resolutions.

Mergeable nervous systems for robots.

PubMed

Mathews, Nithin; Christensen, Anders Lyhne; O'Grady, Rehan; Mondada, Francesco; Dorigo, Marco

2017-09-12

Robots have the potential to display a higher degree of lifetime morphological adaptation than natural organisms. By adopting a modular approach, robots with different capabilities, shapes, and sizes could, in theory, construct and reconfigure themselves as required. However, current modular robots have only been able to display a limited range of hardwired behaviors because they rely solely on distributed control. Here, we present robots whose bodies and control systems can merge to form entirely new robots that retain full sensorimotor control. Our control paradigm enables robots to exhibit properties that go beyond those of any existing machine or of any biological organism: the robots we present can merge to form larger bodies with a single centralized controller, split into separate bodies with independent controllers, and self-heal by removing or replacing malfunctioning body parts. This work takes us closer to robots that can autonomously change their size, form and function.Robots that can self-assemble into different morphologies are desired to perform tasks that require different physical capabilities. Mathews et al. design robots whose bodies and control systems can merge and split to form new robots that retain full sensorimotor control and act as a single entity.

Heterotic sigma models on T 8 and the Borcherds automorphic form Φ 12

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harrison, Sarah M.; Kachru, Shamit; Paquette, Natalie M.

Here, we consider the spectrum of BPS states of the heterotic sigma model with (0, 8) supersymmetry and T 8 target, as well as its second-quantized counterpart. We show that the counting function for such states is intimately related to Borcherds’ automorphic form Φ 12, a modular form which exhibits automorphy for O(2, 26; Ζ). Here, we comment on possible implications for Umbral moonshine and theories of AdS 3 gravity.

Heterotic sigma models on T 8 and the Borcherds automorphic form Φ 12

DOE PAGES

Harrison, Sarah M.; Kachru, Shamit; Paquette, Natalie M.; ...

2017-10-18

Here, we consider the spectrum of BPS states of the heterotic sigma model with (0, 8) supersymmetry and T 8 target, as well as its second-quantized counterpart. We show that the counting function for such states is intimately related to Borcherds’ automorphic form Φ 12, a modular form which exhibits automorphy for O(2, 26; Ζ). Here, we comment on possible implications for Umbral moonshine and theories of AdS 3 gravity.

Split green fluorescent protein as a modular binding partner for protein crystallization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nguyen, Hau B.; Hung, Li-Wei; Yeates, Todd O.

2013-12-01

A strategy using a new split green fluorescent protein (GFP) as a modular binding partner to form stable protein complexes with a target protein is presented. The modular split GFP may open the way to rapidly creating crystallization variants. A modular strategy for protein crystallization using split green fluorescent protein (GFP) as a crystallization partner is demonstrated. Insertion of a hairpin containing GFP β-strands 10 and 11 into a surface loop of a target protein provides two chain crossings between the target and the reconstituted GFP compared with the single connection afforded by terminal GFP fusions. This strategy was testedmore » by inserting this hairpin into a loop of another fluorescent protein, sfCherry. The crystal structure of the sfCherry-GFP(10–11) hairpin in complex with GFP(1–9) was determined at a resolution of 2.6 Å. Analysis of the complex shows that the reconstituted GFP is attached to the target protein (sfCherry) in a structurally ordered way. This work opens the way to rapidly creating crystallization variants by reconstituting a target protein bearing the GFP(10–11) hairpin with a variety of GFP(1–9) mutants engineered for favorable crystallization.« less

Design and Evolution of a Modular Tensegrity Robot Platform

NASA Technical Reports Server (NTRS)

Bruce, Jonathan; Caluwaerts, Ken; Iscen, Atil; Sabelhaus, Andrew P.; SunSpiral, Vytas

2014-01-01

NASA Ames Research Center is developing a compliant modular tensegrity robotic platform for planetary exploration. In this paper we present the design and evolution of the platform's main hardware component, an untethered, robust tensegrity strut, with rich sensor feedback and cable actuation. Each strut is a complete robot, and multiple struts can be combined together to form a wide range of complex tensegrity robots. Our current goal for the tensegrity robotic platform is the development of SUPERball, a 6-strut icosahedron underactuated tensegrity robot aimed at dynamic locomotion for planetary exploration rovers and landers, but the aim is for the modular strut to enable a wide range of tensegrity morphologies. SUPERball is a second generation prototype, evolving from the tensegrity robot ReCTeR, which is also a modular, lightweight, highly compliant 6-strut tensegrity robot that was used to validate our physics based NASA Tensegrity Robot Toolkit (NTRT) simulator. Many hardware design parameters of the SUPERball were driven by locomotion results obtained in our validated simulator. These evolutionary explorations helped constrain motor torque and speed parameters, along with strut and string stress. As construction of the hardware has finalized, we have also used the same evolutionary framework to evolve controllers that respect the built hardware parameters.

Quantifying phase synchronization using instances of Hilbert phase slips

NASA Astrophysics Data System (ADS)

Govindan, R. B.

2018-07-01

We propose to quantify phase synchronization between two signals, x(t) and y(t), by calculating variance in the Hilbert phase of y(t) at instances of phase slips exhibited by x(t). The proposed approach is tested on numerically simulated coupled chaotic Roessler systems and second order autoregressive processes. Furthermore we compare the performance of the proposed and original approaches using uterine electromyogram signals and show that both approaches yield consistent results A standard phase synchronization approach, which involves unwrapping the Hilbert phases (ϕ1(t) and ϕ2(t)) of the two signals and analyzing the variance in the | n ṡϕ1(t) - m ṡϕ2(t) | , mod 2 π, (n and m are integers), was used for comparison. The synchronization indexes obtained from the proposed approach and the standard approach agree reasonably well in all of the systems studied in this work. Our results indicate that the proposed approach, unlike the traditional approach, does not require the non-invertible transformations - unwrapping of the phases and calculation of mod 2 π and it can be used to reliably to quantify phase synchrony between two signals.

Aveiro method in reproducing kernel Hilbert spaces under complete dictionary

NASA Astrophysics Data System (ADS)

Mai, Weixiong; Qian, Tao

2017-12-01

Aveiro Method is a sparse representation method in reproducing kernel Hilbert spaces (RKHS) that gives orthogonal projections in linear combinations of reproducing kernels over uniqueness sets. It, however, suffers from determination of uniqueness sets in the underlying RKHS. In fact, in general spaces, uniqueness sets are not easy to be identified, let alone the convergence speed aspect with Aveiro Method. To avoid those difficulties we propose an anew Aveiro Method based on a dictionary and the matching pursuit idea. What we do, in fact, are more: The new Aveiro method will be in relation to the recently proposed, the so called Pre-Orthogonal Greedy Algorithm (P-OGA) involving completion of a given dictionary. The new method is called Aveiro Method Under Complete Dictionary (AMUCD). The complete dictionary consists of all directional derivatives of the underlying reproducing kernels. We show that, under the boundary vanishing condition, bring available for the classical Hardy and Paley-Wiener spaces, the complete dictionary enables an efficient expansion of any given element in the Hilbert space. The proposed method reveals new and advanced aspects in both the Aveiro Method and the greedy algorithm.

The Hilbert-Huang Transform-Based Denoising Method for the TEM Response of a PRBS Source Signal

NASA Astrophysics Data System (ADS)

Hai, Li; Guo-qiang, Xue; Pan, Zhao; Hua-sen, Zhong; Khan, Muhammad Younis

2016-08-01

The denoising process is critical in processing transient electromagnetic (TEM) sounding data. For the full waveform pseudo-random binary sequences (PRBS) response, an inadequate noise estimation may result in an erroneous interpretation. We consider the Hilbert-Huang transform (HHT) and its application to suppress the noise in the PRBS response. The focus is on the thresholding scheme to suppress the noise and the analysis of the signal based on its Hilbert time-frequency representation. The method first decomposes the signal into the intrinsic mode function, and then, inspired by the thresholding scheme in wavelet analysis; an adaptive and interval thresholding is conducted to set to zero all the components in intrinsic mode function which are lower than a threshold related to the noise level. The algorithm is based on the characteristic of the PRBS response. The HHT-based denoising scheme is tested on the synthetic and field data with the different noise levels. The result shows that the proposed method has a good capability in denoising and detail preservation.

Arbitrary-order Hilbert Spectral Analysis and Intermittency in Solar Wind Density Fluctuations

NASA Astrophysics Data System (ADS)

Carbone, Francesco; Sorriso-Valvo, Luca; Alberti, Tommaso; Lepreti, Fabio; Chen, Christopher H. K.; Němeček, Zdenek; Šafránková, Jana

2018-05-01

The properties of inertial- and kinetic-range solar wind turbulence have been investigated with the arbitrary-order Hilbert spectral analysis method, applied to high-resolution density measurements. Due to the small sample size and to the presence of strong nonstationary behavior and large-scale structures, the classical analysis in terms of structure functions may prove to be unsuccessful in detecting the power-law behavior in the inertial range, and may underestimate the scaling exponents. However, the Hilbert spectral method provides an optimal estimation of the scaling exponents, which have been found to be close to those for velocity fluctuations in fully developed hydrodynamic turbulence. At smaller scales, below the proton gyroscale, the system loses its intermittent multiscaling properties and converges to a monofractal process. The resulting scaling exponents, obtained at small scales, are in good agreement with those of classical fractional Brownian motion, indicating a long-term memory in the process, and the absence of correlations around the spectral-break scale. These results provide important constraints on models of kinetic-range turbulence in the solar wind.

Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform.

PubMed

Huang, Yongxiang; Biferale, Luca; Calzavarini, Enrico; Sun, Chao; Toschi, Federico

2013-04-01

The Hilbert-Huang transform is applied to analyze single-particle Lagrangian velocity data from numerical simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions C(i)(t) and of their instantaneous frequency ω(i)(t). On the basis of this decomposition we define the ω-conditioned statistical moments of the C(i) modes, named q-order Hilbert spectra (HS). We show that such quantities have enhanced scaling properties as compared to traditional Fourier transform- or correlation-based (structure functions) statistical indicators, thus providing better insights into the turbulent energy transfer process. We present clear empirical evidence that the energylike quantity, i.e., the second-order HS, displays a linear scaling in time in the inertial range, as expected from a dimensional analysis. We also measure high-order moment scaling exponents in a direct way, without resorting to the extended self-similarity procedure. This leads to an estimate of the Lagrangian structure function exponents which are consistent with the multifractal prediction in the Lagrangian frame as proposed by Biferale et al. [Phys. Rev. Lett. 93, 064502 (2004)].

ψ-Epistemic Models are Exponentially Bad at Explaining the Distinguishability of Quantum States

NASA Astrophysics Data System (ADS)

Leifer, M. S.

2014-04-01

The status of the quantum state is perhaps the most controversial issue in the foundations of quantum theory. Is it an epistemic state (state of knowledge) or an ontic state (state of reality)? In realist models of quantum theory, the epistemic view asserts that nonorthogonal quantum states correspond to overlapping probability measures over the true ontic states. This naturally accounts for a large number of otherwise puzzling quantum phenomena. For example, the indistinguishability of nonorthogonal states is explained by the fact that the ontic state sometimes lies in the overlap region, in which case there is nothing in reality that could distinguish the two states. For this to work, the amount of overlap of the probability measures should be comparable to the indistinguishability of the quantum states. In this Letter, I exhibit a family of states for which the ratio of these two quantities must be ≤2de-cd in Hilbert spaces of dimension d that are divisible by 4. This implies that, for large Hilbert space dimension, the epistemic explanation of indistinguishability becomes implausible at an exponential rate as the Hilbert space dimension increases.

A New Scheme for the Design of Hilbert Transform Pairs of Biorthogonal Wavelet Bases

NASA Astrophysics Data System (ADS)

Shi, Hongli; Luo, Shuqian

2010-12-01

In designing the Hilbert transform pairs of biorthogonal wavelet bases, it has been shown that the requirements of the equal-magnitude responses and the half-sample phase offset on the lowpass filters are the necessary and sufficient condition. In this paper, the relationship between the phase offset and the vanishing moment difference of biorthogonal scaling filters is derived, which implies a simple way to choose the vanishing moments so that the phase response requirement can be satisfied structurally. The magnitude response requirement is approximately achieved by a constrained optimization procedure, where the objective function and constraints are all expressed in terms of the auxiliary filters of scaling filters rather than the scaling filters directly. Generally, the calculation burden in the design implementation will be less than that of the current schemes. The integral of magnitude response difference between the primal and dual scaling filters has been chosen as the objective function, which expresses the magnitude response requirements in the whole frequency range. Two design examples illustrate that the biorthogonal wavelet bases designed by the proposed scheme are very close to Hilbert transform pairs.

Towards a second law for Lovelock theories

NASA Astrophysics Data System (ADS)

Bhattacharyya, Sayantani; Haehl, Felix M.; Kundu, Nilay; Loganayagam, R.; Rangamani, Mukund

2017-03-01

In classical general relativity described by Einstein-Hilbert gravity, black holes behave as thermodynamic objects. In particular, the laws of black hole mechanics can be interpreted as laws of thermodynamics. The first law of black hole mechanics extends to higher derivative theories via the Noether charge construction of Wald. One also expects the statement of the second law, which in Einstein-Hilbert theory owes to Hawking's area theorem, to extend to higher derivative theories. To argue for this however one needs a notion of entropy for dynamical black holes, which the Noether charge construction does not provide. We propose such an entropy function for the family of Lovelock theories, treating the higher derivative terms as perturbations to the Einstein-Hilbert theory. Working around a dynamical black hole solution, and making no assumptions about the amplitude of departure from equilibrium, we construct a candidate entropy functional valid to all orders in the low energy effective field theory. This entropy functional satisfies a second law, modulo a certain subtle boundary term, which deserves further investigation in non-spherically symmetric situations.

The Baker-Akhiezer Function and Factorization of the Chebotarev-Khrapkov Matrix

NASA Astrophysics Data System (ADS)

Antipov, Yuri A.

2014-10-01

A new technique is proposed for the solution of the Riemann-Hilbert problem with the Chebotarev-Khrapkov matrix coefficient {G(t) = α1(t)I + α2(t)Q(t)} , {α1(t), α2(t) in H(L)} , I = diag{1, 1}, Q(t) is a {2×2} zero-trace polynomial matrix. This problem has numerous applications in elasticity and diffraction theory. The main feature of the method is the removal of essential singularities of the solution to the associated homogeneous scalar Riemann-Hilbert problem on the hyperelliptic surface of an algebraic function by means of the Baker-Akhiezer function. The consequent application of this function for the derivation of the general solution to the vector Riemann-Hilbert problem requires the finding of the {ρ} zeros of the Baker-Akhiezer function ({ρ} is the genus of the surface). These zeros are recovered through the solution to the associated Jacobi problem of inversion of abelian integrals or, equivalently, the determination of the zeros of the associated degree-{ρ} polynomial and solution of a certain linear algebraic system of {ρ} equations.

Thermodynamic limit of random partitions and dispersionless Toda hierarchy

NASA Astrophysics Data System (ADS)

Takasaki, Kanehisa; Nakatsu, Toshio

2012-01-01

We study the thermodynamic limit of random partition models for the instanton sum of 4D and 5D supersymmetric U(1) gauge theories deformed by some physical observables. The physical observables correspond to external potentials in the statistical model. The partition function is reformulated in terms of the density function of Maya diagrams. The thermodynamic limit is governed by a limit shape of Young diagrams associated with dominant terms in the partition function. The limit shape is characterized by a variational problem, which is further converted to a scalar-valued Riemann-Hilbert problem. This Riemann-Hilbert problem is solved with the aid of a complex curve, which may be thought of as the Seiberg-Witten curve of the deformed U(1) gauge theory. This solution of the Riemann-Hilbert problem is identified with a special solution of the dispersionless Toda hierarchy that satisfies a pair of generalized string equations. The generalized string equations for the 5D gauge theory are shown to be related to hidden symmetries of the statistical model. The prepotential and the Seiberg-Witten differential are also considered.

Hilbert-Schmidt quantum coherence in multi-qudit systems

NASA Astrophysics Data System (ADS)

Maziero, Jonas

2017-11-01

Using Bloch's parametrization for qudits ( d-level quantum systems), we write the Hilbert-Schmidt distance (HSD) between two generic n-qudit states as an Euclidean distance between two vectors of observables mean values in R^{Π_{s=1}nds2-1}, where ds is the dimension for qudit s. Then, applying the generalized Gell-Mann's matrices to generate SU(ds), we use that result to obtain the Hilbert-Schmidt quantum coherence (HSC) of n-qudit systems. As examples, we consider in detail one-qubit, one-qutrit, two-qubit, and two copies of one-qubit states. In this last case, the possibility for controlling local and non-local coherences by tuning local populations is studied, and the contrasting behaviors of HSC, l1-norm coherence, and relative entropy of coherence in this regard are noticed. We also investigate the decoherent dynamics of these coherence functions under the action of qutrit dephasing and dissipation channels. At last, we analyze the non-monotonicity of HSD under tensor products and report the first instance of a consequence (for coherence quantification) of this kind of property of a quantum distance measure.

Architectural mutation and leaf form, for the palmate series.

PubMed

White, D A

2005-07-21

Palmate leaf form occurs in both the ferns and angiosperms. The palmate leaf form, and its variants, is present in distantly separated clades within both ferns and angiosperms. There tend not to be intermediate forms which link these palmate leaves to other leaf forms within the taxonomic groups in question. The recurrence of homoplasious leaf forms in separate taxonomic groups could be a consequence of the algorithmic like mode of leaf growth. Leaves develop through the reiteration of modular units. It is probable that the homoplasious leaf forms in different taxa are derived independently through re-combinations of the parameters in the basic leaf form development algorithm.

Analysis of In-Space Assembly of Modular Systems

NASA Technical Reports Server (NTRS)

Moses, Robert W.; VanLaak, James; Johnson, Spencer L.; Chytka, Trina M.; Reeves, John D.; Todd, B. Keith; Moe, Rud V.; Stambolian, Damon B.

2005-01-01

Early system-level life cycle assessments facilitate cost effective optimization of system architectures to enable implementation of both modularity and in-space assembly, two key Exploration Systems Research & Technology (ESR&T) Strategic Challenges. Experiences with the International Space Station (ISS) demonstrate that the absence of this rigorous analysis can result in increased cost and operational risk. An effort is underway, called Analysis of In-Space Assembly of Modular Systems, to produce an innovative analytical methodology, including an evolved analysis toolset and proven processes in a collaborative engineering environment, to support the design and evaluation of proposed concepts. The unique aspect of this work is that it will produce the toolset, techniques and initial products to analyze and compare the detailed, life cycle costs and performance of different implementations of modularity for in-space assembly. A multi-Center team consisting of experienced personnel from the Langley Research Center, Johnson Space Center, Kennedy Space Center, and the Goddard Space Flight Center has been formed to bring their resources and experience to this development. At the end of this 30-month effort, the toolset will be ready to support the Exploration Program with an integrated assessment strategy that embodies all life-cycle aspects of the mission from design and manufacturing through operations to enable early and timely selection of an optimum solution among many competing alternatives. Already there are many different designs for crewed missions to the Moon that present competing views of modularity requiring some in-space assembly. The purpose of this paper is to highlight the approach for scoring competing designs.

Remote preparation of a qudit using maximally entangled states of qubits

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu Changshui; Song Heshan; Wang Yahong

2006-02-15

Known quantum pure states of a qudit can be remotely prepared onto a group of particles of qubits exactly or probabilistically with the aid of two-level Einstein-Podolsky-Rosen states. We present a protocol for such kind of remote state preparation. We are mainly focused on the remote preparation of the ensembles of equatorial states and those of states in real Hilbert space. In particular, a kind of states of qudits in real Hilbert space have been shown to be remotely prepared in faith without the limitation of the input space dimension.

Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach

NASA Astrophysics Data System (ADS)

Tovbis, Alexander; El, Gennady A.

2016-10-01

The main goal of this paper is to put together: a) the Whitham theory applicable to slowly modulated N-phase nonlinear wave solutions to the focusing nonlinear Schrödinger (fNLS) equation, and b) the Riemann-Hilbert Problem approach to particular solutions of the fNLS in the semiclassical (small dispersion) limit that develop slowly modulated N-phase nonlinear wave in the process of evolution. Both approaches have their own merits and limitations. Understanding of the interrelations between them could prove beneficial for a broad range of problems involving the semiclassical fNLS.

Limitations of shallow nets approximation.

PubMed

Lin, Shao-Bo

2017-10-01

In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.

Hilbert and Blaschke phases in the temporal coherence function of stationary broadband light.

PubMed

Fernández-Pousa, Carlos R; Maestre, Haroldo; Torregrosa, Adrián J; Capmany, Juan

2008-10-27

We show that the minimal phase of the temporal coherence function gamma (tau) of stationary light having a partially-coherent symmetric spectral peak can be computed as a relative logarithmic Hilbert transform of its amplitude with respect to its asymptotic behavior. The procedure is applied to experimental data from amplified spontaneous emission broadband sources in the 1.55 microm band with subpicosecond coherence times, providing examples of degrees of coherence with both minimal and non-minimal phase. In the latter case, the Blaschke phase is retrieved and the position of the Blaschke zeros determined.

Wavefront reconstruction from non-modulated pyramid wavefront sensor data using a singular value type expansion

NASA Astrophysics Data System (ADS)

Hutterer, Victoria; Ramlau, Ronny

2018-03-01

The new generation of extremely large telescopes includes adaptive optics systems to correct for atmospheric blurring. In this paper, we present a new method of wavefront reconstruction from non-modulated pyramid wavefront sensor data. The approach is based on a simplified sensor model represented as the finite Hilbert transform of the incoming phase. Due to the non-compactness of the finite Hilbert transform operator the classical theory for singular systems is not applicable. Nevertheless, we can express the Moore-Penrose inverse as a singular value type expansion with weighted Chebychev polynomials.

Transactions of the Conference of Army Mathematicians (28th) Held at Bethesda, Maryland on 28-30 June 1982.

DTIC Science & Technology

1983-02-01

real part is the Hilbert transform of its imaginary part. Thus we have o) d4’ . (5.1)+," _ Here r(o) and 6(o) denote respectively T(4’,0-) and 0(o,0...linear operators A in a Hilbert space H, eigenuv.aueA are critical values of the Raqt.igh quo 5ient (5.1) R(y) = (Ay,y)/(y,y), y # 0. An eigenvalue X...Das Gupta Ballistic Research Laboratory Jim Greenberg National Science Foundation Charles Giardina Fairleigh-Dickinson University Frank P. Kuhl U. S

Properties of highly frustrated magnetic molecules studied by the finite-temperature Lanczos method

NASA Astrophysics Data System (ADS)

Schnack, J.; Wendland, O.

2010-12-01

The very interesting magnetic properties of frustrated magnetic molecules are often hardly accessible due to the prohibitive size of the related Hilbert spaces. The finite-temperature Lanczos method is able to treat spin systems for Hilbert space sizes up to 109. Here we first demonstrate for exactly solvable systems that the method is indeed accurate. Then we discuss the thermal properties of one of the biggest magnetic molecules synthesized to date, the icosidodecahedron with antiferromagnetically coupled spins of s = 1/2. We show how genuine quantum features such as the magnetization plateau behave as a function of temperature.

Spinors in Hilbert Space

NASA Astrophysics Data System (ADS)

Plymen, Roger; Robinson, Paul

1995-01-01

Infinite-dimensional Clifford algebras and their Fock representations originated in the quantum mechanical study of electrons. In this book, the authors give a definitive account of the various Clifford algebras over a real Hilbert space and of their Fock representations. A careful consideration of the latter's transformation properties under Bogoliubov automorphisms leads to the restricted orthogonal group. From there, a study of inner Bogoliubov automorphisms enables the authors to construct infinite-dimensional spin groups. Apart from assuming a basic background in functional analysis and operator algebras, the presentation is self-contained with complete proofs, many of which offer a fresh perspective on the subject.

Noisy bases in Hilbert space: A new class of thermal coherent states and their properties

NASA Technical Reports Server (NTRS)

Vourdas, A.; Bishop, R. F.

1995-01-01

Coherent mixed states (or thermal coherent states) associated with the displaced harmonic oscillator at finite temperature, are introduced as a 'random' (or 'thermal' or 'noisy') basis in Hilbert space. A resolution of the identity for these states is proved and used to generalize the usual coherent state formalism for the finite temperature case. The Bargmann representation of an operator is introduced and its relation to the P and Q representations is studied. Generalized P and Q representations for the finite temperature case are also considered and several interesting relations among them are derived.

Geometry of quantum dynamics in infinite-dimensional Hilbert space

NASA Astrophysics Data System (ADS)

Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe; Shulman, Tatiana

2018-04-01

We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional, i.e. we do not restrict considerations to finite-dimensional Hilbert spaces, contrary to many other works on the geometry of quantum mechanics, and include a Lagrangian formalism in which self-adjoint (Schrödinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we also obtain results concerning coadjoint orbits of the unitary group in infinite dimensions, embedding of pure states in the unitary group, and self-adjoint extensions of symmetric relations.

A degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bertola, Marco, E-mail: Marco.Bertola@concordia.ca; Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec H3C 3J7; SISSA/ISAS, via Bonomea 265, Trieste

2015-06-15

Two-phase solutions of focusing NLS equation are classically constructed out of an appropriate Riemann surface of genus two and expressed in terms of the corresponding theta-function. We show here that in a certain limiting regime, such solutions reduce to some elementary ones called “Solitons on unstable condensate.” This degeneration turns out to be conveniently studied by means of basic tools from the theory of Riemann-Hilbert problems. In particular, no acquaintance with Riemann surfaces and theta-function is required for such analysis.

Development of a beam builder for automatic fabrication of large composite space structures

NASA Technical Reports Server (NTRS)

Bodle, J. G.

1979-01-01

The composite material beam builder which will produce triangular beams from pre-consolidated graphite/glass/thermoplastic composite material through automated mechanical processes is presented, side member storage, feed and positioning, ultrasonic welding, and beam cutoff are formed. Each process lends itself to modular subsystem development. Initial development is concentrated on the key processes for roll forming and ultrasonic welding composite thermoplastic materials. The construction and test of an experimental roll forming machine and ultrasonic welding process control techniques are described.

Eisenstein Hecke algebras and Iwasawa theory

NASA Astrophysics Data System (ADS)

Wake, Preston

We show that if an Eisenstein component of the p-adic Hecke algebra associated to modular forms is Gorenstein, then it is necessary that the plus-part of a certain ideal class group is trivial. We also show that this condition is sufficient whenever a conjecture of Sharifi holds. We also formulate a weaker Gorenstein property, and show that this weak Gorenstein property holds if and only if a weak form of Sharifi's conjecture and a weak form of Greenberg's conjecture hold.

A modular approach for item response theory modeling with the R package flirt.

PubMed

Jeon, Minjeong; Rijmen, Frank

2016-06-01

The new R package flirt is introduced for flexible item response theory (IRT) modeling of psychological, educational, and behavior assessment data. flirt integrates a generalized linear and nonlinear mixed modeling framework with graphical model theory. The graphical model framework allows for efficient maximum likelihood estimation. The key feature of flirt is its modular approach to facilitate convenient and flexible model specifications. Researchers can construct customized IRT models by simply selecting various modeling modules, such as parametric forms, number of dimensions, item and person covariates, person groups, link functions, etc. In this paper, we describe major features of flirt and provide examples to illustrate how flirt works in practice.

Looking for empty topological wormhole spacetimes in F(R)-modified gravity

NASA Astrophysics Data System (ADS)

Di Criscienzo, R.; Myrzakulov, R.; Sebastiani, L.

2013-12-01

Much attention has been recently devoted to modified theories of gravity, the simplest models of which overcome General Relativity simply by replacing R with F(R) in the Einstein-Hilbert action. Unfortunately, such models typically lack most of the beautiful solutions discovered in Einstein’s gravity. Nonetheless, in F(R) gravity, it has been possible to get at least few black holes, but still we do not know any empty wormhole-like spacetime solution. This paper aims to explain why it is so hard to get such solutions (given that they exist!). Few solutions are derived in the simplest cases, while only an implicit form has been obtained in the non-trivial case.

Faithful test of nonlocal realism with entangled coherent states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Chang-Woo; Jeong, Hyunseok; Paternostro, Mauro

2011-02-15

We investigate the violation of Leggett's inequality for nonlocal realism using entangled coherent states and various types of local measurements. We prove mathematically the relation between the violation of the Clauser-Horne-Shimony-Holt form of Bell's inequality and Leggett's one when tested by the same resources. For Leggett inequalities, we generalize the nonlocal realistic bound to systems in Hilbert spaces larger than bidimensional ones and introduce an optimization technique that allows one to achieve larger degrees of violation by adjusting the local measurement settings. Our work describes the steps that should be performed to produce a self-consistent generalization of Leggett's original argumentsmore » to continuous-variable states.« less

Study of the convergence behavior of the complex kernel least mean square algorithm.

PubMed

Paul, Thomas K; Ogunfunmi, Tokunbo

2013-09-01

The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.

Gegenbauer-solvable quantum chain model

NASA Astrophysics Data System (ADS)

Znojil, Miloslav

2010-11-01

An N-level quantum model is proposed in which the energies are represented by an N-plet of zeros of a suitable classical orthogonal polynomial. The family of Gegenbauer polynomials G(n,a,x) is selected for illustrative purposes. The main obstacle lies in the non-Hermiticity (aka crypto-Hermiticity) of Hamiltonians H≠H†. We managed to (i) start from elementary secular equation G(N,a,En)=0, (ii) keep our H, in the nearest-neighbor-interaction spirit, tridiagonal, (iii) render it Hermitian in an ad hoc, nonunique Hilbert space endowed with metric Θ≠I, (iv) construct eligible metrics in closed forms ordered by increasing nondiagonality, and (v) interpret the model as a smeared N-site lattice.

Inertial Spontaneous Symmetry Breaking and Quantum Scale Invariance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferreira, Pedro G.; Hill, Christopher T.; Ross, Graham G.

Weyl invariant theories of scalars and gravity can generate all mass scales spontaneously, initiated by a dynamical process of "inertial spontaneous symmetry breaking" that does not involve a potential. This is dictated by the structure of the Weyl current,more » $$K_\\mu$$, and a cosmological phase during which the universe expands and the Einstein-Hilbert effective action is formed. Maintaining exact Weyl invariance in the renormalised quantum theory is straightforward when renormalisation conditions are referred back to the VEV's of fields in the action of the theory, which implies a conserved Weyl current. We do not require scale invariant regulators. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential.« less

Theory for the Emergence of Modularity in Complex Systems

NASA Astrophysics Data System (ADS)

Deem, Michael; Park, Jeong-Man

2013-03-01

Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here develop a theory for the dynamics of modularity in these systems. We find a principle of least action for the evolved modularity at long times. In addition, we find a fluctuation dissipation relation for the rate of change of modularity at short times. We discuss a number of biological and social systems that can be understood with this framework. The modularity of the protein-protein interaction network increases when yeast are exposed to heat shock, and the modularity of the protein-protein networks in both yeast and E. coli appears to have increased over evolutionary time. Food webs in low-energy, stressful environments are more modular than those in plentiful environments, arid ecologies are more modular during droughts, and foraging of sea otters is more modular when food is limiting. The modularity of social networks changes over time: stock brokers instant messaging networks are more modular under stressful market conditions, criminal networks are more modular under increased police pressure, and world trade network modularity has decreased

Resilience of networks formed of interdependent modular networks

NASA Astrophysics Data System (ADS)

Shekhtman, Louis M.; Shai, Saray; Havlin, Shlomo

2015-12-01

Many infrastructure networks have a modular structure and are also interdependent with other infrastructures. While significant research has explored the resilience of interdependent networks, there has been no analysis of the effects of modularity. Here we develop a theoretical framework for attacks on interdependent modular networks and support our results through simulations. We focus, for simplicity, on the case where each network has the same number of communities and the dependency links are restricted to be between pairs of communities of different networks. This is particularly realistic for modeling infrastructure across cities. Each city has its own infrastructures and different infrastructures are dependent only within the city. However, each infrastructure is connected within and between cities. For example, a power grid will connect many cities as will a communication network, yet a power station and communication tower that are interdependent will likely be in the same city. It has previously been shown that single networks are very susceptible to the failure of the interconnected nodes (between communities) (Shai et al 2014 arXiv:1404.4748) and that attacks on these nodes are even more crippling than attacks based on betweenness (da Cunha et al 2015 arXiv:1502.00353). In our example of cities these nodes have long range links which are more likely to fail. For both treelike and looplike interdependent modular networks we find distinct regimes depending on the number of modules, m. (i) In the case where there are fewer modules with strong intraconnections, the system first separates into modules in an abrupt first-order transition and then each module undergoes a second percolation transition. (ii) When there are more modules with many interconnections between them, the system undergoes a single transition. Overall, we find that modular structure can significantly influence the type of transitions observed in interdependent networks and should be considered in attempts to make interdependent networks more resilient.

Connectional Modularity of Top-Down and Bottom-Up Multimodal Inputs to the Lateral Cortex of the Mouse Inferior Colliculus

PubMed Central

Lesicko, Alexandria M.H.; Hristova, Teodora S.; Maigler, Kathleen C.

2016-01-01

The lateral cortex of the inferior colliculus receives information from both auditory and somatosensory structures and is thought to play a role in multisensory integration. Previous studies in the rat have shown that this nucleus contains a series of distinct anatomical modules that stain for GAD-67 as well as other neurochemical markers. In the present study, we sought to better characterize these modules in the mouse inferior colliculus and determine whether the connectivity of other neural structures with the lateral cortex is spatially related to the distribution of these neurochemical modules. Staining for GAD-67 and other markers revealed a single modular network throughout the rostrocaudal extent of the mouse lateral cortex. Somatosensory inputs from the somatosensory cortex and dorsal column nuclei were found to terminate almost exclusively within these modular zones. However, projections from the auditory cortex and central nucleus of the inferior colliculus formed patches that interdigitate with the GAD-67-positive modules. These results suggest that the lateral cortex of the mouse inferior colliculus exhibits connectional as well as neurochemical modularity and may contain multiple segregated processing streams. This finding is discussed in the context of other brain structures in which neuroanatomical and connectional modularity have functional consequences. SIGNIFICANCE STATEMENT Many brain regions contain subnuclear microarchitectures, such as the matrix-striosome organization of the basal ganglia or the patch-interpatch organization of the visual cortex, that shed light on circuit complexities. In the present study, we demonstrate the presence of one such micro-organization in the rodent inferior colliculus. While this structure is typically viewed as an auditory integration center, its lateral cortex appears to be involved in multisensory operations and receives input from somatosensory brain regions. We show here that the lateral cortex can be further subdivided into multiple processing streams: modular regions, which are targeted by somatosensory inputs, and extramodular zones that receive auditory information. PMID:27798184

Topological strings on singular elliptic Calabi-Yau 3-folds and minimal 6d SCFTs

NASA Astrophysics Data System (ADS)

Del Zotto, Michele; Gu, Jie; Huang, Min-xin; Kashani-Poor, Amir-Kian; Klemm, Albrecht; Lockhart, Guglielmo

2018-03-01

We apply the modular approach to computing the topological string partition function on non-compact elliptically fibered Calabi-Yau 3-folds with higher Kodaira singularities in the fiber. The approach consists in making an ansatz for the partition function at given base degree, exact in all fiber classes to arbitrary order and to all genus, in terms of a rational function of weak Jacobi forms. Our results yield, at given base degree, the elliptic genus of the corresponding non-critical 6d string, and thus the associated BPS invariants of the 6d theory. The required elliptic indices are determined from the chiral anomaly 4-form of the 2d worldsheet theories, or the 8-form of the corresponding 6d theories, and completely fix the holomorphic anomaly equation constraining the partition function. We introduce subrings of the known rings of Weyl invariant Jacobi forms which are adapted to the additional symmetries of the partition function, making its computation feasible to low base wrapping number. In contradistinction to the case of simpler singularities, generic vanishing conditions on BPS numbers are no longer sufficient to fix the modular ansatz at arbitrary base wrapping degree. We show that to low degree, imposing exact vanishing conditions does suffice, and conjecture this to be the case generally.

The Geometry of Quadratic Polynomial Differential Systems with a Finite and an Infinite Saddle-Node (C)

NASA Astrophysics Data System (ADS)

Artés, Joan C.; Rezende, Alex C.; Oliveira, Regilene D. S.

Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert's 16th problem [Hilbert, 1900, 1902], are still open for this family. Our goal is to make a global study of the family QsnSN of all real quadratic polynomial differential systems which have a finite semi-elemental saddle-node and an infinite saddle-node formed by the collision of two infinite singular points. This family can be divided into three different subfamilies, all of them with the finite saddle-node in the origin of the plane with the eigenvectors on the axes and with the eigenvector associated with the zero eigenvalue on the horizontal axis and (A) with the infinite saddle-node in the horizontal axis, (B) with the infinite saddle-node in the vertical axis and (C) with the infinite saddle-node in the bisector of the first and third quadrants. These three subfamilies modulo the action of the affine group and time homotheties are three-dimensional and we give the bifurcation diagram of their closure with respect to specific normal forms, in the three-dimensional real projective space. The subfamilies (A) and (B) have already been studied [Artés et al., 2013b] and in this paper we provide the complete study of the geometry of the last family (C). The bifurcation diagram for the subfamily (C) yields 371 topologically distinct phase portraits with and without limit cycles for systems in the closure /line{QsnSN(C)} within the representatives of QsnSN(C) given by a chosen normal form. Algebraic invariants are used to construct the bifurcation set. The phase portraits are represented on the Poincaré disk. The bifurcation set of /line{QsnSN(C)} is not only algebraic due to the presence of some surfaces found numerically. All points in these surfaces correspond to either connections of separatrices, or the presence of a double limit cycle.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slater, Paul B.

Paralleling our recent computationally intensive (quasi-Monte Carlo) work for the case N=4 (e-print quant-ph/0308037), we undertake the task for N=6 of computing to high numerical accuracy, the formulas of Sommers and Zyczkowski (e-print quant-ph/0304041) for the (N{sup 2}-1)-dimensional volume and (N{sup 2}-2)-dimensional hyperarea of the (separable and nonseparable) NxN density matrices, based on the Bures (minimal monotone) metric--and also their analogous formulas (e-print quant-ph/0302197) for the (nonmonotone) flat Hilbert-Schmidt metric. With the same seven 10{sup 9} well-distributed ('low-discrepancy') sample points, we estimate the unknown volumes and hyperareas based on five additional (monotone) metrics of interest, including the Kubo-Mori and Wigner-Yanase.more » Further, we estimate all of these seven volume and seven hyperarea (unknown) quantities when restricted to the separable density matrices. The ratios of separable volumes (hyperareas) to separable plus nonseparable volumes (hyperareas) yield estimates of the separability probabilities of generically rank-6 (rank-5) density matrices. The (rank-6) separability probabilities obtained based on the 35-dimensional volumes appear to be--independently of the metric (each of the seven inducing Haar measure) employed--twice as large as those (rank-5 ones) based on the 34-dimensional hyperareas. (An additional estimate--33.9982--of the ratio of the rank-6 Hilbert-Schmidt separability probability to the rank-4 one is quite clearly close to integral too.) The doubling relationship also appears to hold for the N=4 case for the Hilbert-Schmidt metric, but not the others. We fit simple exact formulas to our estimates of the Hilbert-Schmidt separable volumes and hyperareas in both the N=4 and N=6 cases.« less

A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials

NASA Astrophysics Data System (ADS)

Deift, P.; Kriecherbauer, T.; McLaughlin, K. T.-R.; Venakides, S.; Zhou, X.

2001-08-01

A few years ago the authors introduced a new approach to study asymptotic questions for orthogonal polynomials. In this paper we give an overview of our method and review the results which have been obtained in Deift et al. (Internat. Math. Res. Notices (1997) 759, Comm. Pure Appl. Math. 52 (1999) 1491, 1335), Deift (Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes, Vol. 3, New York University, 1999), Kriecherbauer and McLaughlin (Internat. Math. Res. Notices (1999) 299) and Baik et al. (J. Amer. Math. Soc. 12 (1999) 1119). We mainly consider orthogonal polynomials with respect to weights on the real line which are either (1) Freud-type weights d[alpha](x)=e-Q(x) dx (Q polynomial or Q(x)=x[beta], [beta]>0), or (2) varying weights d[alpha]n(x)=e-nV(x) dx (V analytic, limx-->[infinity] V(x)/logx=[infinity]). We obtain Plancherel-Rotach-type asymptotics in the entire complex plane as well as asymptotic formulae with error estimates for the leading coefficients, for the recurrence coefficients, and for the zeros of the orthogonal polynomials. Our proof starts from an observation of Fokas et al. (Comm. Math. Phys. 142 (1991) 313) that the orthogonal polynomials can be determined as solutions of certain matrix valued Riemann-Hilbert problems. We analyze the Riemann-Hilbert problems by a steepest descent type method introduced by Deift and Zhou (Ann. Math. 137 (1993) 295) and further developed in Deift and Zhou (Comm. Pure Appl. Math. 48 (1995) 277) and Deift et al. (Proc. Nat. Acad. Sci. USA 95 (1998) 450). A crucial step in our analysis is the use of the well-known equilibrium measure which describes the asymptotic distribution of the zeros of the orthogonal polynomials.

On the Hilbert-Huang Transform Data Processing System Development

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Flatley, Thomas P.; Huang, Norden E.; Cornwell, Evette; Smith, Darell

2003-01-01

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). The Fourier view of nonlinear mechanics that had existed for a long time, and the associated FFT (fairly recent development), carry strong a-priori assumptions about the source data, such as linearity and of being stationary. Natural phenomena measurements are essentially nonlinear and nonstationary. A very recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT) proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using the Empirical Mode Decomposition (EMD) followed by the Hilbert Transform of the empirical decomposition data (HT), the HHT allows spectrum analysis of nonlinear and nonstationary data by using an engineering a-posteriori data processing, based on the EMD algorithm. This results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF) that can be further analyzed for spectrum interpretation by the classical Hilbert Transform. This paper describes phase one of the development of a new engineering tool, the HHT Data Processing System (HHTDPS). The HHTDPS allows applying the "T to a data vector in a fashion similar to the heritage FFT. It is a generic, low cost, high performance personal computer (PC) based system that implements the HHT computational algorithms in a user friendly, file driven environment. This paper also presents a quantitative analysis for a complex waveform data sample, a summary of technology commercialization efforts and the lessons learned from this new technology development.

Method of the Determination of Exterior Orientation of Sensors in Hilbert Type Space.

PubMed

Stępień, Grzegorz

2018-03-17

The following article presents a new isometric transformation algorithm based on the transformation in the newly normed Hilbert type space. The presented method is based on so-called virtual translations, already known in advance, of two relative oblique orthogonal coordinate systems-interior and exterior orientation of sensors-to a common, known in both systems, point. Each of the systems is translated along its axis (the systems have common origins) and at the same time the angular relative orientation of both coordinate systems is constant. The translation of both coordinate systems is defined by the spatial norm determining the length of vectors in the new Hilbert type space. As such, the displacement of two relative oblique orthogonal systems is reduced to zero. This makes it possible to directly calculate the rotation matrix of the sensor. The next and final step is the return translation of the system along an already known track. The method can be used for big rotation angles. The method was verified in laboratory conditions for the test data set and measurement data (field data). The accuracy of the results in the laboratory test is on the level of 10 -6 of the input data. This confirmed the correctness of the assumed calculation method. The method is a further development of the author's 2017 Total Free Station (TFS) transformation to several centroids in Hilbert type space. This is the reason why the method is called Multi-Centroid Isometric Transformation-MCIT. MCIT is very fast and enables, by reducing to zero the translation of two relative oblique orthogonal coordinate systems, direct calculation of the exterior orientation of the sensors.

The open quantum Brownian motions

NASA Astrophysics Data System (ADS)

Bauer, Michel; Bernard, Denis; Tilloy, Antoine

2014-09-01

Using quantum parallelism on random walks as the original seed, we introduce new quantum stochastic processes, the open quantum Brownian motions. They describe the behaviors of quantum walkers—with internal degrees of freedom which serve as random gyroscopes—interacting with a series of probes which serve as quantum coins. These processes may also be viewed as the scaling limit of open quantum random walks and we develop this approach along three different lines: the quantum trajectory, the quantum dynamical map and the quantum stochastic differential equation. We also present a study of the simplest case, with a two level system as an internal gyroscope, illustrating the interplay between the ballistic and diffusive behaviors at work in these processes. Notation H_z : orbital (walker) Hilbert space, {C}^{{Z}} in the discrete, L^2({R}) in the continuum H_c : internal spin (or gyroscope) Hilbert space H_sys=H_z\\otimesH_c : system Hilbert space H_p : probe (or quantum coin) Hilbert space, H_p={C}^2 \\rho^tot_t : density matrix for the total system (walker + internal spin + quantum coins) \\bar \\rho_t : reduced density matrix on H_sys : \\bar\\rho_t=\\int dxdy\\, \\bar\\rho_t(x,y)\\otimes | x \\rangle _z\\langle y | \\hat \\rho_t : system density matrix in a quantum trajectory: \\hat\\rho_t=\\int dxdy\\, \\hat\\rho_t(x,y)\\otimes | x \\rangle _z\\langle y | . If diagonal and localized in position: \\hat \\rho_t=\\rho_t\\otimes| X_t \\rangle _z\\langle X_t | ρt: internal density matrix in a simple quantum trajectory Xt: walker position in a simple quantum trajectory Bt: normalized Brownian motion ξt, \\xi_t^\\dagger : quantum noises

The Case for and against Modularisation.

ERIC Educational Resources Information Center

Jonathan, Ruth

1987-01-01

Presents arguments for and against modularization as a form of curriculum organization. Looks at implications for the content of the curriculum, for the learning experience of students, for the professional experience of teachers, for the development of the educational institution, and for the society at large. (JHZ)

Squashed Toric Sigma Models and Mock Modular Forms

NASA Astrophysics Data System (ADS)

Gupta, Rajesh Kumar; Murthy, Sameer

2018-05-01

We study a class of two-dimensional N}=(2,2)} sigma models called squashed toric sigma models, using their Gauged Linear Sigma Models (GLSM) description. These models are obtained by gauging the global {U(1)} symmetries of toric GLSMs and introducing a set of corresponding compensator superfields. The geometry of the resulting vacuum manifold is a deformation of the corresponding toric manifold in which the torus fibration maintains a constant size in the interior of the manifold, thus producing a neck-like region. We compute the elliptic genus of these models, using localization, in the case when the unsquashed vacuum manifolds obey the Calabi-Yau condition. The elliptic genera have a non-holomorphic dependence on the modular parameter {τ} coming from the continuum produced by the neck. In the simplest case corresponding to squashed {C / Z_{2 the elliptic genus is a mixed mock Jacobi form which coincides with the elliptic genus of the {N=(2,2)} {SL(2,R) / U(1)} cigar coset.

Integrating yoga therapy in the management of urinary incontinence: a case report.

PubMed

Vinchurkar, Suhas Ashok; Arankalle, Dhananjay Vijay

2015-04-01

A 63-year-old overweight female prediagnosed of stress urinary incontinence presented with exacerbated events of urine leakage. She was advised a residential lifestyle and behavioral program, primarily consisting of a monitored yoga therapy module, apart from her ongoing anticholinergic medicine, for 21 days. Assessments were based on a frequency volume chart, a bladder diary for the entire duration of treatment, and the International Consultation on Incontinence Modular Questionnaire-Urinary Incontinence Short Form questionnaire on the days of admission and discharge. A total of 1.9 kg of weight loss was observed during her stay. Usage of pad, as reported in her diary, reduced from 3 to 1 per day. Her International Consultation on Incontinence Modular Questionnaire-Urinary Incontinence Short Form score reduced from 16 to 9, indicating better continence. She expressed subjective well-being and confidence in her social interactions. This is probably the first case report demonstrating feasibility of integration of yoga therapy in the management of urinary incontinence. © The Author(s) 2014.

Laboratory demonstration of image reconstruction for coherent optical system of modular imaging collectors (COSMIC)

NASA Technical Reports Server (NTRS)

Traub, W. A.

1984-01-01

The first physical demonstration of the principle of image reconstruction using a set of images from a diffraction-blurred elongated aperture is reported. This is an optical validation of previous theoretical and numerical simulations of the COSMIC telescope array (coherent optical system of modular imaging collectors). The present experiment utilizes 17 diffraction blurred exposures of a laboratory light source, as imaged by a lens covered by a narrow-slit aperture; the aperture is rotated 10 degrees between each exposure. The images are recorded in digitized form by a CCD camera, Fourier transformed, numerically filtered, and added; the sum is then filtered and inverse Fourier transformed to form the final image. The image reconstruction process is found to be stable with respect to uncertainties in values of all physical parameters such as effective wavelength, rotation angle, pointing jitter, and aperture shape. Future experiments will explore the effects of low counting rates, autoguiding on the image, various aperture configurations, and separated optics.

The short pulse equation by a Riemann-Hilbert approach

NASA Astrophysics Data System (ADS)

Boutet de Monvel, Anne; Shepelsky, Dmitry; Zielinski, Lech

2017-07-01

We develop a Riemann-Hilbert approach to the inverse scattering transform method for the short pulse (SP) equation u_{xt}=u+{1/6}(u^3)_{xx} with zero boundary conditions (as |x|→ ∞). This approach is directly applied to a Lax pair for the SP equation. It allows us to give a parametric representation of the solution to the Cauchy problem. This representation is then used for studying the longtime behavior of the solution as well as for retrieving the soliton solutions. Finally, the analysis of the longtime behavior allows us to formulate, in spectral terms, a sufficient condition for the wave breaking.

Computation and projection of spiral wave trajectories during atrial fibrillation: a computational study.

PubMed

Pashaei, Ali; Bayer, Jason; Meillet, Valentin; Dubois, Rémi; Vigmond, Edward

2015-03-01

To show how atrial fibrillation rotor activity on the heart surface manifests as phase on the torso, fibrillation was induced on a geometrically accurate computer model of the human atria. The Hilbert transform, time embedding, and filament detection were compared. Electrical activity on the epicardium was used to compute potentials on different surfaces from the atria to the torso. The Hilbert transform produces erroneous phase when pacing for longer than the action potential duration. The number of phase singularities, frequency content, and the dominant frequency decreased with distance from the heart, except for the convex hull. Copyright © 2015 Elsevier Inc. All rights reserved.

Towards deconstruction of the Type D (2,0) theory

NASA Astrophysics Data System (ADS)

Bourget, Antoine; Pini, Alessandro; Rodriguez-Gomez, Diego

2017-12-01

We propose a four-dimensional supersymmetric theory that deconstructs, in a particular limit, the six-dimensional (2, 0) theory of type D k . This 4d theory is defined by a necklace quiver with alternating gauge nodes O(2 k) and Sp( k). We test this proposal by comparing the 6d half-BPS index to the Higgs branch Hilbert series of the 4d theory. In the process, we overcome several technical difficulties, such as Hilbert series calculations for non-complete intersections, and the choice of O versus SO gauge groups. Consistently, the result matches the Coulomb branch formula for the mirror theory upon reduction to 3d.

On the Hilbert-Huang Transform Theoretical Foundation

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Blank, Karin; Huang, Norden E.

2004-01-01

The Hilbert-Huang Transform [HHT] is a novel empirical method for spectrum analysis of non-linear and non-stationary signals. The HHT is a recent development and much remains to be done to establish the theoretical foundation of the HHT algorithms. This paper develops the theoretical foundation for the convergence of the HHT sifting algorithm and it proves that the finest spectrum scale will always be the first generated by the HHT Empirical Mode Decomposition (EMD) algorithm. The theoretical foundation for cutting an extrema data points set into two parts is also developed. This then allows parallel signal processing for the HHT computationally complex sifting algorithm and its optimization in hardware.

Decrement of uterine myometrial burst duration as a correlate to active labor: a Hilbert phase approach.

PubMed

Govindan, Rathinaswamy B; Vairavan, Srinivasan; Furdea, Adrian; Murphy, Pam; Preissl, Hubert; Eswaran, Hari

2010-01-01

We propose a novel approach based on Hilbert phase to identify the burst in the uterine myometrial activity. We apply this approach to 24 serial magnetomyographic signals recorded from four pregnant women using a 151 SQUID array system. The bursts identified with this approach are evaluated for duration and are correlated with the gestational age. In all four subjects, we find a decrease in the duration of burst as the subject approaches active labor. As was shown in animal studies, this result indicates a faster conduction time between the muscle cells which activate a larger number of muscle units in a synchronous manner.

A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line

NASA Astrophysics Data System (ADS)

Its, A.; Sukhanov, V.

2016-05-01

The paper is concerned with the inverse scattering problem for the Stark operator on the line with a potential from the Schwartz class. In our study of the inverse problem, we use the Riemann-Hilbert formalism. This allows us to overcome the principal technical difficulties which arise in the more traditional approaches based on the Gel’fand-Levitan-Marchenko equations, and indeed solve the problem. We also produce a complete description of the relevant scattering data (which have not been obtained in the previous works on the Stark operator) and establish the bijection between the Schwartz class potentials and the scattering data.

Minimal sufficient positive-operator valued measure on a separable Hilbert space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuramochi, Yui, E-mail: kuramochi.yui.22c@st.kyoto-u.ac.jp

We introduce a concept of a minimal sufficient positive-operator valued measure (POVM), which is the least redundant POVM among the POVMs that have the equivalent information about the measured quantum system. Assuming the system Hilbert space to be separable, we show that for a given POVM, a sufficient statistic called a Lehmann-Scheffé-Bahadur statistic induces a minimal sufficient POVM. We also show that every POVM has an equivalent minimal sufficient POVM and that such a minimal sufficient POVM is unique up to relabeling neglecting null sets. We apply these results to discrete POVMs and information conservation conditions proposed by the author.

Local quantum measurement and no-signaling imply quantum correlations.

PubMed

Barnum, H; Beigi, S; Boixo, S; Elliott, M B; Wehner, S

2010-04-09

We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that a Hilbert space is assigned to each party, and then all local positive-operator-valued measurements are (in principle) available; however, the joint system is not necessarily described by a Hilbert space. In particular, we do not assume the tensor product formalism between the joint systems. Our result shows that if any experiment would give nonlocal correlations beyond quantum mechanics, quantum theory would be invalidated even locally.

Application of the Hilbert space average method on heat conduction models.

PubMed

Michel, Mathias; Gemmer, Jochen; Mahler, Günter

2006-01-01

We analyze closed one-dimensional chains of weakly coupled many level systems, by means of the so-called Hilbert space average method (HAM). Subject to some concrete conditions on the Hamiltonian of the system, our theory predicts energy diffusion with respect to a coarse-grained description for almost all initial states. Close to the respective equilibrium, we investigate this behavior in terms of heat transport and derive the heat conduction coefficient. Thus, we are able to show that both heat (energy) diffusive behavior as well as Fourier's law follows from and is compatible with a reversible Schrödinger dynamics on the complete level of description.

Remarks on entanglement entropy in string theory

NASA Astrophysics Data System (ADS)

Balasubramanian, Vijay; Parrikar, Onkar

2018-03-01

Entanglement entropy for spatial subregions is difficult to define in string theory because of the extended nature of strings. Here we propose a definition for bosonic open strings using the framework of string field theory. The key difference (compared to ordinary quantum field theory) is that the subregion is chosen inside a Cauchy surface in the "space of open string configurations." We first present a simple calculation of this entanglement entropy in free light-cone string field theory, ignoring subtleties related to the factorization of the Hilbert space. We reproduce the answer expected from an effective field theory point of view, namely a sum over the one-loop entanglement entropies corresponding to all the particle-excitations of the string, and further show that the full string theory regulates ultraviolet divergences in the entanglement entropy. We then revisit the question of factorization of the Hilbert space by analyzing the covariant phase-space associated with a subregion in Witten's covariant string field theory. We show that the pure gauge (i.e., BRST exact) modes in the string field become dynamical at the entanglement cut. Thus, a proper definition of the entropy must involve an extended Hilbert space, with new stringy edge modes localized at the entanglement cut.

A High-Resolution Demodulation Algorithm for FBG-FP Static-Strain Sensors Based on the Hilbert Transform and Cross Third-Order Cumulant

PubMed Central

Huang, Wenzhu; Zhen, Tengkun; Zhang, Wentao; Zhang, Fusheng; Li, Fang

2015-01-01

Static strain can be detected by measuring a cross-correlation of reflection spectra from two fiber Bragg gratings (FBGs). However, the static-strain measurement resolution is limited by the dominant Gaussian noise source when using this traditional method. This paper presents a novel static-strain demodulation algorithm for FBG-based Fabry-Perot interferometers (FBG-FPs). The Hilbert transform is proposed for changing the Gaussian distribution of the two FBG-FPs’ reflection spectra, and a cross third-order cumulant is used to use the results of the Hilbert transform and get a group of noise-vanished signals which can be used to accurately calculate the wavelength difference of the two FBG-FPs. The benefit by these processes is that Gaussian noise in the spectra can be suppressed completely in theory and a higher resolution can be reached. In order to verify the precision and flexibility of this algorithm, a detailed theory model and a simulation analysis are given, and an experiment is implemented. As a result, a static-strain resolution of 0.9 nε under laboratory environment condition is achieved, showing a higher resolution than the traditional cross-correlation method. PMID:25923938

A High-Resolution Demodulation Algorithm for FBG-FP Static-Strain Sensors Based on the Hilbert Transform and Cross Third-Order Cumulant.

PubMed

Huang, Wenzhu; Zhen, Tengkun; Zhang, Wentao; Zhang, Fusheng; Li, Fang

2015-04-27

Static strain can be detected by measuring a cross-correlation of reflection spectra from two fiber Bragg gratings (FBGs). However, the static-strain measurement resolution is limited by the dominant Gaussian noise source when using this traditional method. This paper presents a novel static-strain demodulation algorithm for FBG-based Fabry-Perot interferometers (FBG-FPs). The Hilbert transform is proposed for changing the Gaussian distribution of the two FBG-FPs' reflection spectra, and a cross third-order cumulant is used to use the results of the Hilbert transform and get a group of noise-vanished signals which can be used to accurately calculate the wavelength difference of the two FBG-FPs. The benefit by these processes is that Gaussian noise in the spectra can be suppressed completely in theory and a higher resolution can be reached. In order to verify the precision and flexibility of this algorithm, a detailed theory model and a simulation analysis are given, and an experiment is implemented. As a result, a static-strain resolution of 0.9 nε under laboratory environment condition is achieved, showing a higher resolution than the traditional cross-correlation method.

Continuously tunable photonic fractional Hilbert transformer using a high-contrast germanium-doped silica-on-silicon microring resonator.

PubMed

Shahoei, Hiva; Dumais, Patrick; Yao, Jianping

2014-05-01

We propose and experimentally demonstrate a continuously tunable fractional Hilbert transformer (FHT) based on a high-contrast germanium-doped silica-on-silicon (SOS) microring resonator (MRR). The propagation loss of a high-contrast germanium-doped SOS waveguide can be very small (0.02 dB/cm) while the lossless bend radius can be less than 1 mm. These characteristics lead to the fabrication of an MRR with a high Q-factor and a large free-spectral range (FSR), which is needed to implement a Hilbert transformer (HT). The SOS MRR is strongly polarization dependent. By changing the polarization direction of the input signal, the phase shift introduced at the center of the resonance spectrum is changed. The tunable phase shift at the resonance wavelength can be used to implement a tunable FHT. A germanium-doped SOS MRR with a high-index contrast of 3.8% is fabricated. The use of the fabricated MRR for the implementation of a tunable FHT with tunable orders at 1, 0.85, 0.95, 1.05, and 1.13 for a Gaussian pulse with the temporal full width at half-maximum of 80 ps is experimentally demonstrated.

On Hilbert-Huang Transform Based Synthesis of a Signal Contaminated by Radio Frequency Interference or Fringes

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Shiri, Ron S.; Vootukuru, Meg; Coletti, Alessandro

2015-01-01

Norden E. Huang et al. had proposed and published the Hilbert-Huang Transform (HHT) concept correspondently in 1996, 1998. The HHT is a novel method for adaptive spectral analysis of non-linear and non-stationary signals. The HHT comprises two components: - the Huang Empirical Mode Decomposition (EMD), resulting in an adaptive data-derived basis of Intrinsic Mode functions (IMFs), and the Hilbert Spectral Analysis (HSA1) based on the Hilbert Transform for 1-dimension (1D) applied to the EMD IMF's outcome. Although paper describes the HHT concept in great depth, it does not contain all needed methodology to implement the HHT computer code. In 2004, Semion Kizhner and Karin Blank implemented the reference digital HHT real-time data processing system for 1D (HHT-DPS Version 1.4). The case for 2-Dimension (2D) (HHT2) proved to be difficult due to the computational complexity of EMD for 2D (EMD2) and absence of a suitable Hilbert Transform for 2D spectral analysis (HSA2). The real-time EMD2 and HSA2 comprise the real-time HHT2. Kizhner completed the real-time EMD2 and the HSA2 reference digital implementations respectively in 2013 & 2014. Still, the HHT2 outcome synthesis remains an active research area. This paper presents the initial concepts and preliminary results of HHT2-based synthesis and its application to processing of signals contaminated by Radio-Frequency Interference (RFI), as well as optical systems' fringe detection and mitigation at design stage. The Soil Moisture Active Passive (SMAP mission (SMAP) carries a radiometer instrument that measures Earth soil moisture at L1 frequency (1.4 GHz polarimetric - H, V, 3rd and 4th Stokes parameters). There is abundant RFI at L1 and because soil moisture is a strategic parameter, it is important to be able to recover the RFI-contaminated measurement samples (15% of telemetry). State-of-the-art only allows RFI detection and removes RFI-contaminated measurements. The HHT-based analysis and synthesis facilitates recovery of measurements contaminated by all kinds of RFI, including jamming [7-8]. The fringes are inherent in optical systems and multi-layer complex contour expensive coatings are employed to remove the unwanted fringes. HHT2-based analysis allows test image decomposition to analyze and detect fringes, and HHT2-based synthesis of useful image.

Practical interior tomography with radial Hilbert filtering and a priori knowledge in a small round area.

PubMed

Tang, Shaojie; Yang, Yi; Tang, Xiangyang

2012-01-01

Interior tomography problem can be solved using the so-called differentiated backprojection-projection onto convex sets (DBP-POCS) method, which requires a priori knowledge within a small area interior to the region of interest (ROI) to be imaged. In theory, the small area wherein the a priori knowledge is required can be in any shape, but most of the existing implementations carry out the Hilbert filtering either horizontally or vertically, leading to a vertical or horizontal strip that may be across a large area in the object. In this work, we implement a practical DBP-POCS method with radial Hilbert filtering and thus the small area with the a priori knowledge can be roughly round (e.g., a sinus or ventricles among other anatomic cavities in human or animal body). We also conduct an experimental evaluation to verify the performance of this practical implementation. We specifically re-derive the reconstruction formula in the DBP-POCS fashion with radial Hilbert filtering to assure that only a small round area with the a priori knowledge be needed (namely radial DBP-POCS method henceforth). The performance of the practical DBP-POCS method with radial Hilbert filtering and a priori knowledge in a small round area is evaluated with projection data of the standard and modified Shepp-Logan phantoms simulated by computer, followed by a verification using real projection data acquired by a computed tomography (CT) scanner. The preliminary performance study shows that, if a priori knowledge in a small round area is available, the radial DBP-POCS method can solve the interior tomography problem in a more practical way at high accuracy. In comparison to the implementations of DBP-POCS method demanding the a priori knowledge in horizontal or vertical strip, the radial DBP-POCS method requires the a priori knowledge within a small round area only. Such a relaxed requirement on the availability of a priori knowledge can be readily met in practice, because a variety of small round areas (e.g., air-filled sinuses or fluid-filled ventricles among other anatomic cavities) exist in human or animal body. Therefore, the radial DBP-POCS method with a priori knowledge in a small round area is more feasible in clinical and preclinical practice.

Quantum Superalgebras at Roots of Unity and Topological Invariants of Three-manifolds

NASA Astrophysics Data System (ADS)

Blumen, Sacha C.

2006-01-01

The general method of Reshetikhin and Turaev is followed to develop topological invariants of closed, connected, orientable 3-manifolds from a new class of algebras called pseudo-modular Hopf algebras. Pseudo-modular Hopf algebras are a class of Z_2-graded ribbon Hopf algebras that generalise the concept of a modular Hopf algebra. The quantum superalgebra U_q(osp(1|2n)) over C is considered with q a primitive N^th root of unity for all integers N >= 3. For such a q, a certain left ideal I of U_q(osp(1|2n)) is also a two-sided Hopf ideal, and the quotient algebra U_q^(N)(osp(1|2n)) = U_q(osp(1|2n)) / I is a Z_2-graded ribbon Hopf algebra. For all n and all N >= 3, a finite collection of finite dimensional representations of U_q^(N)(osp(1|2n)) is defined. Each such representation of U_q^(N)(osp(1|2n)) is labelled by an integral dominant weight belonging to the truncated dominant Weyl chamber. Properties of these representations are considered: the quantum superdimension of each representation is calculated, each representation is shown to be self-dual, and more importantly, the decomposition of the tensor product of an arbitrary number of such representations is obtained for even N. It is proved that the quotient algebra U_q^(N)(osp(1|2n)), together with the set of finite dimensional representations discussed above, form a pseudo-modular Hopf algebra when N >= 6 is twice an odd number. Using this pseudo-modular Hopf algebra, we construct a topological invariant of 3-manifolds. This invariant is shown to be different to the topological invariants of 3-manifolds arising from quantum so(2n+1) at roots of unity.

Process, System, Causality, and Quantum Mechanics: A Psychoanalysis of Animal Faith

NASA Astrophysics Data System (ADS)

Etter, Tom; Noyes, H. Pierre

We shall argue in this paper that a central piece of modern physics does not really belong to physics at all but to elementary probability theory. Given a joint probability distribution J on a set of random variables containing x and y, define a link between x and y to be the condition x=y on J. Define the {\\it state} D of a link x=y as the joint probability distribution matrix on x and y without the link. The two core laws of quantum mechanics are the Born probability rule, and the unitary dynamical law whose best known form is the Schrodinger's equation. Von Neumann formulated these two laws in the language of Hilbert space as prob(P) = trace(PD) and D'T = TD respectively, where P is a projection, D and D' are (von Neumann) density matrices, and T is a unitary transformation. We'll see that if we regard link states as density matrices, the algebraic forms of these two core laws occur as completely general theorems about links. When we extend probability theory by allowing cases to count negatively, we find that the Hilbert space framework of quantum mechanics proper emerges from the assumption that all D's are symmetrical in rows and columns. On the other hand, Markovian systems emerge when we assume that one of every linked variable pair has a uniform probability distribution. By representing quantum and Markovian structure in this way, we see clearly both how they differ, and also how they can coexist in natural harmony with each other, as they must in quantum measurement, which we'll examine in some detail. Looking beyond quantum mechanics, we see how both structures have their special places in a much larger continuum of formal systems that we have yet to look for in nature.

Using peptide array to identify binding motifs and interaction networks for modular domains.

PubMed

Li, Shawn S-C; Wu, Chenggang

2009-01-01

Specific protein-protein interactions underlie all essential biological processes and form the basis of cellular signal transduction. The recognition of a short, linear peptide sequence in one protein by a modular domain in another represents a common theme of macromolecular recognition in cells, and the importance of this mode of protein-protein interaction is highlighted by the large number of peptide-binding domains encoded by the human genome. This phenomenon also provides a unique opportunity to identify protein-protein binding events using peptide arrays and complementary biochemical assays. Accordingly, high-density peptide array has emerged as a useful tool by which to map domain-mediated protein-protein interaction networks at the proteome level. Using the Src-homology 2 (SH2) and 3 (SH3) domains as examples, we describe the application of oriented peptide array libraries in uncovering specific motifs recognized by an SH2 domain and the use of high-density peptide arrays in identifying interaction networks mediated by the SH3 domain. Methods reviewed here could also be applied to other modular domains, including catalytic domains, that recognize linear peptide sequences.

Modular Activating Receptors in Innate and Adaptive Immunity.

PubMed

Berry, Richard; Call, Matthew E

2017-03-14

Triggering of cell-mediated immunity is largely dependent on the recognition of foreign or abnormal molecules by a myriad of cell surface-bound receptors. Many activating immune receptors do not possess any intrinsic signaling capacity but instead form noncovalent complexes with one or more dimeric signaling modules that communicate with a common set of kinases to initiate intracellular information-transfer pathways. This modular architecture, where the ligand binding and signaling functions are detached from one another, is a common theme that is widely employed throughout the innate and adaptive arms of immune systems. The evolutionary advantages of this highly adaptable platform for molecular recognition are visible in the variety of ligand-receptor interactions that can be linked to common signaling pathways, the diversification of receptor modules in response to pathogen challenges, and the amplification of cellular responses through incorporation of multiple signaling motifs. Here we provide an overview of the major classes of modular activating immune receptors and outline the current state of knowledge regarding how these receptors assemble, recognize their ligands, and ultimately trigger intracellular signal transduction pathways that activate immune cell effector functions.

Survey of Modular Military Vehicles: Benefits and Burdens

DTIC Science & Technology

2016-01-01

Survey of Modular Military Vehicles: BENEFITS and BURDENS Jean M. Dasch and David J. Gorsich Modularity in military vehicle design is generally...considered a positive attribute that promotes adaptability, resilience, and cost savings. The benefits and burdens of modularity are considered by...Engineering Center, vehicles were considered based on horizontal modularity , vertical modularity , and distributed modularity . Examples were given for each

Hardware-Software Complex for Measurement of Energy and Angular Distributions of Charged Particles Formed in Nuclear Reactions

NASA Astrophysics Data System (ADS)

Vikhlyantsev, O. P.; Generalov, L. N.; Kuryakin, A. V.; Karpov, I. A.; Gurin, N. E.; Tumkin, A. D.; Fil'chagin, S. V.

2017-12-01

A hardware-software complex for measurement of energy and angular distributions of charged particles formed in nuclear reactions is presented. Hardware and software structures of the complex, the basic set of the modular nuclear-physical apparatus of a multichannel detecting system on the basis of Δ E- E telescopes of silicon detectors, and the hardware of experimental data collection, storage, and processing are presented and described.

Battery with modular air cathode and anode cage

DOEpatents

Niksa, Marilyn J.; Pohto, Gerald R.; Lakatos, Leslie K.; Wheeler, Douglas J.; Niksa, Andrew J.; Schue, Thomas J.

1987-01-01

A battery assembly of the consumable metal anode type has now been constructed for ready assembly as well as disassembly. In a non-conductive and at least substantially inert cell body, space is provided for receiving an open-structured, non-consumable anode cage. The cage has an open top for facilitating insertion of an anode. A modular cathode is used, comprising a peripheral current conductor frame clamped about a grid reinforced air cathode in sheet form. The air cathode may be double gridded. The cathode frame can be sealed, during assembly, with electrolyte-resistant-sealant as well as with adhesive. The resulting cathode module can be assembled outside the cell body and readily inserted therein, or can later be easily removed therefrom.

Battery with modular air cathode and anode cage

DOEpatents

Niksa, Marilyn J.; Pohto, Gerald R.; Lakatos, Leslie K.; Wheeler, Douglas J.; Niksa, Andrew J.; Schue, Thomas J.; Turk, Thomas R.

1988-01-01

A battery assembly of the consumable metal anode type has now been constructed for ready assembly as well as disassembly. In a non-conductive and at least substantially inert cell body, space is provided for receiving an open-structured, non-consumable anode cage. The cage has an open top for facilitating insertion of an anode. A modular cathode is used, comprising a peripheral current conductor frame clamped about a grid reinforced air cathode in sheet form. The air cathode may be double gridded. The cathode frame can be sealed, during assembly, with electrolyte-resistant-sealant as well as with adhesive. The resulting cathode module can be assembled outside the cell body and readily inserted therein, or can later be easily removed therefrom.

Digital Material Assembly by Passive Means and Modular Isotropic Lattice Extruder System

NASA Technical Reports Server (NTRS)

Gershenfeld, Neil (Inventor); Carney, Matthew Eli (Inventor); Jenett, Benjamin (Inventor)

2017-01-01

A set of machines and related systems build structures by the additive assembly of discrete parts. These digital material assemblies constrain the constituent parts to a discrete set of possible positions and orientations. In doing so, the structures exhibit many of the properties inherent in digital communication such as error correction, fault tolerance and allow the assembly of precise structures with comparatively imprecise tools. Assembly of discrete cellular lattices by a Modular Isotropic Lattice Extruder System (MILES) is implemented by pulling strings of lattice elements through a forming die that enforces geometry constraints that lock the elements into a rigid structure that can then be pushed against and extruded out of the die as an assembled, loadbearing structure.

A Novel Multilevel DC - AC Converter from Green Energy Power Generators Using Step-Square Waving and PWM Technique

NASA Astrophysics Data System (ADS)

Fajingbesi, F. E.; Midi, N. S.; Khan, S.

2017-06-01

Green energy sources or renewable energy system generally utilize modular approach in their design. This sort of power sources are generally in DC form or in single cases AC. Due to high fluctuation in the natural origin of this energy (wind & solar) source they are stored as DC. DC power however are difficult to transfer over long distances hence DC to AC converters and storage system are very important in green energy system design. In this work we have designed a novel multilevel DC to AC converter that takes into account the modular design of green energy systems. A power conversion efficiency of 99% with reduced total harmonic distortion (THD) was recorded from our simulated system design.

Design and Development of a Low-Cost Aerial Mobile Mapping System for Multi-Purpose Applications

NASA Astrophysics Data System (ADS)

Acevedo Pardo, C.; Farjas Abadía, M.; Sternberg, H.

2015-08-01

The research project with the working title "Design and development of a low-cost modular Aerial Mobile Mapping System" was formed during the last year as the result from numerous discussions and considerations with colleagues from the HafenCity University Hamburg, Department Geomatics. The aim of the project is to design a sensor platform which can be embedded preferentially on an UAV, but also can be integrated on any adaptable vehicle. The system should perform a direct scanning of surfaces with a laser scanner and supported through sensors for determining the position and attitude of the platform. The modular design allows his extension with other sensors such as multispectral cameras, digital cameras or multiple cameras systems.

BeamDyn: A High-Fidelity Wind Turbine Blade Solver in the FAST Modular Framework: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Q.; Sprague, M.; Jonkman, J.

2015-01-01

BeamDyn, a Legendre-spectral-finite-element implementation of geometrically exact beam theory (GEBT), was developed to meet the design challenges associated with highly flexible composite wind turbine blades. In this paper, the governing equations of GEBT are reformulated into a nonlinear state-space form to support its coupling within the modular framework of the FAST wind turbine computer-aided engineering (CAE) tool. Different time integration schemes (implicit and explicit) were implemented and examined for wind turbine analysis. Numerical examples are presented to demonstrate the capability of this new beam solver. An example analysis of a realistic wind turbine blade, the CX-100, is also presented asmore » validation.« less

Complex DNA Brick Assembly.

PubMed

Ong, Luvena L; Ke, Yonggang

2017-01-01

DNA nanostructures are a useful technology for precisely organizing and manipulating nanomaterials. The DNA bricks method is a modular and versatile platform for applications requiring discrete or periodic structures with complex three-dimensional features. Here, we describe how structures are designed from the fundamental strand architecture through assembly and characterization of the formed structures.

Use of heat pipes in electronic hardware

NASA Technical Reports Server (NTRS)

Graves, J. R.

1977-01-01

A modular, multiple output power converter was developed in order to reduce costs of space hardware in future missions. The converter is of reduced size and weight, and utilizes advanced heat removal techniques, in the form of heat pipes which remove internally generated heat more effectively than conventional methods.

General Intelligence Predicts Reasoning Ability Even for Evolutionarily Familiar Content

ERIC Educational Resources Information Center

Kaufman, Scott Barry; DeYoung, Colin G.; Reis, Deidre L.; Gray, Jeremy R.

2011-01-01

The existence of general-purpose cognitive mechanisms related to intelligence, which appear to facilitate all forms of problem solving, conflicts with the strong modularity view of the mind espoused by some evolutionary psychologists. The current study assessed the contribution of general intelligence ("g") to explaining variation in…

Electronically-Scanned Pressure Sensors

NASA Technical Reports Server (NTRS)

Coe, C. F.; Parra, G. T.; Kauffman, R. C.

1984-01-01

Sensors not pneumatically switched. Electronic pressure-transducer scanning system constructed in modular form. Pressure transducer modules and analog to digital converter module small enough to fit within cavities of average-sized wind-tunnel models. All switching done electronically. Temperature controlled environment maintained within sensor modules so accuracy maintained while ambient temperature varies.

Test Information Targeting Strategies for Adaptive Multistage Testing Designs.

ERIC Educational Resources Information Center

Luecht, Richard M.; Burgin, William

Adaptive multistage testlet (MST) designs appear to be gaining popularity for many large-scale computer-based testing programs. These adaptive MST designs use a modularized configuration of preconstructed testlets and embedded score-routing schemes to prepackage different forms of an adaptive test. The conditional information targeting (CIT)…

Portable and Lightweight Ramp Structure

DTIC Science & Technology

2001-04-09

long side of which is in abutting relationship with the 12 short side of the end of the ramp. Fastener receivers are equi- 13 spaced in duplicate...The modular sections are conveniently prefabricated 18 1 and provided in kit form to the number of sections corresponding 2 to the desired ramp

STS ancillary equipment study. [user reference book for multimission modular spacecraft missions

NASA Technical Reports Server (NTRS)

Plough, J. A.

1977-01-01

Spaceborne and ground ancillary equipment for multimission module spacecraft are listed to provide documentation for potential users interested in utilizing existing equipment rather than developing payload unique designs. The format of the data form contained in the Ancillary Equipment user reference book is discussed.

The relative efficiency of modular and non-modular networks of different size

PubMed Central

Tosh, Colin R.; McNally, Luke

2015-01-01

Most biological networks are modular but previous work with small model networks has indicated that modularity does not necessarily lead to increased functional efficiency. Most biological networks are large, however, and here we examine the relative functional efficiency of modular and non-modular neural networks at a range of sizes. We conduct a detailed analysis of efficiency in networks of two size classes: ‘small’ and ‘large’, and a less detailed analysis across a range of network sizes. The former analysis reveals that while the modular network is less efficient than one of the two non-modular networks considered when networks are small, it is usually equally or more efficient than both non-modular networks when networks are large. The latter analysis shows that in networks of small to intermediate size, modular networks are much more efficient that non-modular networks of the same (low) connective density. If connective density must be kept low to reduce energy needs for example, this could promote modularity. We have shown how relative functionality/performance scales with network size, but the precise nature of evolutionary relationship between network size and prevalence of modularity will depend on the costs of connectivity. PMID:25631996

DOE Office of Scientific and Technical Information (OSTI.GOV)

Znojil, Miloslav

An N-level quantum model is proposed in which the energies are represented by an N-plet of zeros of a suitable classical orthogonal polynomial. The family of Gegenbauer polynomials G(n,a,x) is selected for illustrative purposes. The main obstacle lies in the non-Hermiticity (aka crypto-Hermiticity) of Hamiltonians H{ne}H{sup {dagger}.} We managed to (i) start from elementary secular equation G(N,a,E{sub n})=0, (ii) keep our H, in the nearest-neighbor-interaction spirit, tridiagonal, (iii) render it Hermitian in an ad hoc, nonunique Hilbert space endowed with metric {Theta}{ne}I, (iv) construct eligible metrics in closed forms ordered by increasing nondiagonality, and (v) interpret the model as amore » smeared N-site lattice.« less

Zero energy resonance and the logarithmically slow decay of unstable multilevel systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miyamoto, Manabu

2006-08-15

The long time behavior of the reduced time evolution operator for unstable multilevel systems is studied based on the N-level Friedrichs model in the presence of a zero energy resonance. The latter means the divergence of the resolvent at zero energy. Resorting to the technique developed by Jensen and Kato [Duke Math. J. 46, 583 (1979)], the zero energy resonance of this model is characterized by the zero energy eigenstate that does not belong to the Hilbert space. It is then shown that for some kinds of the rational form factors the logarithmically slow decay proportional to (log t){sup -1}more » of the reduced time evolution operator can be realized.« less

Exaggerated heart rate oscillations during two meditation techniques.

PubMed

Peng, C K; Mietus, J E; Liu, Y; Khalsa, G; Douglas, P S; Benson, H; Goldberger, A L

1999-07-31

We report extremely prominent heart rate oscillations associated with slow breathing during specific traditional forms of Chinese Chi and Kundalini Yoga meditation techniques in healthy young adults. We applied both spectral analysis and a novel analytic technique based on the Hilbert transform to quantify these heart rate dynamics. The amplitude of these oscillations during meditation was significantly greater than in the pre-meditation control state and also in three non-meditation control groups: i) elite athletes during sleep, ii) healthy young adults during metronomic breathing, and iii) healthy young adults during spontaneous nocturnal breathing. This finding, along with the marked variability of the beat-to-beat heart rate dynamics during such profound meditative states, challenges the notion of meditation as only an autonomically quiescent state.

LETTER TO THE EDITOR: Landau levels on the hyperbolic plane

NASA Astrophysics Data System (ADS)

Fakhri, H.; Shariati, M.

2004-11-01

The quantum states of a spinless charged particle on a hyperbolic plane in the presence of a uniform magnetic field with a generalized quantization condition are proved to be the bases of the irreducible Hilbert representation spaces of the Lie algebra u(1, 1). The dynamical symmetry group U(1, 1) with the explicit form of the Lie algebra generators is extracted. It is also shown that the energy has an infinite-fold degeneracy in each of the representation spaces which are allocated to the different values of the magnetic field strength. Based on the simultaneous shift of two parameters, it is also noted that the quantum states realize the representations of Lie algebra u(2) by shifting the magnetic field strength.

Well-posedness for a class of doubly nonlinear stochastic PDEs of divergence type

NASA Astrophysics Data System (ADS)

Scarpa, Luca

2017-08-01

We prove well-posedness for doubly nonlinear parabolic stochastic partial differential equations of the form dXt - div γ (∇Xt) dt + β (Xt) dt ∋ B (t ,Xt) dWt, where γ and β are the two nonlinearities, assumed to be multivalued maximal monotone operators everywhere defined on Rd and R respectively, and W is a cylindrical Wiener process. Using variational techniques, suitable uniform estimates (both pathwise and in expectation) and some compactness results, well-posedness is proved under the classical Leray-Lions conditions on γ and with no restrictive smoothness or growth assumptions on β. The operator B is assumed to be Hilbert-Schmidt and to satisfy some classical Lipschitz conditions in the second variable.

The New Quantum Logic

NASA Astrophysics Data System (ADS)

Griffiths, Robert B.

2014-06-01

It is shown how all the major conceptual difficulties of standard (textbook) quantum mechanics, including the two measurement problems and the (supposed) nonlocality that conflicts with special relativity, are resolved in the consistent or decoherent histories interpretation of quantum mechanics by using a modified form of quantum logic to discuss quantum properties (subspaces of the quantum Hilbert space), and treating quantum time development as a stochastic process. The histories approach in turn gives rise to some conceptual difficulties, in particular the correct choice of a framework (probabilistic sample space) or family of histories, and these are discussed. The central issue is that the principle of unicity, the idea that there is a unique single true description of the world, is incompatible with our current understanding of quantum mechanics.

BRST detour quantization: Generating gauge theories from constraints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cherney, D.; Waldron, A.; Latini, E.

2010-06-15

We present the Becchi-Rouet-Stora-Tyutin (BRST) cohomologies of a class of constraint (super) Lie algebras as detour complexes. By interpreting the components of detour complexes as gauge invariances, Bianchi identities, and equations of motion, we obtain a large class of new gauge theories. The pivotal new machinery is a treatment of the ghost Hilbert space designed to manifest the detour structure. Along with general results, we give details for three of these theories which correspond to gauge invariant spinning particle models of totally symmetric, antisymmetric, and Kaehler antisymmetric forms. In particular, we give details of our recent announcement of a (p,q)-formmore » Kaehler electromagnetism. We also discuss how our results generalize to other special geometries.« less

Adaptive multi-resolution Modularity for detecting communities in networks

NASA Astrophysics Data System (ADS)

Chen, Shi; Wang, Zhi-Zhong; Bao, Mei-Hua; Tang, Liang; Zhou, Ji; Xiang, Ju; Li, Jian-Ming; Yi, Chen-He

2018-02-01

Community structure is a common topological property of complex networks, which attracted much attention from various fields. Optimizing quality functions for community structures is a kind of popular strategy for community detection, such as Modularity optimization. Here, we introduce a general definition of Modularity, by which several classical (multi-resolution) Modularity can be derived, and then propose a kind of adaptive (multi-resolution) Modularity that can combine the advantages of different Modularity. By applying the Modularity to various synthetic and real-world networks, we study the behaviors of the methods, showing the validity and advantages of the multi-resolution Modularity in community detection. The adaptive Modularity, as a kind of multi-resolution method, can naturally solve the first-type limit of Modularity and detect communities at different scales; it can quicken the disconnecting of communities and delay the breakup of communities in heterogeneous networks; and thus it is expected to generate the stable community structures in networks more effectively and have stronger tolerance against the second-type limit of Modularity.

THz-bandwidth photonic Hilbert transformers based on fiber Bragg gratings in transmission.

PubMed

Fernández-Ruiz, María R; Wang, Lixian; Carballar, Alejandro; Burla, Maurizio; Azaña, José; LaRochelle, Sophie

2015-01-01

THz-bandwidth photonic Hilbert transformers (PHTs) are implemented for the first time, to the best of our knowledge, based on fiber Bragg grating (FBG) technology. To increase the practical bandwidth limitation of FBGs (typically <200  GHz), a superstructure based on two superimposed linearly-chirped FBGs operating in transmission has been employed. The use of a transmission FBG involves first a conversion of the non-minimum phase response of the PHT into a minimum-phase response by adding an anticipated instantaneous component to the desired system temporal impulse response. Using this methodology, a 3-THz-bandwidth integer PHT and a fractional (order 0.81) PHT are designed, fabricated, and successfully characterized.

Multichannel photonic Hilbert transformers based on complex modulated integrated Bragg gratings.

PubMed

Cheng, Rui; Chrostowski, Lukas

2018-03-01

Multichannel photonic Hilbert transformers (MPHTs) are reported. The devices are based on single compact spiral integrated Bragg gratings on silicon with coupling coefficients precisely modulated by the phase of each grating period. MPHTs with up to nine wavelength channels and a single-channel bandwidth of up to ∼625  GHz are achieved. The potential of the devices for multichannel single-sideband signal generation is suggested. The work offers a new possibility of utilizing wavelength as an extra degree of freedom in designing radio-frequency photonic signal processors. Such multichannel processors are expected to possess improved capacities and a potential to greatly benefit current widespread wavelength division multiplexed systems.

Bell - Kochen - Specker theorem for any finite dimension ?

NASA Astrophysics Data System (ADS)

Cabello, Adán; García-Alcaine, Guillermo

1996-03-01

The Bell - Kochen - Specker theorem against non-contextual hidden variables can be proved by constructing a finite set of `totally non-colourable' directions, as Kochen and Specker did in a Hilbert space of dimension n = 3. We generalize Kochen and Specker's set to Hilbert spaces of any finite dimension 0305-4470/29/5/016/img2, in a three-step process that shows the relationship between different kinds of proofs (`continuum', `probabilistic', `state-specific' and `state-independent') of the Bell - Kochen - Specker theorem. At the same time, this construction of a totally non-colourable set of directions in any dimension explicitly solves the question raised by Zimba and Penrose about the existence of such a set for n = 5.

Andrei Andreevich Bolibrukh's works on the analytic theory of differential equations

NASA Astrophysics Data System (ADS)

Anosov, Dmitry V.; Leksin, Vladimir P.

2011-02-01

This paper contains an account of A.A. Bolibrukh's results obtained in the new directions of research that arose in the analytic theory of differential equations as a consequence of his sensational counterexample to the Riemann-Hilbert problem. A survey of results of his students in developing topics first considered by Bolibrukh is also presented. The main focus is on the role of the reducibility/irreducibility of systems of linear differential equations and their monodromy representations. A brief synopsis of results on the multidimensional Riemann-Hilbert problem and on isomonodromic deformations of Fuchsian systems is presented, and the main methods in the modern analytic theory of differential equations are sketched. Bibliography: 69 titles.

Decrement of uterine myometrial burst duration as a correlate to active labor: A Hilbert phase approach

PubMed Central

Govindan, Rathinaswamy B.; Vairavan, Srinivasan; Furdea, Adrian; Murphy, Pam; Preissl, Hubert; Eswaran, Hari

2011-01-01

We propose a novel approach based on Hilbert phase to identify the burst in the uterine myometrial activity. We apply this approach to 24 serial magnetomyographic signals recorded from four pregnant women using a 151 SQUID array system. The bursts identified with this approach are evaluated for duration and are correlated with the gestational age. In all four subjects, we find a decrease in the duration of burst as the subject approaches active labor. As was shown in animal studies, this result indicates a faster conduction time between the muscle cells which activate a larger number of muscle units in a synchronous manner. PMID:21096231

Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System

NASA Astrophysics Data System (ADS)

Anderson, B. E.; Sosa-Martinez, H.; Riofrío, C. A.; Deutsch, Ivan H.; Jessen, Poul S.

2015-06-01

Unitary transformations are the most general input-output maps available in closed quantum systems. Good control protocols have been developed for qubits, but questions remain about the use of optimal control theory to design unitary maps in high-dimensional Hilbert spaces, and about the feasibility of their robust implementation in the laboratory. Here we design and implement unitary maps in a 16-dimensional Hilbert space associated with the 6 S1 /2 ground state of 133Cs, achieving fidelities >0.98 with built-in robustness to static and dynamic perturbations. Our work has relevance for quantum information processing and provides a template for similar advances on other physical platforms.

Uncertainty Relation on Generalized Skew Information with aMonotone Pair

NASA Astrophysics Data System (ADS)

Liu, Jun-Tong; Wang, Qing-Wen; Li, Lei

2017-08-01

In this paper, we first define a generalized ( f, g)-skew information |I_{ ρ }^{(f, g)} |(A) and two related quantity |J_{ ρ }^{(f, g)} |(A) and |U_{ ρ }^{(f, g)} |(A) for any non-Hermitian Hilbert-Schmidt operator A and a density operator ρ on a Hilbert space H and discuss some properties of them. And then, we obtain the following uncertainty relation in terms of |U_{ ρ }^{(f, g)} |(A): |U_{ ρ}^{(f, g)}|(A)|U_{ ρ}^{(f, g)}|(B)≥ β_{(f, g)}|Tr( f(ρ)g(ρ)[A, B]0)|2, which is a generalization of a known uncertainty relation in Ko and Yoo (J. Math. Anal. Appl. 383, 208-214, 11).

Development of modularity in the neural activity of childrenʼs brains

NASA Astrophysics Data System (ADS)

Chen, Man; Deem, Michael W.

2015-02-01

We study how modularity of the human brain changes as children develop into adults. Theory suggests that modularity can enhance the response function of a networked system subject to changing external stimuli. Thus, greater cognitive performance might be achieved for more modular neural activity, and modularity might likely increase as children develop. The value of modularity calculated from functional magnetic resonance imaging (fMRI) data is observed to increase during childhood development and peak in young adulthood. Head motion is deconvolved from the fMRI data, and it is shown that the dependence of modularity on age is independent of the magnitude of head motion. A model is presented to illustrate how modularity can provide greater cognitive performance at short times, i.e. task switching. A fitness function is extracted from the model. Quasispecies theory is used to predict how the average modularity evolves with age, illustrating the increase of modularity during development from children to adults that arises from selection for rapid cognitive function in young adults. Experiments exploring the effect of modularity on cognitive performance are suggested. Modularity may be a potential biomarker for injury, rehabilitation, or disease.

Localized Triple Modular Redundancy vs. Distributed Triple Modular Redundancy on a ProASIC3E Reprogrammable FPGA

NASA Technical Reports Server (NTRS)

McGuffey, Alex; Berg, Melanie; Pellish, Jonathan

2010-01-01

Field programmable gate arrays (FPGA) are used in every space application. Currently, most space flight applications use radiation hardened (RH) FPGAs, which are very expensive. There is a desire to use cheaper, commercial off the shelf reprogrammable FPGAs, which are more susceptible to radiation effects known as single-event effects (SEE). The RH parts have SEE and total ionizing dose (TID) hardened elements pre-integrated into the part. This means that the designer does not need to implement any hardening techniques while configuring the device. The COTS parts on the other hand must be mitigated by design in order to insure any form of mitigation. The design techniques this project examines concern the use of localized triple modular redundancy (LTMR) and distributed triple modular redundancy (DTMR). LTMR triples every flip flop in the device architecture while DTMR triples everything except for the global routes (clocks, resets, and enables). The testing was performed on a ProASIC3E FPGA at the Texas A&M cyclotron facility. Two design architectures were used: shift registers and counters, both with LTMR and DTMR mitigation techniques. The test results prove that DTMR is more effective at reducing SEE than LTMR. We also determined that there was not a significant difference between the use of shift registers and counters for test purposes. More testing is required to obtain additional linear energy transfer values for each architecture and mitigation technique in order to determine the most cost-effective method of SEE mitigation.

The solution of the sixth Hilbert problem: the ultimate Galilean revolution

NASA Astrophysics Data System (ADS)

D'Ariano, Giacomo Mauro

2018-04-01

I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: `physics from no physics'. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as `clock', `rigid rod', `force', `inertial mass' (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory. This article is part of the theme issue `Hilbert's sixth problem'.

Hilbert space structure in quantum gravity: an algebraic perspective

DOE PAGES

Giddings, Steven B.

2015-12-16

If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. Here, this viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of themore » Hilbert space is problematic. Instead it is better to focus on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of local quantum field theory are found, working in the correspondence limit of long-distances/low-energies. Particularly, there are obstacles to identifying commuting algebras of localized operators. In addition to suggesting important properties of the algebraic structure, this and related observations pose challenges to proposals of a fundamental role for entanglement.« less

The solution of the sixth Hilbert problem: the ultimate Galilean revolution.

PubMed

D'Ariano, Giacomo Mauro

2018-04-28

I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: 'physics from no physics'. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as 'clock', 'rigid rod', 'force', 'inertial mass' (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

General n-dimensional quadrature transform and its application to interferogram demodulation.

PubMed

Servin, Manuel; Quiroga, Juan Antonio; Marroquin, Jose Luis

2003-05-01

Quadrature operators are useful for obtaining the modulating phase phi in interferometry and temporal signals in electrical communications. In carrier-frequency interferometry and electrical communications, one uses the Hilbert transform to obtain the quadrature of the signal. In these cases the Hilbert transform gives the desired quadrature because the modulating phase is monotonically increasing. We propose an n-dimensional quadrature operator that transforms cos(phi) into -sin(phi) regardless of the frequency spectrum of the signal. With the quadrature of the phase-modulated signal, one can easily calculate the value of phi over all the domain of interest. Our quadrature operator is composed of two n-dimensional vector fields: One is related to the gradient of the image normalized with respect to local frequency magnitude, and the other is related to the sign of the local frequency of the signal. The inner product of these two vector fields gives us the desired quadrature signal. This quadrature operator is derived in the image space by use of differential vector calculus and in the frequency domain by use of a n-dimensional generalization of the Hilbert transform. A robust numerical algorithm is given to find the modulating phase of two-dimensional single-image closed-fringe interferograms by use of the ideas put forward.

Context-invariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary Hilbert space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Loubenets, Elena R.

We prove the existence for each Hilbert space of the two new quasi hidden variable (qHV) models, statistically noncontextual and context-invariant, reproducing all the von Neumann joint probabilities via non-negative values of real-valued measures and all the quantum product expectations—via the qHV (classical-like) average of the product of the corresponding random variables. In a context-invariant model, a quantum observable X can be represented by a variety of random variables satisfying the functional condition required in quantum foundations but each of these random variables equivalently models X under all joint von Neumann measurements, regardless of their contexts. The proved existence ofmore » this model negates the general opinion that, in terms of random variables, the Hilbert space description of all the joint von Neumann measurements for dimH≥3 can be reproduced only contextually. The existence of a statistically noncontextual qHV model, in particular, implies that every N-partite quantum state admits a local quasi hidden variable model introduced in Loubenets [J. Math. Phys. 53, 022201 (2012)]. The new results of the present paper point also to the generality of the quasi-classical probability model proposed in Loubenets [J. Phys. A: Math. Theor. 45, 185306 (2012)].« less

Hilbert space structure in quantum gravity: an algebraic perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giddings, Steven B.

If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. Here, this viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of themore » Hilbert space is problematic. Instead it is better to focus on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of local quantum field theory are found, working in the correspondence limit of long-distances/low-energies. Particularly, there are obstacles to identifying commuting algebras of localized operators. In addition to suggesting important properties of the algebraic structure, this and related observations pose challenges to proposals of a fundamental role for entanglement.« less

Feature Extraction and Classification of EHG between Pregnancy and Labour Group Using Hilbert-Huang Transform and Extreme Learning Machine.

PubMed

Chen, Lili; Hao, Yaru

2017-01-01

Preterm birth (PTB) is the leading cause of perinatal mortality and long-term morbidity, which results in significant health and economic problems. The early detection of PTB has great significance for its prevention. The electrohysterogram (EHG) related to uterine contraction is a noninvasive, real-time, and automatic novel technology which can be used to detect, diagnose, or predict PTB. This paper presents a method for feature extraction and classification of EHG between pregnancy and labour group, based on Hilbert-Huang transform (HHT) and extreme learning machine (ELM). For each sample, each channel was decomposed into a set of intrinsic mode functions (IMFs) using empirical mode decomposition (EMD). Then, the Hilbert transform was applied to IMF to obtain analytic function. The maximum amplitude of analytic function was extracted as feature. The identification model was constructed based on ELM. Experimental results reveal that the best classification performance of the proposed method can reach an accuracy of 88.00%, a sensitivity of 91.30%, and a specificity of 85.19%. The area under receiver operating characteristic (ROC) curve is 0.88. Finally, experimental results indicate that the method developed in this work could be effective in the classification of EHG between pregnancy and labour group.

A New Method for Nonlinear and Nonstationary Time Series Analysis and Its Application to the Earthquake and Building Response Records

NASA Technical Reports Server (NTRS)

Huang, Norden E.

1999-01-01

A new method for analyzing nonlinear and nonstationary data has been developed. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum, Example of application of this method to earthquake and building response will be given. The results indicate those low frequency components, totally missed by the Fourier analysis, are clearly identified by the new method. Comparisons with Wavelet and window Fourier analysis show the new method offers much better temporal and frequency resolutions.

Renormalization in Quantum Field Theory and the Riemann-Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

NASA Astrophysics Data System (ADS)

Connes, Alain; Kreimer, Dirk

This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra which is commutative as an algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of . We shall then show that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop where C is a small circle of complex dimensions around the integer dimension D of space-time. Our main result is that the renormalized theory is just the evaluation at z=D of the holomorphic part γ+ of the Birkhoff decomposition of γ. We begin to analyse the group G and show that it is a semi-direct product of an easily understood abelian group by a highly non-trivial group closely tied up with groups of diffeomorphisms. The analysis of this latter group as well as the interpretation of the renormalization group and of anomalous dimensions are the content of our second paper with the same overall title.

Adaptive multiregression in reproducing kernel Hilbert spaces: the multiaccess MIMO channel case.

PubMed

Slavakis, Konstantinos; Bouboulis, Pantelis; Theodoridis, Sergios

2012-02-01

This paper introduces a wide framework for online, i.e., time-adaptive, supervised multiregression tasks. The problem is formulated in a general infinite-dimensional reproducing kernel Hilbert space (RKHS). In this context, a fairly large number of nonlinear multiregression models fall as special cases, including the linear case. Any convex, continuous, and not necessarily differentiable function can be used as a loss function in order to quantify the disagreement between the output of the system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. To this end, we demonstrate a way to calculate the subgradients of robust loss functions, suitable for the multiregression task. As it is by now well documented, when dealing with online schemes in RKHS, the memory keeps increasing with each iteration step. To attack this problem, a simple sparsification strategy is utilized, which leads to an algorithmic scheme of linear complexity with respect to the number of unknown parameters. A convergence analysis of the technique, based on arguments of convex analysis, is also provided. To demonstrate the capacity of the proposed method, the multiregressor is applied to the multiaccess multiple-input multiple-output channel equalization task for a setting with poor resources and nonavailable channel information. Numerical results verify the potential of the method, when its performance is compared with those of the state-of-the-art linear techniques, which, in contrast, use space-time coding, more antenna elements, as well as full channel information.

Dynamics of modularity of neural activity in the brain during development

NASA Astrophysics Data System (ADS)

Deem, Michael; Chen, Man

2014-03-01

Theory suggests that more modular systems can have better response functions at short times. This theory suggests that greater cognitive performance may be achieved for more modular neural activity, and that modularity of neural activity may, therefore, likely increase with development in children. We study the relationship between age and modularity of brain neural activity in developing children. The value of modularity calculated from fMRI data is observed to increase during childhood development and peak in young adulthood. We interpret these results as evidence of selection for plasticity in the cognitive function of the human brain. We present a model to illustrate how modularity can provide greater cognitive performance at short times and enhance fast, low-level, automatic cognitive processes. Conversely, high-level, effortful, conscious cognitive processes may not benefit from modularity. We use quasispecies theory to predict how the average modularity evolves with age, given a fitness function extracted from the model. We suggest further experiments exploring the effect of modularity on cognitive performance and suggest that modularity may be a potential biomarker for injury, rehabilitation, or disease.

A Modularized Tablet-Based Approach to Preparation for Remedial Mathematics

ERIC Educational Resources Information Center

Parker, K. Andrew

2016-01-01

Basic arithmetic forms the foundation of the math courses that students will face in their undergraduate careers. It is therefore crucial that students have a solid understanding of these fundamental concepts. At an open-access university offering both two-year and four-year degrees, incoming freshmen who were identified as lacking in basic…

Solar thermal parabolic dish energy applications

NASA Technical Reports Server (NTRS)

Pijawka, W.

1981-01-01

Vu-graphs are presented that show that applications are a viable distributed renewable power generation option. Quality energy can be produced in the form of electricity and high temperature heat. Modular systems are described that can be distributed to new or existing plants and that are mass producible with the associated economies of production.

Improved Decision Making for School Organization. What and What for

ERIC Educational Resources Information Center

Myers, Donald A.; Sinclair, Robert

1973-01-01

A framework of 13 decision criteria to give educators help in comparing the relative merits of different forms of school organization. The methods of school organization judged to be in widespread use and defined in the article are (1) the self-contained classroom, team teaching, departmentalization, modular scheduling, differentiated staffing,…

75 FR 16080 - Notice of Intent To Prepare an Environmental Impact Statement for Basewide Water Infrastructure...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-03-31

...- design and to develop additional alternatives for analysis. These two water infrastructure projects are... carbon, and reverse osmosis. The facility would be designed in modular form for ease of expandability... lighting, asphalt pavement, and pavement marking and signs. The project includes ``100-year storm'' flood...

Mathematical Designs for Teaching and Learning Composition.

ERIC Educational Resources Information Center

Laque, Carol Feiser

Algebraic equations and geometric forms are useful in teaching and learning composition. Algebraic equations can illustrate the modular nature of paragraph structures and can be refined by students to describe types of paragraphs. Discussion of the "slippery" nature of words and their power of transformation can be a lecture topic as the class…

Modularisation Approaches in Initial Vocational Education: Evidence for Policy Convergence in Europe?

ERIC Educational Resources Information Center

Pilz, Matthias; Li, Junmin; Canning, Roy; Minty, Sarah

2018-01-01

One response to challenges of national vocational training systems has been a move towards greater flexibility within vocational training systems. This article focuses on an investigation of modularisation as a tool for achieving this flexibility. Many European countries have introduced modular forms into their vocational training system. We…

ABSIM. Simulation of Absorption Systems in Flexible and Modular Form

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grossman, G.

1994-06-01

The computer code has been developed for simulation of absorption systems at steady-state in a flexible and modular form, making it possible to investigate various cycle configurations with different working fluids. The code is based on unit subroutines containing the governing equations for the system`s components. When all the equations have been established, a mathematical solver routine is employed to solve them simultaneously. Property subroutines contained in a separate data base serve to provide thermodynamic properties of the working fluids. The code is user-oriented and requires a relatively simple input containing the given operating conditions and the working fluid atmore » each state point. the user conveys to the computer an image of the cycle by specifying the different components and their interconnections. Based on this information, the program calculates the temperature, flowrate, concentration, pressure and vapor fraction at each state point in the system and the heat duty at each unit, from which the coefficient of performance may be determined. A graphical user-interface is provided to facilitate interactive input and study of the output.« less

ABSIM. Simulation of Absorption Systems in Flexible and Modular Form

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grossman, G.

1994-06-01

The computer code has been developed for simulation of absorption systems at steady-state in a flexible and modular form, making it possible to investigate various cycle configurations with different working fluids. The code is based on unit subroutines containing the governing equations for the system's components. When all the equations have been established, a mathematical solver routine is employed to solve them simultaneously. Property subroutines contained in a separate data base serve to provide thermodynamic properties of the working fluids. The code is user-oriented and requires a relatively simple input containing the given operating conditions and the working fluid atmore » each state point. the user conveys to the computer an imagev of the cycle by specifying the different components and their interconnections. Based on this information, the program calculates the temperature, flowrate, concentration, pressure and vapor fraction at each state point in the system and the heat duty at each unit, from which the coefficient of performance may be determined. A graphical user-interface is provided to fcilitate interactive input and study of the output.« less

Enumeration of virtual libraries of combinatorial modular macrocyclic (bracelet, necklace) architectures and their linear counterparts.

PubMed

Taniguchi, Masahiko; Du, Hai; Lindsey, Jonathan S

2013-09-23

A wide variety of cyclic molecular architectures are built of modular subunits and can be formed combinatorially. The mathematics for enumeration of such objects is well-developed yet lacks key features of importance in chemistry, such as specifying (i) the structures of individual members among a set of isomers, (ii) the distribution (i.e., relative amounts) of products, and (iii) the effect of nonequal ratios of reacting monomers on the product distribution. Here, a software program (Cyclaplex) has been developed to determine the number, identity (including isomers), and relative amounts of linear and cyclic architectures from a given number and ratio of reacting monomers. The program includes both mathematical formulas and generative algorithms for enumeration; the latter go beyond the former to provide desired molecular-relevant information and data-mining features. The program is equipped to enumerate four types of architectures: (i) linear architectures with directionality (macroscopic equivalent = electrical extension cords), (ii) linear architectures without directionality (batons), (iii) cyclic architectures with directionality (necklaces), and (iv) cyclic architectures without directionality (bracelets). The program can be applied to cyclic peptides, cycloveratrylenes, cyclens, calixarenes, cyclodextrins, crown ethers, cucurbiturils, annulenes, expanded meso-substituted porphyrin(ogen)s, and diverse supramolecular (e.g., protein) assemblies. The size of accessible architectures encompasses up to 12 modular subunits derived from 12 reacting monomers or larger architectures (e.g. 13-17 subunits) from fewer types of monomers (e.g. 2-4). A particular application concerns understanding the possible heterogeneity of (natural or biohybrid) photosynthetic light-harvesting oligomers (cyclic, linear) formed from distinct peptide subunits.

A Probabilistic Framework for the Validation and Certification of Computer Simulations

NASA Technical Reports Server (NTRS)

Ghanem, Roger; Knio, Omar

2000-01-01

The paper presents a methodology for quantifying, propagating, and managing the uncertainty in the data required to initialize computer simulations of complex phenomena. The purpose of the methodology is to permit the quantitative assessment of a certification level to be associated with the predictions from the simulations, as well as the design of a data acquisition strategy to achieve a target level of certification. The value of a methodology that can address the above issues is obvious, specially in light of the trend in the availability of computational resources, as well as the trend in sensor technology. These two trends make it possible to probe physical phenomena both with physical sensors, as well as with complex models, at previously inconceivable levels. With these new abilities arises the need to develop the knowledge to integrate the information from sensors and computer simulations. This is achieved in the present work by tracing both activities back to a level of abstraction that highlights their commonalities, thus allowing them to be manipulated in a mathematically consistent fashion. In particular, the mathematical theory underlying computer simulations has long been associated with partial differential equations and functional analysis concepts such as Hilbert spares and orthogonal projections. By relying on a probabilistic framework for the modeling of data, a Hilbert space framework emerges that permits the modeling of coefficients in the governing equations as random variables, or equivalently, as elements in a Hilbert space. This permits the development of an approximation theory for probabilistic problems that parallels that of deterministic approximation theory. According to this formalism, the solution of the problem is identified by its projection on a basis in the Hilbert space of random variables, as opposed to more traditional techniques where the solution is approximated by its first or second-order statistics. The present representation, in addition to capturing significantly more information than the traditional approach, facilitates the linkage between different interacting stochastic systems as is typically observed in real-life situations.

Two- and three-dimensional natural and mixed convection simulation using modular zonal models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wurtz, E.; Nataf, J.M.; Winkelmann, F.

We demonstrate the use of the zonal model approach, which is a simplified method for calculating natural and mixed convection in rooms. Zonal models use a coarse grid and use balance equations, state equations, hydrostatic pressure drop equations and power law equations of the form {ital m} = {ital C}{Delta}{sup {ital n}}. The advantage of the zonal approach and its modular implementation are discussed. The zonal model resolution of nonlinear equation systems is demonstrated for three cases: a 2-D room, a 3-D room and a pair of 3-D rooms separated by a partition with an opening. A sensitivity analysis withmore » respect to physical parameters and grid coarseness is presented. Results are compared to computational fluid dynamics (CFD) calculations and experimental data.« less

Modularized TGFbeta-Smad Signaling Pathway

NASA Technical Reports Server (NTRS)

Li, Yongfeng; Wang, M.; Carra, C.; Cucinotta, F. A.

2011-01-01

The Transforming Growth Factor beta (TGFbeta) signaling pathway is a prominent regulatory signaling pathway controlling various important cellular processes. It can be induced by several factors, including ionizing radiation. It is regulated by Smads in a negative feedback loop through promoting increases in the regulatory Smads in the cell nucleus, and subsequent expression of inhibitory Smad, Smad7 to form a ubiquitin ligase with Smurf targeting active TGF receptors for degradation. In this work, we proposed a mathematical model to study the radiation-induced Smad-regulated TGF signaling pathway. By modularization, we are able to analyze each module (subsystem) and recover the nonlinear dynamics of the entire network system. Meanwhile the excitability, a common feature observed in the biological systems, along the TGF signaling pathway is discussed by mathematical analysis and numerical simulation.

Identification of Modules in Protein-Protein Interaction Networks

NASA Astrophysics Data System (ADS)

Erten, Sinan; Koyutürk, Mehmet

In biological systems, most processes are carried out through orchestration of multiple interacting molecules. These interactions are often abstracted using network models. A key feature of cellular networks is their modularity, which contributes significantly to the robustness, as well as adaptability of biological systems. Therefore, modularization of cellular networks is likely to be useful in obtaining insights into the working principles of cellular systems, as well as building tractable models of cellular organization and dynamics. A common, high-throughput source of data on molecular interactions is in the form of physical interactions between proteins, which are organized into protein-protein interaction (PPI) networks. This chapter provides an overview on identification and analysis of functional modules in PPI networks, which has been an active area of research in the last decade.

Modular liquid-cooled helmet liner for thermal comfort

NASA Technical Reports Server (NTRS)

Williams, B. A.; Shitzer, A.

1974-01-01

A modular liquid-cooled helmet liner made of eight form-fitting neoprene patches was constructed. The liner was integrated into the sweatband of an Army SPH-4 helicopter aircrew helmet. This assembly was tested on four subjects seated in a hot (47 C), humid (40%) environment. Results indicate a marked reduction in the rate of increase of physiological body functions. Rectal temperature, weight loss, heart rate, and strain indices are all reduced to approximately 50% of uncooled levels. The cooling liner removed from 10% to 30% of total metabolic heat produced. This study also demonstrated the technical feasilibity of using a cooling liner in conjunction with a standard hard helmet. Potential applications of the cooling liner in thermally stressful environments are numerous, notably for helicopter and other aircrews.

Controllable Modular Growth of Hierarchical MOF-on-MOF Architectures.

PubMed

Gu, Yifan; Wu, Yi-Nan; Li, Liangchun; Chen, Wei; Li, Fengting; Kitagawa, Susumu

2017-12-04

Fabrication of hybrid MOF-on-MOF heteroarchitectures can create novel and multifunctional platforms to achieve desired properties. However, only MOFs with similar crystallographic parameters can be hybridized by the classical epitaxial growth method (EGM), which largely suppressed its applications. A general strategy, called internal extended growth method (IEGM), is demonstrated for the feasible assembly of MOFs with distinct crystallographic parameters in an MOF matrix. Various MOFs with diverse functions could be introduced in a modular MOF matrix to form 3D core-satellite pluralistic hybrid system. The number of different MOF crystals interspersed could be varied on demand. More importantly, the different MOF crystals distributed in individual domains could be used to further incorporate functional units or enhance target functions. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Towards automated human gait disease classification using phase space representation of intrinsic mode functions

NASA Astrophysics Data System (ADS)

Pratiher, Sawon; Patra, Sayantani; Pratiher, Souvik

2017-06-01

A novel analytical methodology for segregating healthy and neurological disorders from gait patterns is proposed by employing a set of oscillating components called intrinsic mode functions (IMF's). These IMF's are generated by the Empirical Mode Decomposition of the gait time series and the Hilbert transformed analytic signal representation forms the complex plane trace of the elliptical shaped analytic IMFs. The area measure and the relative change in the centroid position of the polygon formed by the Convex Hull of these analytic IMF's are taken as the discriminative features. Classification accuracy of 79.31% with Ensemble learning based Adaboost classifier validates the adequacy of the proposed methodology for a computer aided diagnostic (CAD) system for gait pattern identification. Also, the efficacy of several potential biomarkers like Bandwidth of Amplitude Modulation and Frequency Modulation IMF's and it's Mean Frequency from the Fourier-Bessel expansion from each of these analytic IMF's has been discussed for its potency in diagnosis of gait pattern identification and classification.

Realizability of a model in infinite statistics

NASA Astrophysics Data System (ADS)

Zagier, Don

1992-06-01

Following Greenberg and others, we study a space with a collection of operators a(k) satisfying the “ q-mutator relations” a(l)a † (k)a(l)=δ k,l (corresponding for q=±1 to classical Bose and Fermi statistics). We show that the n!×n! matrix A n (q) representing the scalar products of n-particle states is positive definite for all n if q lies between -1 and +1, so that the commutator relations have a Hilbert space representation in this case (this has also been proved by Fivel and by Bozejko and Speicher). We also give an explicit factorization of A n (q) as a product of matrices of the form (1-q jT)±1 with 1≦ j≦ n and T a permutation matrix. In particular, A n (q) is singular if and only if q M=1 for some integer M of the form k 2- k, 2≦ k≦ n.

Linking entanglement and discrete anomaly

NASA Astrophysics Data System (ADS)

Hung, Ling-Yan; Wu, Yong-Shi; Zhou, Yang

2018-05-01

In 3 d Chern-Simons theory, there is a discrete one-form symmetry, whose symmetry group is isomorphic to the center of the gauge group. We study the `t Hooft anomaly associated to this discrete one-form symmetry in theories with generic gauge groups, A, B, C, D-types. We propose to detect the discrete anomaly by computing the Hopf state entanglement in the subspace spanned by the symmetry generators and develop a systematical way based on the truncated modular S matrix. We check our proposal for many examples.

Floating-point function generation routines for 16-bit microcomputers

NASA Technical Reports Server (NTRS)

Mackin, M. A.; Soeder, J. F.

1984-01-01

Several computer subroutines have been developed that interpolate three types of nonanalytic functions: univariate, bivariate, and map. The routines use data in floating-point form. However, because they are written for use on a 16-bit Intel 8086 system with an 8087 mathematical coprocessor, they execute as fast as routines using data in scaled integer form. Although all of the routines are written in assembly language, they have been implemented in a modular fashion so as to facilitate their use with high-level languages.

Modular Aquatic Simulation System 1D

DOE Office of Scientific and Technical Information (OSTI.GOV)

2017-04-19

MASS1 simulates open channel hydrodynamics and transport in branched channel networks, using cross-section averaged forms of the continuity, momentum, and convection diffusion equations. Thermal energy transport (temperature), including meteorological influences is supported. The thermodynamics of total dissolved gas (TDG) can be directly simulated. MASS1 has been developed over the last 20 years. It is currently being used on DOE projects that require MASS1 to beopen source. Hence, the authors would like to distribute MASS1 in source form.

Modular Courses in British Higher Education: A Critical Assessment

ERIC Educational Resources Information Center

Church, Clive

1975-01-01

The trends towards modular course structures is examined. British conceptions of modularization are compared with American interpretations of modular instruction, the former shown to be concerned almost exclusively with content, the latter attempting more radical changes in students' learning behavior. Rationales for British modular schemes are…

Disentangling the co-structure of multilayer interaction networks: degree distribution and module composition in two-layer bipartite networks.

PubMed

Astegiano, Julia; Altermatt, Florian; Massol, François

2017-11-13

Species establish different interactions (e.g. antagonistic, mutualistic) with multiple species, forming multilayer ecological networks. Disentangling network co-structure in multilayer networks is crucial to predict how biodiversity loss may affect the persistence of multispecies assemblages. Existing methods to analyse multilayer networks often fail to consider network co-structure. We present a new method to evaluate the modular co-structure of multilayer networks through the assessment of species degree co-distribution and network module composition. We focus on modular structure because of its high prevalence among ecological networks. We apply our method to two Lepidoptera-plant networks, one describing caterpillar-plant herbivory interactions and one representing adult Lepidoptera nectaring on flowers, thereby possibly pollinating them. More than 50% of the species established either herbivory or visitation interactions, but not both. These species were over-represented among plants and lepidopterans, and were present in most modules in both networks. Similarity in module composition between networks was high but not different from random expectations. Our method clearly delineates the importance of interpreting multilayer module composition similarity in the light of the constraints imposed by network structure to predict the potential indirect effects of species loss through interconnected modular networks.

A modular modulation method for achieving increases in metabolite production.

PubMed

Acerenza, Luis; Monzon, Pablo; Ortega, Fernando

2015-01-01

Increasing the production of overproducing strains represents a great challenge. Here, we develop a modular modulation method to determine the key steps for genetic manipulation to increase metabolite production. The method consists of three steps: (i) modularization of the metabolic network into two modules connected by linking metabolites, (ii) change in the activity of the modules using auxiliary rates producing or consuming the linking metabolites in appropriate proportions and (iii) determination of the key modules and steps to increase production. The mathematical formulation of the method in matrix form shows that it may be applied to metabolic networks of any structure and size, with reactions showing any kind of rate laws. The results are valid for any type of conservation relationships in the metabolite concentrations or interactions between modules. The activity of the module may, in principle, be changed by any large factor. The method may be applied recursively or combined with other methods devised to perform fine searches in smaller regions. In practice, it is implemented by integrating to the producer strain heterologous reactions or synthetic pathways producing or consuming the linking metabolites. The new procedure may contribute to develop metabolic engineering into a more systematic practice. © 2015 American Institute of Chemical Engineers.

Modular amplitudes and flux-superpotentials on elliptic Calabi-Yau fourfolds

NASA Astrophysics Data System (ADS)

Cota, Cesar Fierro; Klemm, Albrecht; Schimannek, Thorsten

2018-01-01

We discuss the period geometry and the topological string amplitudes on elliptically fibered Calabi-Yau fourfolds in toric ambient spaces. In particular, we describe a general procedure to fix integral periods. Using some elementary facts from homological mirror symmetry we then obtain Bridgelands involution and its monodromy action on the integral basis for non-singular elliptically fibered fourfolds. The full monodromy group contains a subgroup that acts as PSL(2,Z) on the Kähler modulus of the fiber and we analyze the consequences of this modularity for the genus zero and genus one amplitudes as well as the associated geometric invariants. We find holomorphic anomaly equations for the amplitudes, reflecting precisely the failure of exact PSL(2,Z) invariance that relates them to quasi-modular forms. Finally we use the integral basis of periods to study the horizontal flux superpotential and the leading order Kähler potential for the moduli fields in F-theory compactifications globally on the complex structure moduli space. For a particular example we verify attractor behaviour at the generic conifold given an aligned choice of flux which we expect to be universal. Furthermore we analyze the superpotential at the orbifold points but find no stable vacua.

Geometric description of modular and weak values in discrete quantum systems using the Majorana representation

NASA Astrophysics Data System (ADS)

Cormann, Mirko; Caudano, Yves

2017-07-01

We express modular and weak values of observables of three- and higher-level quantum systems in their polar form. The Majorana representation of N-level systems in terms of symmetric states of N  -  1 qubits provides us with a description on the Bloch sphere. With this geometric approach, we find that modular and weak values of observables of N-level quantum systems can be factored in N  -  1 contributions. Their modulus is determined by the product of N  -  1 ratios involving projection probabilities between qubits, while their argument is deduced from a sum of N  -  1 solid angles on the Bloch sphere. These theoretical results allow us to study the geometric origin of the quantum phase discontinuity around singularities of weak values in three-level systems. We also analyze the three-box paradox (Aharonov and Vaidman 1991 J. Phys. A: Math. Gen. 24 2315-28) from the point of view of a bipartite quantum system. In the Majorana representation of this paradox, an observer comes to opposite conclusions about the entanglement state of the particles that were successfully pre- and postselected.

Dissociation of modular total hip arthroplasty at the neck-stem interface without dislocation.

PubMed

Kouzelis, A; Georgiou, C S; Megas, P

2012-12-01

Modular femoral and acetabular components are now widely used, but only a few complications related to the modularity itself have been reported. We describe a case of dissociation of the modular total hip arthroplasty (THA) at the femoral neck-stem interface during walking. The possible causes of this dissociation are discussed. Successful treatment was provided with surgical revision and replacement of the modular neck components. Surgeons who use modular components in hip arthroplasties should be aware of possible early complications in which the modularity of the prostheses is the major factor of failure.

Quasispecies theory for evolution of modularity.

PubMed

Park, Jeong-Man; Niestemski, Liang Ren; Deem, Michael W

2015-01-01

Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here develop a quasispecies theory for the dynamics of modularity in populations of these systems. We show how the steady-state fitness in a randomly changing environment can be computed. We derive a fluctuation dissipation relation for the rate of change of modularity and use it to derive a relationship between rate of environmental changes and rate of growth of modularity. We also find a principle of least action for the evolved modularity at steady state. Finally, we compare our predictions to simulations of protein evolution and find them to be consistent.

Minimum Dimension of a Hilbert Space Needed to Generate a Quantum Correlation.

PubMed

Sikora, Jamie; Varvitsiotis, Antonios; Wei, Zhaohui

2016-08-05

Consider a two-party correlation that can be generated by performing local measurements on a bipartite quantum system. A question of fundamental importance is to understand how many resources, which we quantify by the dimension of the underlying quantum system, are needed to reproduce this correlation. In this Letter, we identify an easy-to-compute lower bound on the smallest Hilbert space dimension needed to generate a given two-party quantum correlation. We show that our bound is tight on many well-known correlations and discuss how it can rule out correlations of having a finite-dimensional quantum representation. We show that our bound is multiplicative under product correlations and also that it can witness the nonconvexity of certain restricted-dimensional quantum correlations.

A Riemann-Hilbert Approach to Complex Sharma-Tasso-Olver Equation on Half Line*

NASA Astrophysics Data System (ADS)

Zhang, Ning; Xia, Tie-Cheng; Hu, Bei-Bei

2017-11-01

In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma-Tasso-Olver (cSTO) equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann-Hilbert problem. The relevant jump matrices are explicitly given in terms of the matrix-value spectral functions spectral functions \\{a(λ ),b(λ )\\} and \\{A(λ ),B(λ )\\} , which depending on initial data {u}0(x)=u(x,0) and boundary data {g}0(y)=u(0,y), {g}1(y)={u}x(0,y), {g}2(y)={u}{xx}(0,y). These spectral functions are not independent, they satisfy a global relation.

Public channel cryptography: chaos synchronization and Hilbert's tenth problem.

PubMed

Kanter, Ido; Kopelowitz, Evi; Kinzel, Wolfgang

2008-08-22

The synchronization process of two mutually delayed coupled deterministic chaotic maps is demonstrated both analytically and numerically. The synchronization is preserved when the mutually transmitted signals are concealed by two commutative private filters, a convolution of the truncated time-delayed output signals or some powers of the delayed output signals. The task of a passive attacker is mapped onto Hilbert's tenth problem, solving a set of nonlinear Diophantine equations, which was proven to be in the class of NP-complete problems [problems that are both NP (verifiable in nondeterministic polynomial time) and NP-hard (any NP problem can be translated into this problem)]. This bridge between nonlinear dynamics and NP-complete problems opens a horizon for new types of secure public-channel protocols.

Cooling schemes for two-component fermions in layered optical lattices

NASA Astrophysics Data System (ADS)

Goto, Shimpei; Danshita, Ippei

2017-12-01

Recently, a cooling scheme for ultracold atoms in a bilayer optical lattice has been proposed (A. Kantian et al., arXiv:1609.03579). In their scheme, the energy offset between the two layers is increased dynamically such that the entropy of one layer is transferred to the other layer. Using the full-Hilbert-space approach, we compute cooling dynamics subjected to the scheme in order to show that their scheme fails to cool down two-component fermions. We develop an alternative cooling scheme for two-component fermions, in which the spin-exchange interaction of one layer is significantly reduced. Using both full-Hilbert-space and matrix-product-state approaches, we find that our scheme can decrease the temperature of the other layer by roughly half.

[Realization of Heart Sound Envelope Extraction Implemented on LabVIEW Based on Hilbert-Huang Transform].

PubMed

Tan, Zhixiang; Zhang, Yi; Zeng, Deping; Wang, Hua

2015-04-01

We proposed a research of a heart sound envelope extraction system in this paper. The system was implemented on LabVIEW based on the Hilbert-Huang transform (HHT). We firstly used the sound card to collect the heart sound, and then implemented the complete system program of signal acquisition, pretreatment and envelope extraction on LabVIEW based on the theory of HHT. Finally, we used a case to prove that the system could collect heart sound, preprocess and extract the envelope easily. The system was better to retain and show the characteristics of heart sound envelope, and its program and methods were important to other researches, such as those on the vibration and voice, etc.

Structural stability and chaotic solutions of perturbed Benjamin-Ono equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Birnir, B.; Morrison, P.J.

1986-11-01

A method for proving chaos in partial differential equations is discussed and applied to the Benjamin-Ono equation subject to perturbations. The perturbations are of two types: one that corresponds to viscous dissipation, the so-called Burger's term, and one that involves the Hilbert transform and has been used to model Landau damping. The method proves chaos in the PDE by proving temporal chaos in its pole solutions. The spatial structure of the pole solutions remains intact, but their positions are chaotic in time. Melnikov's method is invoked to show this temporal chaos. It is discovered that the pole behavior is verymore » sensitive to the Burger's perturbation, but is quite insensitive to the perturbation involving the Hilbert transform.« less

Communication: Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

NASA Astrophysics Data System (ADS)

Vanfleteren, Diederik; Van Neck, Dimitri; Bultinck, Patrick; Ayers, Paul W.; Waroquier, Michel

2010-12-01

A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the electron density) is extended to atomic weight matrices. These are constructed to be orthogonal projection operators on atomic subspaces, which has significant advantages in the interpretation of the bond contributions. In close analogy to the iterative Hirshfeld procedure, self-consistency is built in at the level of atomic charges and occupancies. The method is applied to a test set of about 67 molecules, representing various types of chemical binding. A close correlation is observed between the atomic charges and the Hirshfeld-I atomic charges.

Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators

NASA Astrophysics Data System (ADS)

Znojil, Miloslav

2009-08-01

One-dimensional unitary scattering controlled by non-Hermitian (typically, PT-symmetric) quantum Hamiltonians H ≠ H† is considered. Treating these operators via Runge-Kutta approximation, our three-Hilbert-space formulation of quantum theory is reviewed as explaining the unitarity of scattering. Our recent paper on bound states [Znojil M., SIGMA 5 (2009), 001, 19 pages, arXiv:0901.0700] is complemented by the text on scattering. An elementary example illustrates the feasibility of the resulting innovative theoretical recipe. A new family of the so called quasilocal inner products in Hilbert space is found to exist. Constructively, these products are all described in terms of certain non-equivalent short-range metric operators Θ ≠ I represented, in Runge-Kutta approximation, by (2R-1)-diagonal matrices.

Unimodular F ( R ) gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nojiri, S.; Odintsov, S.D.; Oikonomou, V.K., E-mail: nojiri@gravity.phys.nagoya-u.ac.jp, E-mail: odintsov@ieec.uab.es, E-mail: v.k.oikonomou1979@gmail.com

2016-05-01

We extend the formalism of the Einstein-Hilbert unimodular gravity in the context of modified F ( R ) gravity. After appropriately modifying the Friedmann-Robertson-Walker metric in a way that it becomes compatible to the unimodular condition of having a constant metric determinant, we derive the equations of motion of the unimodular F ( R ) gravity by using the metric formalism of modified gravity with Lagrange multiplier constraint. The resulting equations are studied in frames of reconstruction method, which enables us to realize various cosmological scenarios, which was impossible to realize in the standard Einstein-Hilbert unimodular gravity. Several unimodular Fmore » ( R ) inflationary scenarios are presented, and in some cases, concordance with Planck and BICEP2 observational data can be achieved.« less

Self-organized modularization in evolutionary algorithms.

PubMed

Dauscher, Peter; Uthmann, Thomas

2005-01-01

The principle of modularization has proven to be extremely successful in the field of technical applications and particularly for Software Engineering purposes. The question to be answered within the present article is whether mechanisms can also be identified within the framework of Evolutionary Computation that cause a modularization of solutions. We will concentrate on processes, where modularization results only from the typical evolutionary operators, i.e. selection and variation by recombination and mutation (and not, e.g., from special modularization operators). This is what we call Self-Organized Modularization. Based on a combination of two formalizations by Radcliffe and Altenberg, some quantitative measures of modularity are introduced. Particularly, we distinguish Built-in Modularity as an inherent property of a genotype and Effective Modularity, which depends on the rest of the population. These measures can easily be applied to a wide range of present Evolutionary Computation models. It will be shown, both theoretically and by simulation, that under certain conditions, Effective Modularity (as defined within this paper) can be a selection factor. This causes Self-Organized Modularization to take place. The experimental observations emphasize the importance of Effective Modularity in comparison with Built-in Modularity. Although the experimental results have been obtained using a minimalist toy model, they can lead to a number of consequences for existing models as well as for future approaches. Furthermore, the results suggest a complex self-amplification of highly modular equivalence classes in the case of respected relations. Since the well-known Holland schemata are just the equivalence classes of respected relations in most Simple Genetic Algorithms, this observation emphasizes the role of schemata as Building Blocks (in comparison with arbitrary subsets of the search space).

[Modular enteral nutrition in pediatrics].

PubMed

Murillo Sanchís, S; Prenafeta Ferré, M T; Sempere Luque, M D

1991-01-01

Modular Enteral Nutrition may be a substitute for Parenteral Nutrition in children with different pathologies. Study of 4 children with different pathologies selected from a group of 40 admitted to the Maternal-Childrens Hospital "Valle de Hebrón" in Barcelona, who received modular enteral nutrition. They were monitored on a daily basis by the Dietician Service. Modular enteral nutrition consists of modules of proteins, peptides, lipids, glucids and mineral salts-vitamins. 1.--Craneo-encephalic traumatisms with loss of consciousness, Feeding with a combination of parenteral nutrition and modular enteral nutrition for 7 days. In view of the tolerance and good results of the modular enteral nutrition, the parenteral nutrition was suspended and modular enteral nutrition alone used up to a total of 43 days. 2.--55% burns with 36 days of hyperproteic modular enteral nutrition together with normal feeding. A more rapid recovery was achieved with an increase in total proteins and albumin. 3.--Persistent diarrhoea with 31 days of modular enteral nutrition, 5 days on parenteral nutrition alone and 8 days on combined parenteral nutrition and modular enteral nutrition. In view of the tolerance and good results of the modular enteral nutrition, the parenteral nutrition was suspended. 4.--Mucoviscidosis with a total of 19 days on modular enteral nutrition, 12 of which were exclusively on modular enteral nutrition and 7 as a night supplement to normal feeding. We administered proteic intakes of up to 20% of the total calorific intake and in concentrations of up to 1.2 calories/ml of the final preparation, always with a good tolerance. Modular enteral nutrition can and should be used as a substitute for parenteral nutrition in children with different pathologies, thus preventing the complications inherent in parenteral nutrition.

Convergent evolution of modularity in metabolic networks through different community structures.

PubMed

Zhou, Wanding; Nakhleh, Luay

2012-09-14

It has been reported that the modularity of metabolic networks of bacteria is closely related to the variability of their living habitats. However, given the dependency of the modularity score on the community structure, it remains unknown whether organisms achieve certain modularity via similar or different community structures. In this work, we studied the relationship between similarities in modularity scores and similarities in community structures of the metabolic networks of 1021 species. Both similarities are then compared against the genetic distances. We revisited the association between modularity and variability of the microbial living environments and extended the analysis to other aspects of their life style such as temperature and oxygen requirements. We also tested both topological and biological intuition of the community structures identified and investigated the extent of their conservation with respect to the taxonomy. We find that similar modularities are realized by different community structures. We find that such convergent evolution of modularity is closely associated with the number of (distinct) enzymes in the organism's metabolome, a consequence of different life styles of the species. We find that the order of modularity is the same as the order of the number of the enzymes under the classification based on the temperature preference but not on the oxygen requirement. Besides, inspection of modularity-based communities reveals that these communities are graph-theoretically meaningful yet not reflective of specific biological functions. From an evolutionary perspective, we find that the community structures are conserved only at the level of kingdoms. Our results call for more investigation into the interplay between evolution and modularity: how evolution shapes modularity, and how modularity affects evolution (mainly in terms of fitness and evolvability). Further, our results call for exploring new measures of modularity and network communities that better correspond to functional categorizations.

Implicit Contractive Mappings in Modular Metric and Fuzzy Metric Spaces

PubMed Central

Hussain, N.; Salimi, P.

2014-01-01

The notion of modular metric spaces being a natural generalization of classical modulars over linear spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, and Calderon-Lozanovskii spaces was recently introduced. In this paper we investigate the existence of fixed points of generalized α-admissible modular contractive mappings in modular metric spaces. As applications, we derive some new fixed point theorems in partially ordered modular metric spaces, Suzuki type fixed point theorems in modular metric spaces and new fixed point theorems for integral contractions. In last section, we develop an important relation between fuzzy metric and modular metric and deduce certain new fixed point results in triangular fuzzy metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results. PMID:25003157

Does biological intimacy shape ecological network structure? A test using a brood pollination mutualism on continental and oceanic islands.

PubMed

Hembry, David H; Raimundo, Rafael L G; Newman, Erica A; Atkinson, Lesje; Guo, Chang; Guimarães, Paulo R; Gillespie, Rosemary G

2018-04-25

Biological intimacy-the degree of physical proximity or integration of partner taxa during their life cycles-is thought to promote the evolution of reciprocal specialization and modularity in the networks formed by co-occurring mutualistic species, but this hypothesis has rarely been tested. Here, we test this "biological intimacy hypothesis" by comparing the network architecture of brood pollination mutualisms, in which specialized insects are simultaneously parasites (as larvae) and pollinators (as adults) of their host plants to that of other mutualisms which vary in their biological intimacy (including ant-myrmecophyte, ant-extrafloral nectary, plant-pollinator and plant-seed disperser assemblages). We use a novel dataset sampled from leafflower trees (Phyllanthaceae: Phyllanthus s. l. [Glochidion]) and their pollinating leafflower moths (Lepidoptera: Epicephala) on three oceanic islands (French Polynesia) and compare it to equivalent published data from congeners on continental islands (Japan). We infer taxonomic diversity of leafflower moths using multilocus molecular phylogenetic analysis and examine several network structural properties: modularity (compartmentalization), reciprocality (symmetry) of specialization and algebraic connectivity. We find that most leafflower-moth networks are reciprocally specialized and modular, as hypothesized. However, we also find that two oceanic island networks differ in their modularity and reciprocal specialization from the others, as a result of a supergeneralist moth taxon which interacts with nine of 10 available hosts. Our results generally support the biological intimacy hypothesis, finding that leafflower-moth networks (usually) share a reciprocally specialized and modular structure with other intimate mutualisms such as ant-myrmecophyte symbioses, but unlike nonintimate mutualisms such as seed dispersal and nonintimate pollination. Additionally, we show that generalists-common in nonintimate mutualisms-can also evolve in intimate mutualisms, and that their effect is similar in both types of assemblages: once generalists emerge they reshape the network organization by connecting otherwise isolated modules. © 2018 The Authors. Journal of Animal Ecology © 2018 British Ecological Society.

Modular Power Standard for Space Explorations Missions

NASA Technical Reports Server (NTRS)

Oeftering, Richard C.; Gardner, Brent G.

2016-01-01

Future human space exploration will most likely be composed of assemblies of multiple modular spacecraft elements with interconnected electrical power systems. An electrical system composed of a standardized set modular building blocks provides significant development, integration, and operational cost advantages. The modular approach can also provide the flexibility to configure power systems to meet the mission needs. A primary goal of the Advanced Exploration Systems (AES) Modular Power System (AMPS) project is to establish a Modular Power Standard that is needed to realize these benefits. This paper is intended to give the space exploration community a "first look" at the evolving Modular Power Standard and invite their comments and technical contributions.

New Kids on the Block Schedule: Beginning Teachers Face Challenges

ERIC Educational Resources Information Center

Zepeda, Sally J.; Mayers, R. Stewart

2001-01-01

Across the United States, an ever-increasing number of high schools have reevaluated their use of instructional time and have adopted some form of a block schedule. Block scheduling, an innovation grounded in Trump's Flexible Modular Scheduling Design, reorganizes the school day into extended blocks of time, each approximately 70 to 90 minutes.…

Curved noncommutative tori as Leibniz quantum compact metric spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Latrémolière, Frédéric, E-mail: frederic@math.du.edu

We prove that curved noncommutative tori are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the image of the quantum tori for the conjugation by modular conjugation operator in the regular representation, when this group is endowed with a natural length function.

Order Reduction, Projectability and Constraints of Second-Order Field Theories and Higher-Order Mechanics

NASA Astrophysics Data System (ADS)

Gaset, Jordi; Román-Roy, Narciso

2016-12-01

The projectability of Poincaré-Cartan forms in a third-order jet bundle J3π onto a lower-order jet bundle is a consequence of the degenerate character of the corresponding Lagrangian. This fact is analyzed using the constraint algorithm for the associated Euler-Lagrange equations in J3π. The results are applied to study the Hilbert Lagrangian for the Einstein equations (in vacuum) from a multisymplectic point of view. Thus we show how these equations are a consequence of the application of the constraint algorithm to the geometric field equations, meanwhile the other constraints are related with the fact that this second-order theory is equivalent to a first-order theory. Furthermore, the case of higher-order mechanics is also studied as a particular situation.

Exploring the Tomlin-Varadarajan quantum constraints in U (1 )3 loop quantum gravity: Solutions and the Minkowski theorem

NASA Astrophysics Data System (ADS)

Lewandowski, Jerzy; Lin, Chun-Yen

2017-03-01

We explicitly solved the anomaly-free quantum constraints proposed by Tomlin and Varadarajan for the weak Euclidean model of canonical loop quantum gravity, in a large subspace of the model's kinematic Hilbert space, which is the space of the charge network states. In doing so, we first identified the subspace on which each of the constraints acts convergingly, and then by explicitly evaluating such actions we found the complete set of the solutions in the identified subspace. We showed that the space of solutions consists of two classes of states, with the first class having a property that involves the condition known from the Minkowski theorem on polyhedra, and the second class satisfying a weaker form of the spatial diffeomorphism invariance.

Noether’s second theorem and Ward identities for gauge symmetries

DOE PAGES

Avery, Steven G.; Schwab, Burkhard U. W.

2016-02-04

Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We present and use Noether’s second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether’s second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether’s secondmore » theorem and known results in the recent literature. Finally, our approach suggests a novel point of view with important physical consequences.« less

Symmetries of hyper-Kähler (or Poisson gauge field) hierarchy

NASA Astrophysics Data System (ADS)

Takasaki, K.

1990-08-01

Symmetry properties of the space of complex (or formal) hyper-Kähler metrics are studied in the language of hyper-Kähler hierarchies. The construction of finite symmetries is analogous to the theory of Riemann-Hilbert transformations, loop group elements now taking values in a (pseudo-) group of canonical transformations of a simplectic manifold. In spite of their highly nonlinear and involved nature, infinitesimal expressions of these symmetries are shown to have a rather simple form. These infinitesimal transformations are extended to the Plebanski key functions to give rise to a nonlinear realization of a Poisson loop algebra. The Poisson algebra structure turns out to originate in a contact structure behind a set of symplectic structures inherent in the hyper-Kähler hierarchy. Possible relations to membrane theory are briefly discussed.

Quantum search algorithms on a regular lattice

NASA Astrophysics Data System (ADS)

Hein, Birgit; Tanner, Gregor

2010-07-01

Quantum algorithms for searching for one or more marked items on a d-dimensional lattice provide an extension of Grover’s search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behavior for the search time and the localization probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions.

Boundary term in metric f ( R) gravity: field equations in the metric formalism

NASA Astrophysics Data System (ADS)

Guarnizo, Alejandro; Castañeda, Leonardo; Tejeiro, Juan M.

2010-11-01

The main goal of this paper is to get in a straightforward form the field equations in metric f ( R) gravity, using elementary variational principles and adding a boundary term in the action, instead of the usual treatment in an equivalent scalar-tensor approach. We start with a brief review of the Einstein-Hilbert action, together with the Gibbons-York-Hawking boundary term, which is mentioned in some literature, but is generally missing. Next we present in detail the field equations in metric f ( R) gravity, including the discussion about boundaries, and we compare with the Gibbons-York-Hawking term in General Relativity. We notice that this boundary term is necessary in order to have a well defined extremal action principle under metric variation.

Beyond Lovelock gravity: Higher derivative metric theories

NASA Astrophysics Data System (ADS)

Crisostomi, M.; Noui, K.; Charmousis, C.; Langlois, D.

2018-02-01

We consider theories describing the dynamics of a four-dimensional metric, whose Lagrangian is diffeomorphism invariant and depends at most on second derivatives of the metric. Imposing degeneracy conditions we find a set of Lagrangians that, apart form the Einstein-Hilbert one, are either trivial or contain more than 2 degrees of freedom. Among the partially degenerate theories, we recover Chern-Simons gravity, endowed with constraints whose structure suggests the presence of instabilities. Then, we enlarge the class of parity violating theories of gravity by introducing new "chiral scalar-tensor theories." Although they all raise the same concern as Chern-Simons gravity, they can nevertheless make sense as low energy effective field theories or, by restricting them to the unitary gauge (where the scalar field is uniform), as Lorentz breaking theories with a parity violating sector.

Complex correlation approach for high frequency financial data

NASA Astrophysics Data System (ADS)

Wilinski, Mateusz; Ikeda, Yuichi; Aoyama, Hideaki

2018-02-01

We propose a novel approach that allows the calculation of a Hilbert transform based complex correlation for unevenly spaced data. This method is especially suitable for high frequency trading data, which are of a particular interest in finance. Its most important feature is the ability to take into account lead-lag relations on different scales, without knowing them in advance. We also present results obtained with this approach while working on Tokyo Stock Exchange intraday quotations. We show that individual sectors and subsectors tend to form important market components which may follow each other with small but significant delays. These components may be recognized by analysing eigenvectors of complex correlation matrix for Nikkei 225 stocks. Interestingly, sectorial components are also found in eigenvectors corresponding to the bulk eigenvalues, traditionally treated as noise.

Emergent Bloch excitations in Mott matter

DOE PAGES

Lanata, Nicola; Lee, Tsung -Han; Yao, Yong -Xin; ...

2017-11-14

Here, we develop a unified theoretical picture for excitations in Mott systems, portraying both the heavy quasiparticle excitations and the Hubbard bands as features of an emergent Fermi liquid state formed in an extended Hilbert space, which is nonperturbatively connected to the physical system. This observation sheds light on the fact that even the incoherent excitations in strongly correlated matter often display a well-defined Bloch character, with pronounced momentum dispersion. Furthermore, it indicates that the Mott point can be viewed as a topological transition, where the number of distinct dispersing bands displays a sudden change at the critical point. Ourmore » results, obtained from an appropriate variational principle, display also remarkable quantitative accuracy. This opens an exciting avenue for fast realistic modeling of strongly correlated materials.« less

Development of a Modular Research Platform to Create Medical Observational Studies for Mobile Devices.

PubMed

Zens, Martin; Grotejohann, Birgit; Tassoni, Adrian; Duttenhoefer, Fabian; Südkamp, Norbert P; Niemeyer, Philipp

2017-05-23

Observational studies have proven to be a valuable resource in medical research, especially when performed on a large scale. Recently, mobile device-based observational studies have been discovered by an increasing number of researchers as a promising new source of information. However, the development and deployment of app-based studies is not trivial and requires profound programming skills. The aim of this project was to develop a modular online research platform that allows researchers to create medical studies for mobile devices without extensive programming skills. The platform approach for a modular research platform consists of three major components. A Web-based platform forms the researchers' main workplace. This platform communicates via a shared database with a platform independent mobile app. Furthermore, a separate Web-based login platform for physicians and other health care professionals is outlined and completes the concept. A prototype of the research platform has been developed and is currently in beta testing. Simple questionnaire studies can be created within minutes and published for testing purposes. Screenshots of an example study are provided, and the general working principle is displayed. In this project, we have created a basis for a novel research platform. The necessity and implications of a modular approach were displayed and an outline for future development given. International researchers are invited and encouraged to participate in this ongoing project. ©Martin Zens, Birgit Grotejohann, Adrian Tassoni, Fabian Duttenhoefer, Norbert P Südkamp, Philipp Niemeyer. Originally published in JMIR Research Protocols (http://www.researchprotocols.org), 23.05.2017.