Application of Contraction Mappings to the Control of Nonlinear Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Killingsworth, W. R., Jr.

1972-01-01

The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.

Ensuring Positiveness of the Scaled Difference Chi-square Test Statistic.

PubMed

Satorra, Albert; Bentler, Peter M

2010-06-01

A scaled difference test statistic [Formula: see text] that can be computed from standard software of structural equation models (SEM) by hand calculations was proposed in Satorra and Bentler (2001). The statistic [Formula: see text] is asymptotically equivalent to the scaled difference test statistic T̄(d) introduced in Satorra (2000), which requires more involved computations beyond standard output of SEM software. The test statistic [Formula: see text] has been widely used in practice, but in some applications it is negative due to negativity of its associated scaling correction. Using the implicit function theorem, this note develops an improved scaling correction leading to a new scaled difference statistic T̄(d) that avoids negative chi-square values.

Fully Quantum Fluctuation Theorems

NASA Astrophysics Data System (ADS)

Åberg, Johan

2018-02-01

Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.

The Equilibrium State of Colliding Electron Beams

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

Warnock, R

2003-12-12

We study a nonlinear integral equation that is a necessary condition on the equilibrium phase space distribution function of stored, colliding electron beams. It is analogous to the Haissinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. The equation is analyzed for the case of the Chao-Ruth model of the beam-beam interaction in one degree of freedom, a so-called strong-strong model with nonlinear beam-beam force. We prove existence of a unique solution, for sufficiently small beam current, by an application of the implicit function theorem. We have not yet proved that this solution is positive, asmore » would be required to establish existence of an equilibrium. There is, however, numerical evidence of a positive solution. We expect that our analysis can be extended to more realistic models.« less

Novel neural control for a class of uncertain pure-feedback systems.

PubMed

Shen, Qikun; Shi, Peng; Zhang, Tianping; Lim, Cheng-Chew

2014-04-01

This paper is concerned with the problem of adaptive neural tracking control for a class of uncertain pure-feedback nonlinear systems. Using the implicit function theorem and backstepping technique, a practical robust adaptive neural control scheme is proposed to guarantee that the tracking error converges to an adjusted neighborhood of the origin by choosing appropriate design parameters. In contrast to conventional Lyapunov-based design techniques, an alternative Lyapunov function is constructed for the development of control law and learning algorithms. Differing from the existing results in the literature, the control scheme does not need to compute the derivatives of virtual control signals at each step in backstepping design procedures. Furthermore, the scheme requires the desired trajectory and its first derivative rather than its first n derivatives. In addition, the useful property of the basis function of the radial basis function, which will be used in control design, is explored. Simulation results illustrate the effectiveness of the proposed techniques.

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Using Tranformation Group Priors and Maximum Relative Entropy for Bayesian Glaciological Inversions

NASA Astrophysics Data System (ADS)

Arthern, R. J.; Hindmarsh, R. C. A.; Williams, C. R.

2014-12-01

One of the key advances that has allowed better simulations of the large ice sheets of Greenland and Antarctica has been the use of inverse methods. These have allowed poorly known parameters such as the basal drag coefficient and ice viscosity to be constrained using a wide variety of satellite observations. Inverse methods used by glaciologists have broadly followed one of two related approaches. The first is minimization of a cost function that describes the misfit to the observations, often accompanied by some kind of explicit or implicit regularization that promotes smallness or smoothness in the inverted parameters. The second approach is a probabilistic framework that makes use of Bayes' theorem to update prior assumptions about the probability of parameters, making use of data with known error estimates. Both approaches have much in common and questions of regularization often map onto implicit choices of prior probabilities that are made explicit in the Bayesian framework. In both approaches questions can arise that seem to demand subjective input. What should the functional form of the cost function be if there are alternatives? What kind of regularization should be applied, and how much? How should the prior probability distribution for a parameter such as basal slipperiness be specified when we know so little about the details of the subglacial environment? Here we consider some approaches that have been used to address these questions and discuss ways that probabilistic prior information used for regularizing glaciological inversions might be specified with greater objectivity.

On the addition theorem of spherical functions

NASA Astrophysics Data System (ADS)

Shkodrov, V. G.

The addition theorem of spherical functions is expressed in two reference systems, viz., an inertial system and a system rigidly fixed to a planet. A generalized addition theorem of spherical functions and a particular addition theorem for the rigidly fixed system are derived. The results are applied to the theory of a planetary potential.

A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

DOE PAGES

Chacon, L.; Chen, G.

2016-04-19

Here, we extend a recently proposed fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (Φ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. Anmore » asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.« less

A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

NASA Astrophysics Data System (ADS)

Chacón, L.; Chen, G.

2016-07-01

We extend a recently proposed fully implicit PIC algorithm for the Vlasov-Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (ϕ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ ṡ A = 0 exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.

A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

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

Chacon, L.; Chen, G.

Here, we extend a recently proposed fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (Φ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. Anmore » asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.« less

A Note on a Sampling Theorem for Functions over GF(q)n Domain

NASA Astrophysics Data System (ADS)

Ukita, Yoshifumi; Saito, Tomohiko; Matsushima, Toshiyasu; Hirasawa, Shigeichi

In digital signal processing, the sampling theorem states that any real valued function ƒ can be reconstructed from a sequence of values of ƒ that are discretely sampled with a frequency at least twice as high as the maximum frequency of the spectrum of ƒ. This theorem can also be applied to functions over finite domain. Then, the range of frequencies of ƒ can be expressed in more detail by using a bounded set instead of the maximum frequency. A function whose range of frequencies is confined to a bounded set is referred to as bandlimited function. And a sampling theorem for bandlimited functions over Boolean domain has been obtained. Here, it is important to obtain a sampling theorem for bandlimited functions not only over Boolean domain (GF(q)n domain) but also over GF(q)n domain, where q is a prime power and GF(q) is Galois field of order q. For example, in experimental designs, although the model can be expressed as a linear combination of the Fourier basis functions and the levels of each factor can be represented by GF(q)n, the number of levels often take a value greater than two. However, the sampling theorem for bandlimited functions over GF(q)n domain has not been obtained. On the other hand, the sampling points are closely related to the codewords of a linear code. However, the relation between the parity check matrix of a linear code and any distinct error vectors has not been obtained, although it is necessary for understanding the meaning of the sampling theorem for bandlimited functions. In this paper, we generalize the sampling theorem for bandlimited functions over Boolean domain to a sampling theorem for bandlimited functions over GF(q)n domain. We also present a theorem for the relation between the parity check matrix of a linear code and any distinct error vectors. Lastly, we clarify the relation between the sampling theorem for functions over GF(q)n domain and linear codes.

Le contenu astronomique des Sphériques de Ménélaos

NASA Astrophysics Data System (ADS)

Nadal, Robert; Taha, Abdelkaddous; Pinel, Pierre

2004-07-01

The Spherics were written by Menelaos in the form of a purely mathematical treatise. However, the material developed in the second and third book is closely linked to problems met in astronomy: computation of equatorial coordinates of the Sun, setting up of rising-time tables, study of the motion of the Sun in the sphaera obliqua, simultaneous risings. This link, which remains implicit in the text, was clearly displayed by two arabo-islamic mathematicians and astronomers, who expounded the astronomical meaning of some theorems of the Spherics. We describe, comment and complement their explanations, by classifying the implications of the theorems in three groups: direction of variation of some quantities on the sphere, spherical trigonometry and applications, direction of variation of ratios of some quantities on the sphere. An erratum to this article can be found at http://dx.doi.org/10.1007/s00407-004-0084-7

A theoretical study on tunneling based biosensor having a redox-active monolayer using physics based simulation

NASA Astrophysics Data System (ADS)

Kim, Kyoung Yeon; Lee, Won Cheol; Yun, Jun Yeon; Lee, Youngeun; Choi, Seoungwook; Jin, Seonghoon; Park, Young June

2018-01-01

We developed a numerical simulator to model the operation of a tunneling based biosensor which has a redox-active monolayer. The simulator takes a realistic device structure as a simulation domain, and it employs the drift-diffusion equation for ion transport, the non-equilibrium Green's function formalism for electron tunneling, and the Ramo-Shockley theorem for accurate calculation of non-faradaic current. We also accounted for the buffer reaction and the immobilized peptide layer. For efficient transient simulation, the implicit time integration scheme is employed where the solution at each time step is obtained from the coupled Newton-Raphson method. As an application, we studied the operation of a recently fabricated reference-electrode free biosensor in various bias conditions and confirmed the effect of buffer reaction and the current flowing mechanism. Using the simulator, we also found a strategy to maximize the sensitivity of the tunneling based sensor.

On Euler's Theorem for Homogeneous Functions and Proofs Thereof.

ERIC Educational Resources Information Center

Tykodi, R. J.

1982-01-01

Euler's theorem for homogenous functions is useful when developing thermodynamic distinction between extensive and intensive variables of state and when deriving the Gibbs-Duhem relation. Discusses Euler's theorem and thermodynamic applications. Includes six-step instructional strategy for introducing the material to students. (Author/JN)

Characterization of Generalized Young Measures Generated by Symmetric Gradients

NASA Astrophysics Data System (ADS)

De Philippis, Guido; Rindler, Filip

2017-06-01

This work establishes a characterization theorem for (generalized) Young measures generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of the classical Kinderlehrer-Pedregal theorem. Our result places such Young measures in duality with symmetric-quasiconvex functions with linear growth. The "local" proof strategy combines blow-up arguments with the singular structure theorem in BD (the analogue of Alberti's rank-one theorem in BV), which was recently proved by the authors. As an application of our characterization theorem we show how an atomic part in a BD-Young measure can be split off in generating sequences.

Restoring the consistency with the contact density theorem of a classical density functional theory of ions at a planar electrical double layer.

PubMed

Gillespie, Dirk

2014-11-01

Classical density functional theory (DFT) of fluids is a fast and efficient theory to compute the structure of the electrical double layer in the primitive model of ions where ions are modeled as charged, hard spheres in a background dielectric. While the hard-core repulsive component of this ion-ion interaction can be accurately computed using well-established DFTs, the electrostatic component is less accurate. Moreover, many electrostatic functionals fail to satisfy a basic theorem, the contact density theorem, that relates the bulk pressure, surface charge, and ion densities at their distances of closest approach for ions in equilibrium at a smooth, hard, planar wall. One popular electrostatic functional that fails to satisfy the contact density theorem is a perturbation approach developed by Kierlik and Rosinberg [Phys. Rev. A 44, 5025 (1991)PLRAAN1050-294710.1103/PhysRevA.44.5025] and Rosenfeld [J. Chem. Phys. 98, 8126 (1993)JCPSA60021-960610.1063/1.464569], where the full free-energy functional is Taylor-expanded around a bulk (homogeneous) reference fluid. Here, it is shown that this functional fails to satisfy the contact density theorem because it also fails to satisfy the known low-density limit. When the functional is corrected to satisfy this limit, a corrected bulk pressure is derived and it is shown that with this pressure both the contact density theorem and the Gibbs adsorption theorem are satisfied.

Discrete-time online learning control for a class of unknown nonaffine nonlinear systems using reinforcement learning.

PubMed

Yang, Xiong; Liu, Derong; Wang, Ding; Wei, Qinglai

2014-07-01

In this paper, a reinforcement-learning-based direct adaptive control is developed to deliver a desired tracking performance for a class of discrete-time (DT) nonlinear systems with unknown bounded disturbances. We investigate multi-input-multi-output unknown nonaffine nonlinear DT systems and employ two neural networks (NNs). By using Implicit Function Theorem, an action NN is used to generate the control signal and it is also designed to cancel the nonlinearity of unknown DT systems, for purpose of utilizing feedback linearization methods. On the other hand, a critic NN is applied to estimate the cost function, which satisfies the recursive equations derived from heuristic dynamic programming. The weights of both the action NN and the critic NN are directly updated online instead of offline training. By utilizing Lyapunov's direct method, the closed-loop tracking errors and the NN estimated weights are demonstrated to be uniformly ultimately bounded. Two numerical examples are provided to show the effectiveness of the present approach. Copyright © 2014 Elsevier Ltd. All rights reserved.

Strong Convergence for a Finite Family of Generalized Asymptotically Nonexpansive Mappings

NASA Astrophysics Data System (ADS)

Ma, Zhi-Hong; Chen, Ru-Dond

The purpose of this paper is to show the convergence theorems for generalized asymptotically nonexpansive mappings and asymptotically nonexpansive mappings in Banach spaces by using a new iteration which is a natural generalization of the implicit iteration. In the meantime, we give the necessary and sufficient conditions of the strong convergence to approximate a common fixed point and modify some flaw in the results of Thakur [11]. As one will see, the results presented in this paper are an extension of the corresponding results [8,11].

Numerical solution of the stochastic parabolic equation with the dependent operator coefficient

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

Ashyralyev, Allaberen; Department of Mathematics, ITTU, Ashgabat; Okur, Ulker

2015-09-18

In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.

A Unified Approach to Adaptive Neural Control for Nonlinear Discrete-Time Systems With Nonlinear Dead-Zone Input.

PubMed

Liu, Yan-Jun; Gao, Ying; Tong, Shaocheng; Chen, C L Philip

2016-01-01

In this paper, an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction. Different from linear dead zone, the dead zone, in this paper, is a kind of nonlinear dead zone. To overcome the noncausal problem, which leads to the control scheme infeasible, the systems can be transformed into a m -step-ahead predictor. Due to nonlinear dead-zone appearance, the transformed predictor still contains the nonaffine function. In addition, it is assumed that the gain function of dead-zone input and the control direction are unknown. These conditions bring about the difficulties and the complicacy in the controller design. Thus, the implicit function theorem is applied to deal with nonaffine dead-zone appearance, the problem caused by the unknown control direction can be resolved through applying the discrete Nussbaum gain, and the neural networks are used to approximate the unknown function. Based on the Lyapunov theory, all the signals of the resulting closed-loop system are proved to be semiglobal uniformly ultimately bounded. Moreover, the tracking error is proved to be regulated to a small neighborhood around zero. The feasibility of the proposed approach is demonstrated by a simulation example.

Generalized Browder's and Weyl's theorems for Banach space operators

NASA Astrophysics Data System (ADS)

Curto, Raúl E.; Han, Young Min

2007-12-01

We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder's theorem. We also prove that the spectral mapping theorem holds for the Drazin spectrum and for analytic functions on an open neighborhood of [sigma](T). As applications, we show that if T is algebraically M-hyponormal, or if T is algebraically paranormal, then the generalized Weyl's theorem holds for f(T), where f[set membership, variant]H((T)), the space of functions analytic on an open neighborhood of [sigma](T). We also show that if T is reduced by each of its eigenspaces, then the generalized Browder's theorem holds for f(T), for each f[set membership, variant]H([sigma](T)).

RATIONAL APPROXIMATIONS TO GENERALIZED HYPERGEOMETRIC FUNCTIONS.

DTIC Science & Technology

Under weak restrictions on the various free parameters, general theorems for rational representations of the generalized hypergeometric functions...and certain Meijer G-functions are developed. Upon specialization, these theorems yield a sequency of rational approximations which converge to the

Exploiting structure: Introduction and motivation

NASA Technical Reports Server (NTRS)

Xu, Zhong Ling

1994-01-01

This annual report summarizes the research activities that were performed from 26 Jun. 1993 to 28 Feb. 1994. We continued to investigate the Robust Stability of Systems where transfer functions or characteristic polynomials are affine multilinear functions of parameters. An approach that differs from 'Stability by Linear Process' and that reduces the computational burden of checking the robust stability of the system with multilinear uncertainty was found for low order, 2-order, and 3-order cases. We proved a crucial theorem, the so-called Face Theorem. Previously, we have proven Kharitonov's Vertex Theorem and the Edge Theorem by Bartlett. The detail of this proof is contained in the Appendix. This Theorem provides a tool to describe the boundary of the image of the affine multilinear function. For SPR design, we have developed some new results. The third objective for this period is to design a controller for IHM by the H-infinity optimization technique. The details are presented in the Appendix.

Wave function for harmonically confined electrons in time-dependent electric and magnetostatic fields.

PubMed

Zhu, Hong-Ming; Chen, Jin-Wang; Pan, Xiao-Yin; Sahni, Viraht

2014-01-14

We derive via the interaction "representation" the many-body wave function for harmonically confined electrons in the presence of a magnetostatic field and perturbed by a spatially homogeneous time-dependent electric field-the Generalized Kohn Theorem (GKT) wave function. In the absence of the harmonic confinement - the uniform electron gas - the GKT wave function reduces to the Kohn Theorem wave function. Without the magnetostatic field, the GKT wave function is the Harmonic Potential Theorem wave function. We further prove the validity of the connection between the GKT wave function derived and the system in an accelerated frame of reference. Finally, we provide examples of the application of the GKT wave function.

CONTRIBUTIONS TO RATIONAL APPROXIMATION,

DTIC Science & Technology

Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)

The art of spacecraft design: A multidisciplinary challenge

NASA Technical Reports Server (NTRS)

Abdi, F.; Ide, H.; Levine, M.; Austel, L.

1989-01-01

Actual design turn-around time has become shorter due to the use of optimization techniques which have been introduced into the design process. It seems that what, how and when to use these optimization techniques may be the key factor for future aircraft engineering operations. Another important aspect of this technique is that complex physical phenomena can be modeled by a simple mathematical equation. The new powerful multilevel methodology reduces time-consuming analysis significantly while maintaining the coupling effects. This simultaneous analysis method stems from the implicit function theorem and system sensitivity derivatives of input variables. Use of the Taylor's series expansion and finite differencing technique for sensitivity derivatives in each discipline makes this approach unique for screening dominant variables from nondominant variables. In this study, the current Computational Fluid Dynamics (CFD) aerodynamic and sensitivity derivative/optimization techniques are applied for a simple cone-type forebody of a high-speed vehicle configuration to understand basic aerodynamic/structure interaction in a hypersonic flight condition.

Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations.

PubMed

Zhang, Ling

2017-01-01

The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

Lindeberg theorem for Gibbs-Markov dynamics

NASA Astrophysics Data System (ADS)

Denker, Manfred; Senti, Samuel; Zhang, Xuan

2017-12-01

A dynamical array consists of a family of functions \\{ fn, i: 1≤slant i≤slant k_n, n≥slant 1\\} and a family of initial times \\{τn, i: 1≤slant i≤slant k_n, n≥slant 1\\} . For a dynamical system (X, T) we identify distributional limits for sums of the form for suitable (non-random) constants s_n>0 and an, i\\in { R} . We derive a Lindeberg-type central limit theorem for dynamical arrays. Applications include new central limit theorems for functions which are not locally Lipschitz continuous and central limit theorems for statistical functions of time series obtained from Gibbs-Markov systems. Our results, which hold for more general dynamics, are stated in the context of Gibbs-Markov dynamical systems for convenience.

Some functional limit theorems for compound Cox processes

NASA Astrophysics Data System (ADS)

Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.

2016-06-01

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

Some functional limit theorems for compound Cox processes

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

Korolev, Victor Yu.; Institute of Informatics Problems FRC CSC RAS; Chertok, A. V.

2016-06-08

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

Four Theorems on the Psychometric Function

PubMed Central

May, Keith A.; Solomon, Joshua A.

2013-01-01

In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, . This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull “slope” parameter, , can be approximated by , where is the of the Weibull function that fits best to the cumulative noise distribution, and depends on the transducer. We derive general expressions for and , from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when , . We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4–0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of for contrast discrimination suggests that, if internal noise is stimulus-independent, it has lower kurtosis than a Gaussian. PMID:24124456

Invertibility of retarded response functions for Laplace transformable potentials: Application to one-body reduced density matrix functional theory.

PubMed

Giesbertz, K J H

2015-08-07

A theorem for the invertibility of arbitrary response functions is presented under the following conditions: the time dependence of the potentials should be Laplace transformable and the initial state should be a ground state, though it might be degenerate. This theorem provides a rigorous foundation for all density-functional-like theories in the time-dependent linear response regime. Especially for time-dependent one-body reduced density matrix (1RDM) functional theory, this is an important step forward, since a solid foundation has currently been lacking. The theorem is equally valid for static response functions in the non-degenerate case, so can be used to characterize the uniqueness of the potential in the ground state version of the corresponding density-functional-like theory. Such a classification of the uniqueness of the non-local potential in ground state 1RDM functional theory has been lacking for decades. With the aid of presented invertibility theorem presented here, a complete classification of the non-uniqueness of the non-local potential in 1RDM functional theory can be given for the first time.

Unifying three perspectives on information processing in stochastic thermodynamics.

PubMed

Barato, A C; Seifert, U

2014-03-07

So far, feedback-driven systems have been discussed using (i) measurement and control, (ii) a tape interacting with a system, or (iii) by identifying an implicit Maxwell demon in steady-state transport. We derive the corresponding second laws from one master fluctuation theorem and discuss their relationship. In particular, we show that both the entropy production involving mutual information between system and controller and the one involving a Shannon entropy difference of an information reservoir like a tape carry an extra term different from the usual current times affinity. We, thus, generalize stochastic thermodynamics to the presence of an information reservoir.

Ideal solar cell equation in the presence of photon recycling

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

Lan, Dongchen, E-mail: d.lan@unsw.edu.au; Green, Martin A., E-mail: m.green@unsw.edu.au

Previous derivations of the ideal solar cell equation based on Shockley's p-n junction diode theory implicitly assume negligible effects of photon recycling. This paper derives the equation in the presence of photon recycling that modifies the values of dark saturation and light-generated currents, using an approach applicable to arbitrary three-dimensional geometries with arbitrary doping profile and variable band gap. The work also corrects an error in previous work and proves the validity of the reciprocity theorem for charge collection in such a more general case with the previously neglected junction depletion region included.

Zero-Bounded Limits as a Special Case of the Squeeze Theorem for Evaluating Single-Variable and Multivariable Limits

ERIC Educational Resources Information Center

Gkioulekas, Eleftherios

2013-01-01

Many limits, typically taught as examples of applying the "squeeze" theorem, can be evaluated more easily using the proposed zero-bounded limit theorem. The theorem applies to functions defined as a product of a factor going to zero and a factor that remains bounded in some neighborhood of the limit. This technique is immensely useful…

Tree-manipulating systems and Church-Rosser theorems.

NASA Technical Reports Server (NTRS)

Rosen, B. K.

1973-01-01

Study of a broad class of tree-manipulating systems called subtree replacement systems. The use of this framework is illustrated by general theorems analogous to the Church-Rosser theorem and by applications of these theorems. Sufficient conditions are derived for the Church-Rosser property, and their applications to recursive definitions, the lambda calculus, and parallel programming are discussed. McCarthy's (1963) recursive calculus is extended by allowing a choice between call-by-value and call-by-name. It is shown that recursively defined functions are single-valued despite the nondeterminism of the evaluation algorithm. It is also shown that these functions solve their defining equations in a 'canonical' manner.

Implicit and Explicit Associations with Erotic Stimuli in Sexually Functional and Dysfunctional Men.

PubMed

van Lankveld, Jacques; Odekerken, Ingrid; Kok-Verhoeven, Lydia; van Hooren, Susan; de Vries, Peter; van den Hout, Anja; Verboon, Peter

2015-08-01

Although conceptual models of sexual functioning have suggested a major role for implicit cognitive processing in sexual functioning, this has thus far, only been investigated in women. The aim of this study was to investigate the role of implicit cognition in sexual functioning in men. Men with (N = 29) and without sexual dysfunction (N = 31) were compared. Participants performed two single-target implicit association tests (ST-IAT), measuring the implicit association of visual erotic stimuli with attributes representing, respectively, valence ('liking') and motivation ('wanting'). Participants also rated the erotic pictures that were shown in the ST-IAT on the dimensions of valence, attractiveness, and sexual excitement to assess their explicit associations with these erotic stimuli. Participants completed the International Index of Erectile Functioning for a continuous measure of sexual functioning. Unexpectedly, compared with sexually functional men, sexually dysfunctional men were found to show stronger implicit associations of erotic stimuli with positive valence than with negative valence. Level of sexual functioning, however, was not predicted by explicit nor implicit associations. Level of sexual distress was predicted by explicit valence ratings, with positive ratings predicting higher levels of sexual distress. Men with and without sexual dysfunction differed significantly with regard to implicit liking. Research recommendations and implications are discussed. © 2015 International Society for Sexual Medicine.

An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.; Barnes, D. C.

2011-08-01

This paper discusses a novel fully implicit formulation for a one-dimensional electrostatic particle-in-cell (PIC) plasma simulation approach. Unlike earlier implicit electrostatic PIC approaches (which are based on a linearized Vlasov-Poisson formulation), ours is based on a nonlinearly converged Vlasov-Ampére (VA) model. By iterating particles and fields to a tight nonlinear convergence tolerance, the approach features superior stability and accuracy properties, avoiding most of the accuracy pitfalls in earlier implicit PIC implementations. In particular, the formulation is stable against temporal (Courant-Friedrichs-Lewy) and spatial (aliasing) instabilities. It is charge- and energy-conserving to numerical round-off for arbitrary implicit time steps (unlike the earlier "energy-conserving" explicit PIC formulation, which only conserves energy in the limit of arbitrarily small time steps). While momentum is not exactly conserved, errors are kept small by an adaptive particle sub-stepping orbit integrator, which is instrumental to prevent particle tunneling (a deleterious effect for long-term accuracy). The VA model is orbit-averaged along particle orbits to enforce an energy conservation theorem with particle sub-stepping. As a result, very large time steps, constrained only by the dynamical time scale of interest, are possible without accuracy loss. Algorithmically, the approach features a Jacobian-free Newton-Krylov solver. A main development in this study is the nonlinear elimination of the new-time particle variables (positions and velocities). Such nonlinear elimination, which we term particle enslavement, results in a nonlinear formulation with memory requirements comparable to those of a fluid computation, and affords us substantial freedom in regards to the particle orbit integrator. Numerical examples are presented that demonstrate the advertised properties of the scheme. In particular, long-time ion acoustic wave simulations show that numerical accuracy does not degrade even with very large implicit time steps, and that significant CPU gains are possible.

Implicit and Explicit Associations with Erotic Stimuli in Women with and Without Sexual Problems.

PubMed

van Lankveld, Jacques J D M; Bandell, Myrthe; Bastin-Hurek, Eva; van Beurden, Myra; Araz, Suzan

2018-02-20

Conceptual models of sexual functioning have suggested a major role for implicit cognitive processing in sexual functioning. The present study aimed to investigate implicit and explicit cognition in sexual functioning in women. Gynecological patients with (N = 38) and without self-reported sexual problems (N = 41) were compared. Participants performed two Single-Target Implicit Association Tests (ST-IAT), measuring the implicit association of visual erotic stimuli with attributes representing, respectively, valence and motivation. Participants also rated the erotic pictures that were shown in the ST-IATs on the dimensions of valence, attractiveness, and sexual excitement, to assess their explicit associations with these erotic stimuli. Participants completed the Female Sexual Functioning Index and the Female Sexual Distress Scale for continuous measures of sexual functioning, and the Hospital Anxiety and Depression Scale to assess depressive symptoms. Compared to nonsymptomatic women, women with sexual problems were found to show more negative implicit associations of erotic stimuli with wanting (implicit sexual motivation). Across both groups, stronger implicit associations of erotic stimuli with wanting predicted higher level of sexual functioning. More positive explicit ratings of erotic stimuli predicted lower level of sexual distress across both groups.

Three Lectures on Theorem-proving and Program Verification

NASA Technical Reports Server (NTRS)

Moore, J. S.

1983-01-01

Topics concerning theorem proving and program verification are discussed with particlar emphasis on the Boyer/Moore theorem prover, and approaches to program verification such as the functional and interpreter methods and the inductive assertion approach. A history of the discipline and specific program examples are included.

O(2) Hopf bifurcation of viscous shock waves in a channel

NASA Astrophysics Data System (ADS)

Pogan, Alin; Yao, Jinghua; Zumbrun, Kevin

2015-07-01

Extending work of Texier and Zumbrun in the semilinear non-reflection symmetric case, we study O(2) transverse Hopf bifurcation, or "cellular instability", of viscous shock waves in a channel, for a class of quasilinear hyperbolic-parabolic systems including the equations of thermoviscoelasticity. The main difficulties are to (i) obtain Fréchet differentiability of the time- T solution operator by appropriate hyperbolic-parabolic energy estimates, and (ii) handle O(2) symmetry in the absence of either center manifold reduction (due to lack of spectral gap) or (due to nonstandard quasilinear hyperbolic-parabolic form) the requisite framework for treatment by spatial dynamics on the space of time-periodic functions, the two standard treatments for this problem. The latter issue is resolved by Lyapunov-Schmidt reduction of the time- T map, yielding a four-dimensional problem with O(2) plus approximate S1 symmetry, which we treat "by hand" using direct Implicit Function Theorem arguments. The former is treated by balancing information obtained in Lagrangian coordinates with that from associated constraints. Interestingly, this argument does not apply to gas dynamics or magnetohydrodynamics (MHD), due to the infinite-dimensional family of Lagrangian symmetries corresponding to invariance under arbitrary volume-preserving diffeomorphisms.

Girsanov reweighting for path ensembles and Markov state models

NASA Astrophysics Data System (ADS)

Donati, L.; Hartmann, C.; Keller, B. G.

2017-06-01

The sensitivity of molecular dynamics on changes in the potential energy function plays an important role in understanding the dynamics and function of complex molecules. We present a method to obtain path ensemble averages of a perturbed dynamics from a set of paths generated by a reference dynamics. It is based on the concept of path probability measure and the Girsanov theorem, a result from stochastic analysis to estimate a change of measure of a path ensemble. Since Markov state models (MSMs) of the molecular dynamics can be formulated as a combined phase-space and path ensemble average, the method can be extended to reweight MSMs by combining it with a reweighting of the Boltzmann distribution. We demonstrate how to efficiently implement the Girsanov reweighting in a molecular dynamics simulation program by calculating parts of the reweighting factor "on the fly" during the simulation, and we benchmark the method on test systems ranging from a two-dimensional diffusion process and an artificial many-body system to alanine dipeptide and valine dipeptide in implicit and explicit water. The method can be used to study the sensitivity of molecular dynamics on external perturbations as well as to reweight trajectories generated by enhanced sampling schemes to the original dynamics.

Circulant Matrices and Affine Equivalence of Monomial Rotation Symmetric Boolean Functions

DTIC Science & Technology

2015-01-01

definitions , including monomial rotation symmetric (MRS) Boolean functions and affine equivalence, and a known result for such quadratic functions...degree of the MRS is, we have a similar result as [40, Theorem 1.1] for n = 4p (p prime), or squarefree integers n, which along with our Theorem 5.2

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

Chen, Yong, E-mail: 83229994@qq.com; Ge, Hao, E-mail: haoge@pku.edu.cn; Xiong, Jie, E-mail: jiexiong@umac.mo

Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. There exist very few results for steady-state fluctuation theorem of sample entropy production rate in terms of large deviation principle for diffusion processes due to the technical difficulties. Here we give a proof for the steady-state fluctuation theorem of a diffusion process in magnetic fields, with explicit expressions of the free energy function and rate function. The proof is based on the Karhunen-Loève expansion of complex-valued Ornstein-Uhlenbeck process.

Four theorems on the psychometric function.

PubMed

May, Keith A; Solomon, Joshua A

2013-01-01

In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise) x β(Transducer), where β(Noise) is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer) depends on the transducer. We derive general expressions for β(Noise) and β(Transducer), from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx)(b), β ≈ β(Noise) x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus-independent, it has lower kurtosis than a Gaussian.

Inference of Functionally-Relevant N-acetyltransferase Residues Based on Statistical Correlations.

PubMed

Neuwald, Andrew F; Altschul, Stephen F

2016-12-01

Over evolutionary time, members of a superfamily of homologous proteins sharing a common structural core diverge into subgroups filling various functional niches. At the sequence level, such divergence appears as correlations that arise from residue patterns distinct to each subgroup. Such a superfamily may be viewed as a population of sequences corresponding to a complex, high-dimensional probability distribution. Here we model this distribution as hierarchical interrelated hidden Markov models (hiHMMs), which describe these sequence correlations implicitly. By characterizing such correlations one may hope to obtain information regarding functionally-relevant properties that have thus far evaded detection. To do so, we infer a hiHMM distribution from sequence data using Bayes' theorem and Markov chain Monte Carlo (MCMC) sampling, which is widely recognized as the most effective approach for characterizing a complex, high dimensional distribution. Other routines then map correlated residue patterns to available structures with a view to hypothesis generation. When applied to N-acetyltransferases, this reveals sequence and structural features indicative of functionally important, yet generally unknown biochemical properties. Even for sets of proteins for which nothing is known beyond unannotated sequences and structures, this can lead to helpful insights. We describe, for example, a putative coenzyme-A-induced-fit substrate binding mechanism mediated by arginine residue switching between salt bridge and π-π stacking interactions. A suite of programs implementing this approach is available (psed.igs.umaryland.edu).

A Polarimetric Extension of the van Cittert-Zernike Theorem for Use with Microwave Interferometers

NASA Technical Reports Server (NTRS)

Piepmeier, J. R.; Simon, N. K.

2004-01-01

The van Cittert-Zernike theorem describes the Fourier-transform relationship between an extended source and its visibility function. Developments in classical optics texts use scalar field formulations for the theorem. Here, we develop a polarimetric extension to the van Cittert-Zernike theorem with applications to passive microwave Earth remote sensing. The development provides insight into the mechanics of two-dimensional interferometric imaging, particularly the effects of polarization basis differences between the scene and the observer.

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

Lindgren, Ingvar; Salomonson, Sten

The locality theorem in density-functional theory (DFT) states that the functional derivative of the Hohenberg-Kohn universal functional can be expressed as a local multiplicative potential function, and this is the basis of DFT and of the successful Kohn-Sham model. Nesbet has in several papers [Phys. Rev. A 58, R12 (1998); ibid.65, 010502 (2001); Adv. Quant. Chem, 43, 1 (2003)] claimed that this theorem is in conflict with fundamental quantum physics, and as a consequence that the Hohenberg-Kohn theory cannot be generally valid. We have commented upon these works [Comment, Phys. Rev. A 67, 056501 (2003)] and recently extended the argumentsmore » [Adv. Quantum Chem. 43, 95 (2003)]. We have shown that there is no such conflict and that the locality theorem is inherently exact. In the present work we have furthermore verified this numerically by constructing a local Kohn-Sham potential for the 1s2s{sup 3}S state of helium that generates the many-body electron density and shown that the corresponding 2s Kohn-Sham orbital eigenvalue agrees with the ionization energy to nine digits. Similar result is obtained with the Hartree-Fock density. Therefore, in addition to verifying the locality theorem, this result also confirms the so-called ionization-potential theorem.« less

A specific implicit sequence learning deficit as an underlying cause of dyslexia? Investigating the role of attention in implicit learning tasks.

PubMed

Staels, Eva; Van den Broeck, Wim

2017-05-01

Recently, a general implicit sequence learning deficit was proposed as an underlying cause of dyslexia. This new hypothesis was investigated in the present study by including a number of methodological improvements, for example, the inclusion of appropriate control conditions. The second goal of the study was to explore the role of attentional functioning in implicit and explicit learning tasks. In a 2 × 2 within-subjects design 4 tasks were administered in 30 dyslexic and 38 control children: an implicit and explicit serial reaction time (RT) task and an implicit and explicit contextual cueing task. Attentional functioning was also administered. The entire learning curves of all tasks were analyzed using latent growth curve modeling in order to compare performances between groups and to examine the role of attentional functioning on the learning curves. The amount of implicit learning was similar for both groups. However, the dyslexic group showed slower RTs throughout the entire task. This group difference reduced and became nonsignificant after controlling for attentional functioning. Both implicit learning tasks, but none of the explicit learning tasks, were significantly affected by attentional functioning. Dyslexic children do not suffer from a specific implicit sequence learning deficit. The slower RTs of the dyslexic children throughout the entire implicit sequence learning process are caused by their comorbid attention problems and overall slowness. A key finding of the present study is that, in contrast to what was assumed for a long time, implicit learning relies on attentional resources, perhaps even more than explicit learning does. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Approximation of functions and their conjugates in variable Lebesgue spaces

NASA Astrophysics Data System (ADS)

Volosivets, S. S.

2017-01-01

One-sided Steklov means are used to introduce moduli of continuity of natural order in variable Lp(\\cdot)2π-spaces. A direct theorem of Jackson- Stechkin type and an inverse theorem of Salem-Stechkin type are given. Similar results are obtained for the conjugate functions. Bibliography: 24 titles.

Recovering a function from its trigonometric integral

NASA Astrophysics Data System (ADS)

Sworowska, Tat'yana A.

2010-09-01

The approximate symmetric Henstock-Kurzweil integral is shown as solving the problem of the recovery of a function from its trigonometric integral. This being so, we generalize Offord's theorem, which is an analogue of de la Vallée Poussin's theorem for trigonometric series. A new condition for a function to be representable by a singular Fourier integral is also obtained.Bibliography: 10 titles.

The geometric Mean Value Theorem

NASA Astrophysics Data System (ADS)

de Camargo, André Pierro

2018-05-01

In a previous article published in the American Mathematical Monthly, Tucker (Amer Math Monthly. 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying Rolle's theorem to a function like Although short and effective, such reasoning is not intuitive. Perhaps for this reason, Tucker classified the Mean Value Theorem as a technical existence theorem used to prove intuitively obvious statements. Moreover, he argued that there is nothing obvious about the Mean Value Theorem without the continuity of the derivative. Under so unfair discrimination, we felt the need to come to the defense of this beautiful theorem in order to clear up these misunderstandings.

A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth-Fokker-Planck equation

NASA Astrophysics Data System (ADS)

Taitano, W. T.; Chacón, L.; Simakov, A. N.; Molvig, K.

2015-09-01

In this study, we demonstrate a fully implicit algorithm for the multi-species, multidimensional Rosenbluth-Fokker-Planck equation which is exactly mass-, momentum-, and energy-conserving, and which preserves positivity. Unlike most earlier studies, we base our development on the Rosenbluth (rather than Landau) form of the Fokker-Planck collision operator, which reduces complexity while allowing for an optimal fully implicit treatment. Our discrete conservation strategy employs nonlinear constraints that force the continuum symmetries of the collision operator to be satisfied upon discretization. We converge the resulting nonlinear system iteratively using Jacobian-free Newton-Krylov methods, effectively preconditioned with multigrid methods for efficiency. Single- and multi-species numerical examples demonstrate the advertised accuracy properties of the scheme, and the superior algorithmic performance of our approach. In particular, the discretization approach is numerically shown to be second-order accurate in time and velocity space and to exhibit manifestly positive entropy production. That is, H-theorem behavior is indicated for all the examples we have tested. The solution approach is demonstrated to scale optimally with respect to grid refinement (with CPU time growing linearly with the number of mesh points), and timestep (showing very weak dependence of CPU time with time-step size). As a result, the proposed algorithm delivers several orders-of-magnitude speedup vs. explicit algorithms.

A Stochastic Version of the Noether Theorem

NASA Astrophysics Data System (ADS)

González Lezcano, Alfredo; Cabo Montes de Oca, Alejandro

2018-06-01

A stochastic version of the Noether theorem is derived for systems under the action of external random forces. The concept of moment generating functional is employed to describe the symmetry of the stochastic forces. The theorem is applied to two kinds of random covariant forces. One of them generated in an electrodynamic way and the other is defined in the rest frame of the particle as a function of the proper time. For both of them, it is shown the conservation of the mean value of a random drift momentum. The validity of the theorem makes clear that random systems can produce causal stochastic correlations between two faraway separated systems, that had interacted in the past. In addition possible connections of the discussion with the Ives Couder's experimental results are remarked.

Quantitative Voronovskaya and Grüss-Voronovskaya type theorems for Jain-Durrmeyer operators of blending type

NASA Astrophysics Data System (ADS)

Kajla, Arun; Deshwal, Sheetal; Agrawal, P. N.

2018-05-01

In the present paper we introduce a Durrmeyer variant of Jain operators based on a function ρ (x) where ρ is a continuously differentiable function on [0,∞), ρ (0)=0 and \\inf ρ '(x)≥ a, a >0, x \\in [0,∞) . For these new operators, some indispensable auxiliary results are established first. Then, the degree of approximation with the aid of Ditzian-Totik modulus of smoothness and the rate of convergence for functions whose derivatives are of bounded variation, is obtained. Further, we focus on the study of a Voronovskaja type asymptotic theorem, quantitative Voronovskaya and Grüss-Voronovskaya type theorems.

Casimir effect within D=3+1 Maxwell-Chern-Simons electrodynamics

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

Kharlanov, O. G.; Zhukovsky, V. Ch.

2010-01-15

Within the framework of the (3+1)-dimensional Lorentz-violating extended electrodynamics including the CPT-odd Chern-Simons term, we consider the electromagnetic field between two parallel perfectly conducting plates. We find the one-particle eigenstates of such a field, as well as the implicit expression for the photon energy spectrum. We also show that the tachyon-induced vacuum instability is negligible when the separation between the plates is sufficiently small though finite. In order to find the leading Chern-Simons correction to the vacuum energy, we renormalize and evaluate the sum over all one-particle eigenstate energies using the two different methods, the zeta function technique and themore » transformation of the discrete sum into a complex plane integral via the residue theorem. The resulting correction to the Casimir force, which is attractive and quadratic in the Chern-Simons term, disagrees with the one obtained in [M. Frank and I. Turan, Phys. Rev. D 74, 033016 (2006)], using the misinterpreted equations of motion. Compared with experimental data, our result places a constraint on the absolute value of the Chern-Simons term.« less

A Cameron-Storvick Theorem for Analytic Feynman Integrals on Product Abstract Wiener Space and Applications

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

Choi, Jae Gil, E-mail: jgchoi@dankook.ac.kr; Chang, Seung Jun, E-mail: sejchang@dankook.ac.kr

In this paper we derive a Cameron-Storvick theorem for the analytic Feynman integral of functionals on product abstract Wiener space B{sup 2}. We then apply our result to obtain an evaluation formula for the analytic Feynman integral of unbounded functionals on B{sup 2}. We also present meaningful examples involving functionals which arise naturally in quantum mechanics.

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

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

Pribram-Jones, Aurora; Grabowski, Paul E.; Burke, Kieron

We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

DOE PAGES

Pribram-Jones, Aurora; Grabowski, Paul E.; Burke, Kieron

2016-06-08

We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

Perturbation corrections to Koopmans' theorem. V - A study with large basis sets

NASA Technical Reports Server (NTRS)

Chong, D. P.; Langhoff, S. R.

1982-01-01

The vertical ionization potentials of N2, F2 and H2O were calculated by perturbation corrections to Koopmans' theorem using six different basis sets. The largest set used includes several sets of polarization functions. Comparison is made with measured values and with results of computations using Green's functions.

Asynchronous networks: modularization of dynamics theorem

NASA Astrophysics Data System (ADS)

Bick, Christian; Field, Michael

2017-02-01

Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or dynamical modules. For these networks we can give a complete description of the network function in terms of the function of the events comprising the network: the modularization of dynamics theorem. We give examples to illustrate the main results.

Exact charge and energy conservation in implicit PIC with mapped computational meshes

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

Chen, Guangye; Barnes, D. C.

This paper discusses a novel fully implicit formulation for a one-dimensional electrostatic particle-in-cell (PIC) plasma simulation approach. Unlike earlier implicit electrostatic PIC approaches (which are based on a linearized Vlasov Poisson formulation), ours is based on a nonlinearly converged Vlasov Amp re (VA) model. By iterating particles and fields to a tight nonlinear convergence tolerance, the approach features superior stability and accuracy properties, avoiding most of the accuracy pitfalls in earlier implicit PIC implementations. In particular, the formulation is stable against temporal (Courant Friedrichs Lewy) and spatial (aliasing) instabilities. It is charge- and energy-conserving to numerical round-off for arbitrary implicitmore » time steps (unlike the earlier energy-conserving explicit PIC formulation, which only conserves energy in the limit of arbitrarily small time steps). While momentum is not exactly conserved, errors are kept small by an adaptive particle sub-stepping orbit integrator, which is instrumental to prevent particle tunneling (a deleterious effect for long-term accuracy). The VA model is orbit-averaged along particle orbits to enforce an energy conservation theorem with particle sub-stepping. As a result, very large time steps, constrained only by the dynamical time scale of interest, are possible without accuracy loss. Algorithmically, the approach features a Jacobian-free Newton Krylov solver. A main development in this study is the nonlinear elimination of the new-time particle variables (positions and velocities). Such nonlinear elimination, which we term particle enslavement, results in a nonlinear formulation with memory requirements comparable to those of a fluid computation, and affords us substantial freedom in regards to the particle orbit integrator. Numerical examples are presented that demonstrate the advertised properties of the scheme. In particular, long-time ion acoustic wave simulations show that numerical accuracy does not degrade even with very large implicit time steps, and that significant CPU gains are possible.« less

Quantization of Chirikov Map and Quantum KAM Theorem.

NASA Astrophysics Data System (ADS)

Shi, Kang-Jie

KAM theorem is one of the most important theorems in classical nonlinear dynamics and chaos. To extend KAM theorem to the regime of quantum mechanics, we first study the quantum Chirikov map, whose classical counterpart provides a good example of KAM theorem. Under resonance condition 2pihbar = 1/N, we obtain the eigenstates of the evolution operator of this system. We find that the wave functions in the coherent state representation (CSR) are very similar to the classical trajectories. In particular, some of these wave functions have wall-like structure at the locations of classical KAM curves. We also find that a local average is necessary for a Wigner function to approach its classical limit in the phase space. We then study the general problem theoretically. Under similar conditions for establishing the classical KAM theorem, we obtain a quantum extension of KAM theorem. By constructing successive unitary transformations, we can greatly reduce the perturbation part of a near-integrable Hamiltonian system in a region associated with a Diophantine number {rm W}_{o}. This reduction is restricted only by the magnitude of hbar.. We can summarize our results as follows: In the CSR of a nearly integrable quantum system, associated with a Diophantine number {rm W}_ {o}, there is a band near the corresponding KAM torus of the classical limit of the system. In this band, a Gaussian wave packet moves quasi-periodically (and remain close to the KAM torus) for a long time, with possible diffusion in both the size and the shape of its wave packet. The upper bound of the tunnelling rate out of this band for the wave packet can be made much smaller than any given power of hbar, if the original perturbation is sufficiently small (but independent of hbar). When hbarto 0, we reproduce the classical KAM theorem. For most near-integrable systems the eigenstate wave function in the above band can either have a wall -like structure or have a vanishing amplitude. These conclusions agree with the numerical results of the quantum Chirikov map.

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.

Towards and FVE-FAC Method for Determining Thermocapillary Effects on Weld Pool Shape

NASA Technical Reports Server (NTRS)

Canright, David; Henson, Van Emden

1996-01-01

Several practical materials processes, e.g., welding, float-zone purification, and Czochralski crystal growth, involve a pool of molten metal with a free surface, with strong temperature gradients along the surface. In some cases, the resulting thermocapillary flow is vigorous enough to convect heat toward the edges of the pool, increasing the driving force in a sort of positive feedback. In this work we examine this mechanism and its effect on the solid-liquid interface through a model problem: a half space of pure substance with concentrated axisymmetric surface heating, where surface tension is strong enough to keep the liquid free surface flat. The numerical method proposed for this problem utilizes a finite volume element (FVE) discretization in cylindrical coordinates. Because of the axisymmetric nature of the model problem, the control volumes used are torroidal prisms, formed by taking a polygonal cross-section in the (r, z) plane and sweeping it completely around the z-axis. Conservation of energy (in the solid), and conservation of energy, momentum, and mass (in the liquid) are enforced globally by integrating these quantities and enforcing conservation over each control volume. Judicious application of the Divergence Theorem and Stokes' Theorem, combined with a Crank-Nicolson time-stepping scheme leads to an implicit algebraic system to be solved at each time step. It is known that near the boundary of the pool, that is, near the solid-liquid interface, the full conduction-convection solution will require extremely fine length scales to resolve the physical behavior of the system. Furthermore, this boundary moves as a function of time. Accordingly, we develop the foundation of an adaptive refinement scheme based on the principles of Fast Adaptive Composite Grid methods (FAC). Implementation of the method and numerical results will appear in a later report.

About the best approximations with trigonometric polynomials on the class W0Hω¯ of the space L, part II

NASA Astrophysics Data System (ADS)

Nikolova, Yanka

2013-12-01

In this paper we obtain estimation for the best approximation En(W0Hω¯) in the L-metric, where W0Hω¯ is the conjugate of the class W0Hω, i.e. W0Hω¯ =def {f¯,f∈W0Hω}. Our results concern evaluations of the function Φ(\\overlineG\\overline;x), where Φ(G;x) is the so-called ∑-representation of the function G, as defined in [2, p.144], and \\overlineG\\overline(x) denotes the conjugate of the function G(x). After some preliminaries, we formulate three basic theorems (Theorems 2, 3, 4) from the first part of this work [9], necessary for the estimation of the functional Fω(g¯) = supf∈Hω ∫ 02πf(t)ṡg¯(t)dt. Specially, in Theorem 4 we prove an inequality for this functional and show that the estimation is exact, i.e. the inequality becomes equality for some specific conjugate functions. Next, the new results in this paper are given as Theorems 5 and 6, with detailed proofs. Furthermore, in our work we prove the following estimation: f¯n,0‖L≤En(W0Hω¯)L≤2f¯n,0‖L.

An efficient sampling technique for sums of bandpass functions

NASA Technical Reports Server (NTRS)

Lawton, W. M.

1982-01-01

A well known sampling theorem states that a bandlimited function can be completely determined by its values at a uniformly placed set of points whose density is at least twice the highest frequency component of the function (Nyquist rate). A less familiar but important sampling theorem states that a bandlimited narrowband function can be completely determined by its values at a properly chosen, nonuniformly placed set of points whose density is at least twice the passband width. This allows for efficient digital demodulation of narrowband signals, which are common in sonar, radar and radio interferometry, without the side effect of signal group delay from an analog demodulator. This theorem was extended by developing a technique which allows a finite sum of bandlimited narrowband functions to be determined by its values at a properly chosen, nonuniformly placed set of points whose density can be made arbitrarily close to the sum of the passband widths.

Special ergodic theorems and dynamical large deviations

NASA Astrophysics Data System (ADS)

Kleptsyn, Victor; Ryzhov, Dmitry; Minkov, Stanislav

2012-11-01

Let f : M → M be a self-map of a compact Riemannian manifold M, admitting a global SRB measure μ. For a continuous test function \\varphi\\colon M\\to R and a constant α > 0, consider the set Kφ,α of the initial points for which the Birkhoff time averages of the function φ differ from its μ-space average by at least α. As the measure μ is a global SRB one, the set Kφ,α should have zero Lebesgue measure. The special ergodic theorem, whenever it holds, claims that, moreover, this set has a Hausdorff dimension less than the dimension of M. We prove that for Lipschitz maps, the special ergodic theorem follows from the dynamical large deviations principle. We also define and prove analogous result for flows. Applying the theorems of Young and of Araújo and Pacifico, we conclude that the special ergodic theorem holds for transitive hyperbolic attractors of C2-diffeomorphisms, as well as for some other known classes of maps (including the one of partially hyperbolic non-uniformly expanding maps) and flows.

A Hamilton-Jacobi theory for implicit differential systems

NASA Astrophysics Data System (ADS)

Esen, Oǧul; de León, Manuel; Sardón, Cristina

2018-02-01

In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, described in terms of Lagrangian submanifolds of TT*Q generated by Morse families. The implicit character implies the nonexistence of a Hamiltonian function describing the dynamics. This fact is here amended by a generating family of Morse functions which plays the role of a Hamiltonian. A Hamilton-Jacobi equation is obtained with the aid of this generating family of functions. To conclude, we apply our results to singular Lagrangians by employing the construction of special symplectic structures.

Haptics-based dynamic implicit solid modeling.

PubMed

Hua, Jing; Qin, Hong

2004-01-01

This paper systematically presents a novel, interactive solid modeling framework, Haptics-based Dynamic Implicit Solid Modeling, which is founded upon volumetric implicit functions and powerful physics-based modeling. In particular, we augment our modeling framework with a haptic mechanism in order to take advantage of additional realism associated with a 3D haptic interface. Our dynamic implicit solids are semi-algebraic sets of volumetric implicit functions and are governed by the principles of dynamics, hence responding to sculpting forces in a natural and predictable manner. In order to directly manipulate existing volumetric data sets as well as point clouds, we develop a hierarchical fitting algorithm to reconstruct and represent discrete data sets using our continuous implicit functions, which permit users to further design and edit those existing 3D models in real-time using a large variety of haptic and geometric toolkits, and visualize their interactive deformation at arbitrary resolution. The additional geometric and physical constraints afford more sophisticated control of the dynamic implicit solids. The versatility of our dynamic implicit modeling enables the user to easily modify both the geometry and the topology of modeled objects, while the inherent physical properties can offer an intuitive haptic interface for direct manipulation with force feedback.

Linear and quadratic static response functions and structure functions in Yukawa liquids.

PubMed

Magyar, Péter; Donkó, Zoltán; Kalman, Gabor J; Golden, Kenneth I

2014-08-01

We compute linear and quadratic static density response functions of three-dimensional Yukawa liquids by applying an external perturbation potential in molecular dynamics simulations. The response functions are also obtained from the equilibrium fluctuations (static structure factors) in the system via the fluctuation-dissipation theorems. The good agreement of the quadratic response functions, obtained in the two different ways, confirms the quadratic fluctuation-dissipation theorem. We also find that the three-point structure function may be factorizable into two-point structure functions, leading to a cluster representation of the equilibrium triplet correlation function.

The nature of declarative and nondeclarative knowledge for implicit and explicit learning.

PubMed

Kirkhart, M W

2001-10-01

Using traditional implicit and explicit artificial-grammar learning tasks, the author investigated the similarities and differences between the acquisition of declarative knowledge under implicit and explicit learning conditions and the functions of the declarative knowledge during testing. Results suggested that declarative knowledge was not predictive of or required for implicit learning but was related to consistency in implicit learning performance. In contrast, declarative knowledge was predictive of and required for explicit learning and was related to consistency in performance. For explicit learning, the declarative knowledge functioned as a guide for other behavior. In contrast, for implicit learning, the declarative knowledge did not serve as a guide for behavior but was instead a post hoc description of the most commonly seen stimuli.

A theorem about Hamiltonian systems.

PubMed

Case, K M

1984-09-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation.

Differentiability of correlations in realistic quantum mechanics

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

Cabrera, Alejandro; Faria, Edson de; Pujals, Enrique

2015-09-15

We prove a version of Bell’s theorem in which the locality assumption is weakened. We start by assuming theoretical quantum mechanics and weak forms of relativistic causality and of realism (essentially the fact that observable values are well defined independently of whether or not they are measured). Under these hypotheses, we show that only one of the correlation functions that can be formulated in the framework of the usual Bell theorem is unknown. We prove that this unknown function must be differentiable at certain angular configuration points that include the origin. We also prove that, if this correlation is assumedmore » to be twice differentiable at the origin, then we arrive at a version of Bell’s theorem. On the one hand, we are showing that any realistic theory of quantum mechanics which incorporates the kinematic aspects of relativity must lead to this type of rough correlation function that is once but not twice differentiable. On the other hand, this study brings us a single degree of differentiability away from a relativistic von Neumann no hidden variables theorem.« less

How Explicit and Implicit Test Instructions in an Implicit Learning Task Affect Performance

PubMed Central

Witt, Arnaud; Puspitawati, Ira; Vinter, Annie

2013-01-01

Typically developing children aged 5 to 8 years were exposed to artificial grammar learning. Following an implicit exposure phase, half of the participants received neutral instructions at test while the other half received instructions making a direct, explicit reference to the training phase. We first aimed to assess whether implicit learning operated in the two test conditions. We then evaluated the differential impact of age on learning performances as a function of test instructions. The results showed that performance did not vary as a function of age in the implicit instructions condition, while age effects emerged when explicit instructions were employed at test. However, performance was affected differently by age and the instructions given at test, depending on whether the implicit learning of short or long units was assessed. These results suggest that the claim that the implicit learning process is independent of age needs to be revised. PMID:23326409

Coincidence degree and periodic solutions of neutral equations

NASA Technical Reports Server (NTRS)

Hale, J. K.; Mawhin, J.

1973-01-01

The problem of existence of periodic solutions for some nonautonomous neutral functional differential equations is examined. It is an application of a basic theorem on the Fredholm alternative for periodic solutions of some linear neutral equations and of a generalized Leray-Schauder theory. Although proofs are simple, the results are nontrivial extensions to the neutral case of existence theorems for periodic solutions of functional differential equations.

A theorem about Hamiltonian systems

PubMed Central

Case, K. M.

1984-01-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation. PMID:16593515

Stochastic stability

NASA Technical Reports Server (NTRS)

Kushner, H. J.

1972-01-01

The field of stochastic stability is surveyed, with emphasis on the invariance theorems and their potential application to systems with randomly varying coefficients. Some of the basic ideas are reviewed, which underlie the stochastic Liapunov function approach to stochastic stability. The invariance theorems are discussed in detail.

Real World Cognitive Multi-Tasking and Problem Solving: A Large Scale Cognitive Architecture Simulation Through High Performance Computing-Project Casie

DTIC Science & Technology

2008-03-01

computational version of the CASIE architecture serves to demonstrate the functionality of our primary theories. However, implementation of several other...following facts. First, based on Theorem 3 and Theorem 5, the objective function is non -increasing under updating rule (6); second, by the criteria for...reassignment in updating rule (7), it is trivial to show that the objective function is non -increasing under updating rule (7). A Unified View to Graph

The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum

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

Alpay, Daniel, E-mail: dany@math.bgu.ac.il; Kimsey, David P., E-mail: dpkimsey@gmail.com; Colombo, Fabrizio, E-mail: fabrizio.colombo@polimi.it

In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of S-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and then using a transformation which maps a quaternionic unbounded normal operator to a quaternionic bounded normal operator. With this paper we complete the foundation of spectral analysis of quaternionic operators. The S-spectrum has been introduced to define the quaternionic functional calculus but it turns out to be the correct object also for the spectral theorem for quaternionic normal operators. The lack of a suitable notion ofmore » spectrum was a major obstruction to fully understand the spectral theorem for quaternionic normal operators. A prime motivation for studying the spectral theorem for quaternionic unbounded normal operators is given by the subclass of unbounded anti-self adjoint quaternionic operators which play a crucial role in the quaternionic quantum mechanics.« less

Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability

NASA Technical Reports Server (NTRS)

Haddad, Wassim M.; Bernstein, Dennis S.

1991-01-01

Lyapunov function proofs of sufficient conditions for asymptotic stability are given for feedback interconnections of bounded real and positive real transfer functions. Two cases are considered: (1) a proper bounded real (resp., positive real) transfer function with a bounded real (resp., positive real) time-varying memoryless nonlinearity; and (2) two strictly proper bounded real (resp., positive real) transfer functions. A similar treatment is given for the circle and Popov theorems. Application of these results to robust stability with time-varying bounded real, positive real, and sector-bounded uncertainty is discussed.

The type k universal portfolio generated by the f-divergence

NASA Astrophysics Data System (ADS)

Tan, Choon Peng; Seng, Kuang Kee

2017-11-01

The logarithm of the estimated next-day wealth return is approximated by k terms of its Taylor series. The resulting Type k universal portfolio generated by the f -divergence is obtained. An implicit form of the portfolio is also obtained by exploiting the mean-value theorem. An empirical study of the performance of the portfolio is focused on the Type 2 Helmbold universal portfolio. A few generalizations of the Helmbold universal portfolio have recently been studied, namely the reverse Helmbold and the parametric Helmbold portfolios. This new type of portfolio can be regarded a contribution to the inventory of Helmbold related universal portfolios. It is verified experimentally that an investor's wealth can be significantly increased by using the Type 2 Helmbold portfolio in investment.

Generalization of the Bogoliubov-Zubarev Theorem for Dynamic Pressure to the Case of Compressibility

NASA Astrophysics Data System (ADS)

Rudoi, Yu. G.

2018-01-01

We present the motivation, formulation, and modified proof of the Bogoliubov-Zubarev theorem connecting the pressure of a dynamical object with its energy within the framework of a classical description and obtain a generalization of this theorem to the case of dynamical compressibility. In both cases, we introduce the volume of the object into consideration using a singular addition to the Hamiltonian function of the physical object, which allows using the concept of the Bogoliubov quasiaverage explicitly already on a dynamical level of description. We also discuss the relation to the same result known as the Hellmann-Feynman theorem in the framework of the quantum description of a physical object.

Some constructions of biharmonic maps and Chen’s conjecture on biharmonic hypersurfaces

NASA Astrophysics Data System (ADS)

Ou, Ye-Lin

2012-04-01

We give several construction methods and use them to produce many examples of proper biharmonic maps including biharmonic tori of any dimension in Euclidean spheres (Theorem 2.2, Corollaries 2.3, 2.4 and 2.6), biharmonic maps between spheres (Theorem 2.9) and into spheres (Theorem 2.10) via orthogonal multiplications and eigenmaps. We also study biharmonic graphs of maps, derive the equation for a function whose graph is a biharmonic hypersurface in a Euclidean space, and give an equivalent formulation of Chen's conjecture on biharmonic hypersurfaces by using the biharmonic graph equation (Theorem 4.1) which paves a way for the analytic study of the conjecture.

One-range addition theorems for derivatives of Slater-type orbitals.

PubMed

Guseinov, Israfil

2004-06-01

Using addition theorems for STOs introduced by the author with the help of complete orthonormal sets of psi(alpha)-ETOs (Guseinov II (2003) J Mol Model 9:190-194), where alpha=1, 0, -1, -2, ..., a large number of one-range addition theorems for first and second derivatives of STOs are established. These addition theorems are especially useful for computation of multicenter-multielectron integrals over STOs that arise in the Hartree-Fock-Roothaan approximation and also in the Hylleraas function method, which play a significant role for the study of electronic structure and electron-nuclei interaction properties of atoms, molecules, and solids. The relationships obtained are valid for arbitrary quantum numbers, screening constants and location of STOs.

Out-of-time-order fluctuation-dissipation theorem

NASA Astrophysics Data System (ADS)

Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito

2018-01-01

We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n -partite OTOCs as well as in the form of generalized covariance.

Some theorems and properties of multi-dimensional fractional Laplace transforms

NASA Astrophysics Data System (ADS)

Ahmood, Wasan Ajeel; Kiliçman, Adem

2016-06-01

The aim of this work is to study theorems and properties for the one-dimensional fractional Laplace transform, generalize some properties for the one-dimensional fractional Lapalce transform to be valid for the multi-dimensional fractional Lapalce transform and is to give the definition of the multi-dimensional fractional Lapalce transform. This study includes: dedicate the one-dimensional fractional Laplace transform for functions of only one independent variable with some of important theorems and properties and develop of some properties for the one-dimensional fractional Laplace transform to multi-dimensional fractional Laplace transform. Also, we obtain a fractional Laplace inversion theorem after a short survey on fractional analysis based on the modified Riemann-Liouville derivative.

An environment-dependent semi-empirical tight binding model suitable for electron transport in bulk metals, metal alloys, metallic interfaces, and metallic nanostructures. I. Model and validation

NASA Astrophysics Data System (ADS)

Hegde, Ganesh; Povolotskyi, Michael; Kubis, Tillmann; Boykin, Timothy; Klimeck, Gerhard

2014-03-01

Semi-empirical Tight Binding (TB) is known to be a scalable and accurate atomistic representation for electron transport for realistically extended nano-scaled semiconductor devices that might contain millions of atoms. In this paper, an environment-aware and transferable TB model suitable for electronic structure and transport simulations in technologically relevant metals, metallic alloys, metal nanostructures, and metallic interface systems are described. Part I of this paper describes the development and validation of the new TB model. The new model incorporates intra-atomic diagonal and off-diagonal elements for implicit self-consistency and greater transferability across bonding environments. The dependence of the on-site energies on strain has been obtained by appealing to the Moments Theorem that links closed electron paths in the system to energy moments of angular momentum resolved local density of states obtained ab initio. The model matches self-consistent density functional theory electronic structure results for bulk face centered cubic metals with and without strain, metallic alloys, metallic interfaces, and metallic nanostructures with high accuracy and can be used in predictive electronic structure and transport problems in metallic systems at realistically extended length scales.

Casimir effect within D=3+1 Maxwell-Chern-Simons electrodynamics

NASA Astrophysics Data System (ADS)

Kharlanov, O. G.; Zhukovsky, V. Ch.

2010-01-01

Within the framework of the (3+1)-dimensional Lorentz-violating extended electrodynamics including the CPT-odd Chern-Simons term, we consider the electromagnetic field between two parallel perfectly conducting plates. We find the one-particle eigenstates of such a field, as well as the implicit expression for the photon energy spectrum. We also show that the tachyon-induced vacuum instability is negligible when the separation between the plates is sufficiently small though finite. In order to find the leading Chern-Simons correction to the vacuum energy, we renormalize and evaluate the sum over all one-particle eigenstate energies using the two different methods, the zeta function technique and the transformation of the discrete sum into a complex plane integral via the residue theorem. The resulting correction to the Casimir force, which is attractive and quadratic in the Chern-Simons term, disagrees with the one obtained in [M. Frank and I. Turan, Phys. Rev. DPRVDAQ1550-7998 74, 033016 (2006)10.1103/PhysRevD.74.033016], using the misinterpreted equations of motion. Compared with experimental data, our result places a constraint on the absolute value of the Chern-Simons term.

Existence of Corotating and Counter-Rotating Vortex Pairs for Active Scalar Equations

NASA Astrophysics Data System (ADS)

Hmidi, Taoufik; Mateu, Joan

2017-03-01

In this paper, we study the existence of corotating and counter-rotating pairs of simply connected patches for Euler equations and the {(SQG)_{α}} equations with {α in (0,1)}. From the numerical experiments implemented for Euler equations in Deem and Zabusky (Phys Rev Lett 40(13):859-862, 1978), Pierrehumbert (J Fluid Mech 99:129-144, 1980), Saffman and Szeto (Phys Fluids 23(12):2339-2342, 1980) it is conjectured the existence of a curve of steady vortex pairs passing through the point vortex pairs. There are some analytical proofs based on variational principle (Keady in J Aust Math Soc Ser B 26:487-502, 1985; Turkington in Nonlinear Anal Theory Methods Appl 9(4):351-369, 1985); however, they do not give enough information about the pairs, such as the uniqueness or the topological structure of each single vortex. We intend in this paper to give direct proofs confirming the numerical experiments and extend these results for the {(SQG)_{α}} equation when {α in (0,1)}. The proofs rely on the contour dynamics equations combined with a desingularization of the point vortex pairs and the application of the implicit function theorem.

Implicit and explicit false belief development in preschool children.

PubMed

Grosse Wiesmann, Charlotte; Friederici, Angela D; Singer, Tania; Steinbeis, Nikolaus

2017-09-01

The ability to represent the mental states of other agents is referred to as Theory of Mind (ToM). A developmental breakthrough in ToM consists of understanding that others can have false beliefs about the world. Recently, infants younger than 2 years of age have been shown to pass novel implicit false belief tasks. However, the processes underlying these tasks and their relation to later-developing explicit false belief understanding, as well as to other cognitive abilities, are not yet understood. Here, we study a battery of implicit and explicit false belief tasks in 3- and 4-year-old children, relating their performance to linguistic abilities and executive functions. The present data show a significant developmental change from failing explicit false belief tasks at 3 years of age to passing them at the age of 4, while both age groups pass implicit false belief tasks. This differential developmental trajectory is reflected by the finding that explicit and implicit false belief tasks do not correlate. Further, we demonstrate that explicit false belief tasks correlate with syntactic and executive functions, whereas implicit false belief tasks do not. The study thus indicates that the processes underlying implicit false belief tasks are different from later-developing explicit false belief understanding. Moreover, our results speak for a critical role of syntactic and executive functions for passing standard explicit false belief tasks in contrast to implicit tasks. © 2016 John Wiley & Sons Ltd.

A Meinardus Theorem with Multiple Singularities

NASA Astrophysics Data System (ADS)

Granovsky, Boris L.; Stark, Dudley

2012-09-01

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing (Granovsky et al., Adv. Appl. Math. 41:307-328, 2008), we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size n, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.

The detailed balance principle and the reciprocity theorem between photocarrier collection and dark carrier distribution in solar cells

NASA Astrophysics Data System (ADS)

Rau, Uwe; Brendel, Rolf

1998-12-01

It is shown that a recently described general relationship between the local collection efficiency of solar cells and the dark carrier concentration (reciprocity theorem) directly follows from the principle of detailed balance. We derive the relationship for situations where transport of charge carriers occurs between discrete states as well as for the situation where electronic transport is described in terms of continuous functions. Combining both situations allows to extend the range of applicability of the reciprocity theorem to all types of solar cells, including, e.g., metal-insulator-semiconductor-type, electrochemical solar cells, as well as the inclusion of the impurity photovoltaic effect. We generalize the theorem further to situations where the occupation probability of electronic states is governed by Fermi-Dirac statistics instead of Boltzmann statistics as underlying preceding work. In such a situation the reciprocity theorem is restricted to small departures from equilibrium.

Patients with Parkinson's disease learn to control complex systems-an indication for intact implicit cognitive skill learning.

PubMed

Witt, Karsten; Daniels, Christine; Daniel, Victoria; Schmitt-Eliassen, Julia; Volkmann, Jens; Deuschl, Günther

2006-01-01

Implicit memory and learning mechanisms are composed of multiple processes and systems. Previous studies demonstrated a basal ganglia involvement in purely cognitive tasks that form stimulus response habits by reinforcement learning such as implicit classification learning. We will test the basal ganglia influence on two cognitive implicit tasks previously described by Berry and Broadbent, the sugar production task and the personal interaction task. Furthermore, we will investigate the relationship between certain aspects of an executive dysfunction and implicit learning. To this end, we have tested 22 Parkinsonian patients and 22 age-matched controls on two implicit cognitive tasks, in which participants learned to control a complex system. They interacted with the system by choosing an input value and obtaining an output that was related in a complex manner to the input. The objective was to reach and maintain a specific target value across trials (dynamic system learning). The two tasks followed the same underlying complex rule but had different surface appearances. Subsequently, participants performed an executive test battery including the Stroop test, verbal fluency and the Wisconsin card sorting test (WCST). The results demonstrate intact implicit learning in patients, despite an executive dysfunction in the Parkinsonian group. They lead to the conclusion that the basal ganglia system affected in Parkinson's disease does not contribute to the implicit acquisition of a new cognitive skill. Furthermore, the Parkinsonian patients were able to reach a specific goal in an implicit learning context despite impaired goal directed behaviour in the WCST, a classic test of executive functions. These results demonstrate a functional independence of implicit cognitive skill learning and certain aspects of executive functions.

Aging Wiener-Khinchin theorem and critical exponents of 1/f^{β} noise.

PubMed

Leibovich, N; Dechant, A; Lutz, E; Barkai, E

2016-11-01

The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum 〈S_{t_{m}}(ω)〉 where t_{m} is the measurement time. For processes with an aging autocorrelation function of the form 〈I(t)I(t+τ)〉=t^{Υ}ϕ_{EA}(τ/t), where ϕ_{EA}(x) is a nonanalytic function when x is small, we find aging 1/f^{β} noise. Aging 1/f^{β} noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of 1/f^{β} noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.

A Guided Tour of Mathematical Methods

NASA Astrophysics Data System (ADS)

Snieder, Roel

2009-04-01

1. Introduction; 2. Dimensional analysis; 3. Power series; 4. Spherical and cylindrical co-ordinates; 5. The gradient; 6. The divergence of a vector field; 7. The curl of a vector field; 8. The theorem of Gauss; 9. The theorem of Stokes; 10. The Laplacian; 11. Conservation laws; 12. Scale analysis; 13. Linear algebra; 14. The Dirac delta function; 15. Fourier analysis; 16. Analytic functions; 17. Complex integration; 18. Green's functions: principles; 19. Green's functions: examples; 20. Normal modes; 21. Potential theory; 22. Cartesian tensors; 23. Perturbation theory; 24. Asymptotic evaluation of integrals; 25. Variational calculus; 26. Epilogue, on power and knowledge; References.

Quantum calculus of classical vortex images, integrable models and quantum states

NASA Astrophysics Data System (ADS)

Pashaev, Oktay K.

2016-10-01

From two circle theorem described in terms of q-periodic functions, in the limit q→1 we have derived the strip theorem and the stream function for N vortex problem. For regular N-vortex polygon we find compact expression for the velocity of uniform rotation and show that it represents a nonlinear oscillator. We describe q-dispersive extensions of the linear and nonlinear Schrodinger equations, as well as the q-semiclassical expansions in terms of Bernoulli and Euler polynomials. Different kind of q-analytic functions are introduced, including the pq-analytic and the golden analytic functions.

Geometric Demonstration of the Fundamental Theorems of the Calculus

ERIC Educational Resources Information Center

Sauerheber, Richard D.

2010-01-01

After the monumental discovery of the fundamental theorems of the calculus nearly 350 years ago, it became possible to answer extremely complex questions regarding the natural world. Here, a straightforward yet profound demonstration, employing geometrically symmetric functions, describes the validity of the general power rules for integration and…

Noether's Theorem and its Inverse of Birkhoffian System in Event Space Based on Herglotz Variational Problem

NASA Astrophysics Data System (ADS)

Tian, X.; Zhang, Y.

2018-03-01

Herglotz variational principle, in which the functional is defined by a differential equation, generalizes the classical ones defining the functional by an integral. The principle gives a variational principle description of nonconservative systems even when the Lagrangian is independent of time. This paper focuses on studying the Noether's theorem and its inverse of a Birkhoffian system in event space based on the Herglotz variational problem. Firstly, according to the Herglotz variational principle of a Birkhoffian system, the principle of a Birkhoffian system in event space is established. Secondly, its parametric equations and two basic formulae for the variation of Pfaff-Herglotz action of a Birkhoffian system in event space are obtained. Furthermore, the definition and criteria of Noether symmetry of the Birkhoffian system in event space based on the Herglotz variational problem are given. Then, according to the relationship between the Noether symmetry and conserved quantity, the Noether's theorem is derived. Under classical conditions, Noether's theorem of a Birkhoffian system in event space based on the Herglotz variational problem reduces to the classical ones. In addition, Noether's inverse theorem of the Birkhoffian system in event space based on the Herglotz variational problem is also obtained. In the end of the paper, an example is given to illustrate the application of the results.

Direct and inverse theorems on approximation by root functions of a regular boundary-value problem

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

Radzievskii, G V

2006-08-31

One considers the spectral problem x{sup (n)}+ Fx={lambda}x with boundary conditions U{sub j}(x)=0, j=1,...,n, for functions x on [0,1]. It is assumed that F is a linear bounded operator from the Hoelder space C{sup {gamma}}, {gamma} element of [0,n-1), into L{sub 1} and the U{sub j} are bounded linear functionals on C{sup k{sub j}} with k{sub j} element of {l_brace}0,...,n- 1{r_brace}. Let P{sub {zeta}} be the linear span of the root functions of the problem x{sup (n)}+ Fx={lambda}x, U{sub j}(x)=0, j=1,...,n, corresponding to the eigenvalues {lambda}{sub k} with |{lambda}{sub k}|<{zeta}{sup n}, and let E{sub {zeta}}(f){sub W{sub p}{sup l}}:=inf{l_brace}||f-g||{sub W{sub p}{supmore » l}}:g element of P{sub {zeta}}{r_brace}. An estimate of E{sub {zeta}}(f){sub W{sub p}{sup l}} is obtained in terms of the K-functional K({zeta}{sup -m},f;W{sub p}{sup l},W{sub p,U}{sup l+m}):= inf{l_brace}||f-x||{sub W{sub p}{sup l}}+{zeta}{sup -m}||x||{sub W{sub p}{sup l}{sup +}{sup m}}:x element of W{sub p}{sup l+m}, U{sub j}(x)=0 for k{sub j}

The OXTR gene, implicit learning and social processing: Does empathy evolve from perceptual skills for details?

PubMed

Melchers, Martin; Montag, Christian; Markett, Sebastian; Niazy, Nawael; Groß-Bölting, Johanna; Zimmermann, Jelena; Reuter, Martin

2017-06-30

Oxytocin is an important messenger in the brain that has been linked to a variety of social functions in pharmacological studies. Besides, functional genetic variations on the oxytocin receptor gene have been repeatedly associated with social processing and functioning. Despite this knowledge, there are very few studies investigating the mechanisms that may explain the link between oxytocin and social functions. In the endeavor to fill this gap in the literature, the current study searches for associations between the prominent rs2268498 polymorphism on the oxytocin receptor gene and participants' ability to perceive and store implicit social information, which is a fundamental function in social information processing. N=121 healthy participants were experimentally tested with an implicit learning paradigm, answered questionnaires assessing empathy and autistic traits, and were genotyped for the rs2268498 polymorphism. T-allele carriers (TT and TC genotypes) exhibited significantly better implicit learning performance than carriers of the CC-genotype, and learning performance was positively associated with self-reported empathy and negatively with self-reported autistic traits. Results indicate that differences in implicit perception and storing of environmental details while watching social interactions could be an important mechanism to explain the association between differences in endogenous oxytocin activity and social functioning. Copyright © 2017 Elsevier B.V. All rights reserved.

Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation

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

Mundt, Michael; Kuemmel, Stephan; Leeuwen, Robert van

2007-05-15

We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the zero-force theorem. By analyzing the time-dependent dipole moment of Na{sub 5} and Na{sub 9}{sup +}, we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the zero-force theorem and the generalized-translation invariance of the potential, are discussed.

Effects of Attention and Levels of Processing on Explicit and Implicit Memory Function with Interesting and Uninteresting Tasks in University Students

NASA Astrophysics Data System (ADS)

Mahdavian, Alireza; Kormi-Nouri, Reza

This study aims to investigate the effect of attention and levels of processing on memory function and recalling words in two situations when students are interested in the subject and when they are not. This is an experimental study of 160 students conducted individually using a computer software. Results reveal focused attention, interest in the subject and deep processing caused the explicit memory to be at its highest level of functionality. On the contrary, shallow processing, divided attention and lack of interest in the subject plunged memory function into its lowest levels. Variables have different effects on attention, explicit and implicit memory. That is, interesting tasks with focused attention and deep processing have the highest effect on explicit memory in order. Also, interesting tasks, focused attention, respectively affect implicit memory. But level of processing does not affect implicit memory significantly.

KECSA-Movable Type Implicit Solvation Model (KMTISM)

PubMed Central

2015-01-01

Computation of the solvation free energy for chemical and biological processes has long been of significant interest. The key challenges to effective solvation modeling center on the choice of potential function and configurational sampling. Herein, an energy sampling approach termed the “Movable Type” (MT) method, and a statistical energy function for solvation modeling, “Knowledge-based and Empirical Combined Scoring Algorithm” (KECSA) are developed and utilized to create an implicit solvation model: KECSA-Movable Type Implicit Solvation Model (KMTISM) suitable for the study of chemical and biological systems. KMTISM is an implicit solvation model, but the MT method performs energy sampling at the atom pairwise level. For a specific molecular system, the MT method collects energies from prebuilt databases for the requisite atom pairs at all relevant distance ranges, which by its very construction encodes all possible molecular configurations simultaneously. Unlike traditional statistical energy functions, KECSA converts structural statistical information into categorized atom pairwise interaction energies as a function of the radial distance instead of a mean force energy function. Within the implicit solvent model approximation, aqueous solvation free energies are then obtained from the NVT ensemble partition function generated by the MT method. Validation is performed against several subsets selected from the Minnesota Solvation Database v2012. Results are compared with several solvation free energy calculation methods, including a one-to-one comparison against two commonly used classical implicit solvation models: MM-GBSA and MM-PBSA. Comparison against a quantum mechanics based polarizable continuum model is also discussed (Cramer and Truhlar’s Solvation Model 12). PMID:25691832

New strings for old Veneziano amplitudes. II. Group-theoretic treatment

NASA Astrophysics Data System (ADS)

Kholodenko, A. L.

2006-09-01

In this part of our four parts work we use theory of polynomial invariants of finite pseudo-reflection groups in order to reconstruct both the Veneziano and Veneziano-like (tachyon-free) amplitudes and the generating function reproducing these amplitudes. We demonstrate that such generating function and amplitudes associated with it can be recovered with help of finite dimensional exactly solvableN=2 supersymmetric quantum mechanical model known earlier from works of Witten, Stone and others. Using the Lefschetz isomorphism theorem we replace traditional supersymmetric calculations by the group-theoretic thus solving the Veneziano model exactly using standard methods of representation theory. Mathematical correctness of our arguments relies on important theorems by Shepard and Todd, Serre and Solomon proven respectively in the early 50s and 60s and documented in the monograph by Bourbaki. Based on these theorems, we explain why the developed formalism leaves all known results of conformal field theories unchanged. We also explain why these theorems impose stringent requirements connecting analytical properties of scattering amplitudes with symmetries of space-time in which such amplitudes act.

Evolution families of conformal mappings with fixed points and the Löwner-Kufarev equation

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

Goryainov, V V

2015-01-31

The paper is concerned with evolution families of conformal mappings of the unit disc to itself that fix an interior point and a boundary point. Conditions are obtained for the evolution families to be differentiable, and an existence and uniqueness theorem for an evolution equation is proved. A convergence theorem is established which describes the topology of locally uniform convergence of evolution families in terms of infinitesimal generating functions. The main result in this paper is the embedding theorem which shows that any conformal mapping of the unit disc to itself with two fixed points can be embedded into a differentiable evolution familymore » of such mappings. This result extends the range of the parametric method in the theory of univalent functions. In this way the problem of the mutual change of the derivative at an interior point and the angular derivative at a fixed point on the boundary is solved for a class of mappings of the unit disc to itself. In particular, the rotation theorem is established for this class of mappings. Bibliography: 27 titles.« less

Quantum regression theorem and non-Markovianity of quantum dynamics

NASA Astrophysics Data System (ADS)

Guarnieri, Giacomo; Smirne, Andrea; Vacchini, Bassano

2014-08-01

We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behavior in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behavior of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two-point correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation.

Factorization and resummation of Higgs boson differential distributions in soft-collinear effective theory

NASA Astrophysics Data System (ADS)

Mantry, Sonny; Petriello, Frank

2010-05-01

We derive a factorization theorem for the Higgs boson transverse momentum (pT) and rapidity (Y) distributions at hadron colliders, using the soft-collinear effective theory (SCET), for mh≫pT≫ΛQCD, where mh denotes the Higgs mass. In addition to the factorization of the various scales involved, the perturbative physics at the pT scale is further factorized into two collinear impact-parameter beam functions (IBFs) and an inverse soft function (ISF). These newly defined functions are of a universal nature for the study of differential distributions at hadron colliders. The additional factorization of the pT-scale physics simplifies the implementation of higher order radiative corrections in αs(pT). We derive formulas for factorization in both momentum and impact parameter space and discuss the relationship between them. Large logarithms of the relevant scales in the problem are summed using the renormalization group equations of the effective theories. Power corrections to the factorization theorem in pT/mh and ΛQCD/pT can be systematically derived. We perform multiple consistency checks on our factorization theorem including a comparison with known fixed-order QCD results. We compare the SCET factorization theorem with the Collins-Soper-Sterman approach to low-pT resummation.

Orientational Order on Surfaces: The Coupling of Topology, Geometry, and Dynamics

NASA Astrophysics Data System (ADS)

Nestler, M.; Nitschke, I.; Praetorius, S.; Voigt, A.

2018-02-01

We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient flow equation of a weak surface Frank-Oseen energy. The energy is composed of intrinsic and extrinsic contributions, as well as a penalization term to enforce the unity of the vector field. Four different numerical discretizations, namely a discrete exterior calculus approach, a method based on vector spherical harmonics, a surface finite element method, and an approach utilizing an implicit surface description, the diffuse interface method, are described and compared with each other for surfaces with Euler characteristic 2. We demonstrate the influence of geometric properties on realizations of the Poincaré-Hopf theorem and show examples where the energy is decreased by introducing additional orientational defects.

A Guided Tour of Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Snieder, Roel; van Wijk, Kasper

2015-05-01

1. Introduction; 2. Dimensional analysis; 3. Power series; 4. Spherical and cylindrical coordinates; 5. Gradient; 6. Divergence of a vector field; 7. Curl of a vector field; 8. Theorem of Gauss; 9. Theorem of Stokes; 10. The Laplacian; 11. Scale analysis; 12. Linear algebra; 13. Dirac delta function; 14. Fourier analysis; 15. Analytic functions; 16. Complex integration; 17. Green's functions: principles; 18. Green's functions: examples; 19. Normal modes; 20. Potential-field theory; 21. Probability and statistics; 22. Inverse problems; 23. Perturbation theory; 24. Asymptotic evaluation of integrals; 25. Conservation laws; 26. Cartesian tensors; 27. Variational calculus; 28. Epilogue on power and knowledge.

How Good Am I? Implicit and Explicit Self-Esteem as a Function of Perceived Parenting Styles Among Children With ADHD.

PubMed

Kurman, Jenny; Rothschild-Yakar, Lily; Angel, Ruth; Katz, Miri

2015-02-11

To investigate implicit and explicit self-esteem and academic self-evaluation among children with ADHD as a function of parenting styles, namely, authoritarian, authoritative and permissive parenting. Participants included 43 children with ADHD and 35 non-ADHD controls who filled out self-concept and perceived parenting style questionnaires. They also took an Implicit Association Test (IAT) that measured unacknowledged self-esteem. Lower self-esteem was found among children with ADHD than among controls, with stronger effect on the implicit level. Perceived authoritarian parenting was related to lower implicit self-esteem among children with ADHD. Higher self-esteem was found in the authoritative than in the permissive parenting groups in the non-ADHD control group but not among children with ADHD. The role of parental support versus authoritarian parenting in terms of implicit self-esteem points to the importance of promoting responsiveness strategies among parents in the treatment of children with ADHD. © 2015 SAGE Publications.

Morera-type theorems in the hyperbolic disc

NASA Astrophysics Data System (ADS)

Volchkov, V. V.; Volchkov, V. V.

2018-02-01

Let G be the group of conformal automorphisms of the unit disc {D}=\\{z\\in{C}\\colon \\vert z\\vert<1\\}. We study the problem of the holomorphicity of functions f on {D} satisfying the equation where γ\\varrho=\\{z\\in{C}\\colon \\vert z\\vert=\\varrho\\} and ρ\\in(0,1) is fixed. We find exact conditions for holomorphicity in terms of the boundary behaviour of such functions. A by-product of our work is a new proof of the Berenstein-Pascuas two-radii theorem.

Logical errors on proving theorem

NASA Astrophysics Data System (ADS)

Sari, C. K.; Waluyo, M.; Ainur, C. M.; Darmaningsih, E. N.

2018-01-01

In tertiary level, students of mathematics education department attend some abstract courses, such as Introduction to Real Analysis which needs an ability to prove mathematical statements almost all the time. In fact, many students have not mastered this ability appropriately. In their Introduction to Real Analysis tests, even though they completed their proof of theorems, they achieved an unsatisfactory score. They thought that they succeeded, but their proof was not valid. In this study, a qualitative research was conducted to describe logical errors that students made in proving the theorem of cluster point. The theorem was given to 54 students. Misconceptions on understanding the definitions seem to occur within cluster point, limit of function, and limit of sequences. The habit of using routine symbol might cause these misconceptions. Suggestions to deal with this condition are described as well.

On the analogues of Szegő's theorem for ergodic operators

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

Kirsch, W; Pastur, L A

2015-01-31

Szegő's theorem on the asymptotic behaviour of the determinants of large Toeplitz matrices is generalized to the class of ergodic operators. The generalization is formulated in terms of a triple consisting of an ergodic operator and two functions, the symbol and the test function. It is shown that in the case of the one-dimensional discrete Schrödinger operator with random ergodic or quasiperiodic potential and various choices of the symbol and the test function this generalization leads to asymptotic formulae which have no analogues in the situation of Toeplitz operators. Bibliography: 22 titles.

Does the Coase theorem hold in real markets? An application to the negotiations between waterworks and farmers in Denmark.

PubMed

Abildtrup, Jens; Jensen, Frank; Dubgaard, Alex

2012-01-01

The Coase theorem depends on a number of assumptions, among others, perfect information about each other's payoff function, maximising behaviour and zero transaction costs. An important question is whether the Coase theorem holds for real market transactions when these assumptions are violated. This is the question examined in this paper. We consider the results of Danish waterworks' attempts to establish voluntary cultivation agreements with Danish farmers. A survey of these negotiations shows that the Coase theorem is not robust in the presence of imperfect information, non-maximising behaviour and transaction costs. Thus, negotiations between Danish waterworks and farmers may not be a suitable mechanism to achieve efficiency in the protection of groundwater quality due to violations of the assumptions of the Coase theorem. The use of standard schemes or government intervention (e.g. expropriation) may, under some conditions, be a more effective and cost efficient approach for the protection of vulnerable groundwater resources in Denmark. Copyright © 2011 Elsevier Ltd. All rights reserved.

A Formally-Verified Decision Procedure for Univariate Polynomial Computation Based on Sturm's Theorem

NASA Technical Reports Server (NTRS)

Narkawicz, Anthony J.; Munoz, Cesar A.

2014-01-01

Sturm's Theorem is a well-known result in real algebraic geometry that provides a function that computes the number of roots of a univariate polynomial in a semiopen interval. This paper presents a formalization of this theorem in the PVS theorem prover, as well as a decision procedure that checks whether a polynomial is always positive, nonnegative, nonzero, negative, or nonpositive on any input interval. The soundness and completeness of the decision procedure is proven in PVS. The procedure and its correctness properties enable the implementation of a PVS strategy for automatically proving existential and universal univariate polynomial inequalities. Since the decision procedure is formally verified in PVS, the soundness of the strategy depends solely on the internal logic of PVS rather than on an external oracle. The procedure itself uses a combination of Sturm's Theorem, an interval bisection procedure, and the fact that a polynomial with exactly one root in a bounded interval is always nonnegative on that interval if and only if it is nonnegative at both endpoints.

Theoretical and Empirical Studies on Using Program Mutation to Test the Functional Correctness of Programs.

DTIC Science & Technology

1980-02-01

implemented to test ANSI FORTRAN set D3. Using theorem 6 we then have programs. In building real testing tools for Theorem 18 : The recursion constructors...constants, scalar in theorems 10, 15, 16, and 18 , then Q must be variables, and array references) times the number equivalent to P. of unique data...for j,,rd1s longer thlan a fixed .1; 0. erot 2., .12.’Ie 1). Ullman2. li21122 arnd isolates and plrints each telegram along hI 2 .. 222.2.J~12.2.1 It

Sanov and central limit theorems for output statistics of quantum Markov chains

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

Horssen, Merlijn van, E-mail: merlijn.vanhorssen@nottingham.ac.uk; Guţă, Mădălin, E-mail: madalin.guta@nottingham.ac.uk

2015-02-15

In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Suchmore » higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not.« less

Understanding band gaps of solids in generalized Kohn-Sham theory.

PubMed

Perdew, John P; Yang, Weitao; Burke, Kieron; Yang, Zenghui; Gross, Eberhard K U; Scheffler, Matthias; Scuseria, Gustavo E; Henderson, Thomas M; Zhang, Igor Ying; Ruzsinszky, Adrienn; Peng, Haowei; Sun, Jianwei; Trushin, Egor; Görling, Andreas

2017-03-14

The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. However, the gap in the band structure of the exact multiplicative Kohn-Sham (KS) potential substantially underestimates the fundamental gap, a major limitation of KS density-functional theory. Here, we give a simple proof of a theorem: In generalized KS theory (GKS), the band gap of an extended system equals the fundamental gap for the approximate functional if the GKS potential operator is continuous and the density change is delocalized when an electron or hole is added. Our theorem explains how GKS band gaps from metageneralized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential. The theorem also follows from earlier work. The band edges in the GKS one-electron spectrum are also related to measurable energies. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations.

Understanding band gaps of solids in generalized Kohn–Sham theory

PubMed Central

Perdew, John P.; Yang, Weitao; Burke, Kieron; Yang, Zenghui; Gross, Eberhard K. U.; Scheffler, Matthias; Scuseria, Gustavo E.; Henderson, Thomas M.; Zhang, Igor Ying; Ruzsinszky, Adrienn; Peng, Haowei; Sun, Jianwei; Trushin, Egor; Görling, Andreas

2017-01-01

The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. However, the gap in the band structure of the exact multiplicative Kohn–Sham (KS) potential substantially underestimates the fundamental gap, a major limitation of KS density-functional theory. Here, we give a simple proof of a theorem: In generalized KS theory (GKS), the band gap of an extended system equals the fundamental gap for the approximate functional if the GKS potential operator is continuous and the density change is delocalized when an electron or hole is added. Our theorem explains how GKS band gaps from metageneralized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential. The theorem also follows from earlier work. The band edges in the GKS one-electron spectrum are also related to measurable energies. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations. PMID:28265085

Analyzing Mathematics Textbooks through a Constructive-Empirical Perspective on Abstraction: The Case of Pythagoras' Theorem

ERIC Educational Resources Information Center

Yang, Kai-Lin

2016-01-01

This study aims at analyzing how Pythagoras' theorem is handled in three versions of Taiwanese textbooks using a conceptual framework of a constructive-empirical perspective on abstraction, which comprises three key attributes: the generality of the object, the connectivity of the subject and the functionality of diagrams as the focused semiotic…

A Complete Set for the Maass Laplacians on the Pseudosphere

NASA Astrophysics Data System (ADS)

Oshima, K.

1989-02-01

We obtain a completeness relation from eigenfunctions of the Maass laplacians in terms of the pseudospherical polar coordinates. We derive addition theorems of ``generalized'' associated Legendre functions. With the help of the addition theorems, we get a simple path integral picture for a charged particle on the Poincaré upper half plane with a constant magnetic field.

Learning stage-dependent effect of M1 disruption on value-based motor decisions.

PubMed

Derosiere, Gerard; Vassiliadis, Pierre; Demaret, Sophie; Zénon, Alexandre; Duque, Julie

2017-11-15

The present study aimed at characterizing the impact of M1 disruption on the implementation of implicit value information in motor decisions, at both early stages (during reinforcement learning) and late stages (after consolidation) of action value encoding. Fifty subjects performed, over three consecutive days, a task that required them to select between two finger responses according to the color (instruction) and to the shape (implicit, undisclosed rule) of an imperative signal: considering the implicit rule in addition to the instruction allowed subjects to earn more money. We investigated the functional contribution of M1 to the implementation of the implicit rule in subjects' motor decisions. Continuous theta burst stimulation (cTBS) was applied over M1 either on Day 1 or on Day 3, producing a temporary lesion either during reinforcement learning (cTBS Learning group) or after consolidation of the implicit rule, during decision-making (cTBS Decision group), respectively. Interestingly, disrupting M1 activity on Day 1 improved the reliance on the implicit rule, plausibly because M1 cTBS increased dopamine release in the putamen in an indirect way. This finding corroborates the view that cTBS may affect activity in unstimulated areas, such as the basal ganglia. Notably, this effect was short-lasting; it did not persist overnight, suggesting that the functional integrity of M1 during learning is a prerequisite for the consolidation of implicit value information to occur. Besides, cTBS over M1 did not impact the use of the implicit rule when applied on Day 3, although it did so when applied on Day 2 in a recent study where the reliance on the implicit rule declined following cTBS (Derosiere et al., 2017). Overall, these findings indicate that the human M1 is functionally involved in the consolidation and implementation of implicit value information underlying motor decisions. However, M1 contribution seems to vanish as subjects become more experienced in using the implicit value information to make their motor decisions. Copyright © 2017 Elsevier Inc. All rights reserved.

Face puzzle—two new video-based tasks for measuring explicit and implicit aspects of facial emotion recognition

PubMed Central

Kliemann, Dorit; Rosenblau, Gabriela; Bölte, Sven; Heekeren, Hauke R.; Dziobek, Isabel

2013-01-01

Recognizing others' emotional states is crucial for effective social interaction. While most facial emotion recognition tasks use explicit prompts that trigger consciously controlled processing, emotional faces are almost exclusively processed implicitly in real life. Recent attempts in social cognition suggest a dual process perspective, whereby explicit and implicit processes largely operate independently. However, due to differences in methodology the direct comparison of implicit and explicit social cognition has remained a challenge. Here, we introduce a new tool to comparably measure implicit and explicit processing aspects comprising basic and complex emotions in facial expressions. We developed two video-based tasks with similar answer formats to assess performance in respective facial emotion recognition processes: Face Puzzle, implicit and explicit. To assess the tasks' sensitivity to atypical social cognition and to infer interrelationship patterns between explicit and implicit processes in typical and atypical development, we included healthy adults (NT, n = 24) and adults with autism spectrum disorder (ASD, n = 24). Item analyses yielded good reliability of the new tasks. Group-specific results indicated sensitivity to subtle social impairments in high-functioning ASD. Correlation analyses with established implicit and explicit socio-cognitive measures were further in favor of the tasks' external validity. Between group comparisons provide first hints of differential relations between implicit and explicit aspects of facial emotion recognition processes in healthy compared to ASD participants. In addition, an increased magnitude of between group differences in the implicit task was found for a speed-accuracy composite measure. The new Face Puzzle tool thus provides two new tasks to separately assess explicit and implicit social functioning, for instance, to measure subtle impairments as well as potential improvements due to social cognitive interventions. PMID:23805122

Brain response to masked and unmasked facial emotions as a function of implicit and explicit personality self-concept of extraversion.

PubMed

Suslow, Thomas; Kugel, Harald; Lindner, Christian; Dannlowski, Udo; Egloff, Boris

2017-01-06

Extraversion-introversion is a personality dimension referring to individual differences in social behavior. In the past, neurobiological research on extraversion was almost entirely based upon questionnaires which inform about the explicit self-concept. Today, indirect measures are available that tap into the implicit self-concept of extraversion which is assumed to result from automatic processing functions. In our study, brain activation while viewing facial expression of affiliation relevant (i.e., happiness, and disgust) and irrelevant (i.e., fear) emotions was examined as a function of the implicit and explicit self-concept of extraversion and processing mode (automatic vs. controlled). 40 healthy volunteers watched blocks of masked and unmasked emotional faces while undergoing functional magnetic resonance imaging. The Implicit Association Test and the NEO Five-Factor Inventory were applied as implicit and explicit measures of extraversion which were uncorrelated in our sample. Implicit extraversion was found to be positively associated with neural response to masked happy faces in the thalamus and temporo-parietal regions and to masked disgust faces in cerebellar areas. Moreover, it was positively correlated with brain response to unmasked disgust faces in the amygdala and cortical areas. Explicit extraversion was not related to brain response to facial emotions when controlling trait anxiety. The implicit compared to the explicit self-concept of extraversion seems to be more strongly associated with brain activation not only during automatic but also during controlled processing of affiliation relevant facial emotions. Enhanced neural response to facial disgust could reflect high sensitivity to signals of interpersonal rejection in extraverts (i.e., individuals with affiliative tendencies). Copyright © 2016 IBRO. Published by Elsevier Ltd. All rights reserved.

Generalization of Jacobi's Decomposition Theorem to the Rotation and Translation of a Solid in a Fluid.

NASA Astrophysics Data System (ADS)

Chiang, Rong-Chang

Jacobi found that the rotation of a symmetrical heavy top about a fixed point is composed of the two torque -free rotations of two triaxial bodies about their centers of mass. His discovery rests on the fact that the orthogonal matrix which represents the rotation of a symmetrical heavy top is decomposed into a product of two orthogonal matrices, each of which represents the torque-free rotations of two triaxial bodies. This theorem is generalized to the Kirchhoff's case of the rotation and translation of a symmetrical solid in a fluid. This theorem requires the explicit computation, by means of theta functions, of the nine direction cosines between the rotating body axes and the fixed space axes. The addition theorem of theta functions makes it possible to decompose the rotational matrix into a product of similar matrices. This basic idea of utilizing the addition theorem is simple but the carry-through of the computation is quite involved and the full proof turns out to be a lengthy process of computing rather long and complex expressions. For the translational motion we give a new treatment. The position of the center of mass as a function of the time is found by a direct evaluation of the elliptic integral by means of a new theta interpretation of Legendre's reduction formula of the elliptic integral. For the complete solution of the problem we have added further the study of the physical aspects of the motion. Based on a complete examination of the all possible manifolds of the steady helical cases it is possible to obtain a full qualitative description of the motion. Many numerical examples and graphs are given to illustrate the rotation and translation of the solid in a fluid.

Task-related functional connectivity of the caudate mediates the association between trait mindfulness and implicit learning in older adults.

PubMed

Stillman, Chelsea M; You, Xiaozhen; Seaman, Kendra L; Vaidya, Chandan J; Howard, James H; Howard, Darlene V

2016-08-01

Accumulating evidence shows a positive relationship between mindfulness and explicit cognitive functioning, i.e., that which occurs with conscious intent and awareness. However, recent evidence suggests that there may be a negative relationship between mindfulness and implicit types of learning, or those that occur without conscious awareness or intent. Here we examined the neural mechanisms underlying the recently reported negative relationship between dispositional mindfulness and implicit probabilistic sequence learning in both younger and older adults. We tested the hypothesis that the relationship is mediated by communication, or functional connectivity, of brain regions once traditionally considered to be central to dissociable learning systems: the caudate, medial temporal lobe (MTL), and prefrontal cortex (PFC). We first replicated the negative relationship between mindfulness and implicit learning in a sample of healthy older adults (60-90 years old) who completed three event-related runs of an implicit sequence learning task. Then, using a seed-based connectivity approach, we identified task-related connectivity associated with individual differences in both learning and mindfulness. The main finding was that caudate-MTL connectivity (bilaterally) was positively correlated with learning and negatively correlated with mindfulness. Further, the strength of task-related connectivity between these regions mediated the negative relationship between mindfulness and learning. This pattern of results was limited to the older adults. Thus, at least in healthy older adults, the functional communication between two interactive learning-relevant systems can account for the relationship between mindfulness and implicit probabilistic sequence learning.

Diminished Neural Adaptation during Implicit Learning in Autism

PubMed Central

Schipul, Sarah E.; Just, Marcel Adam

2015-01-01

Neuroimaging studies have shown evidence of disrupted neural adaptation during learning in individuals with autism spectrum disorder (ASD) in several types of tasks, potentially stemming from frontal-posterior cortical underconnectivity (Schipul et al., 2012). The aim of the current study was to examine neural adaptations in an implicit learning task that entails participation of frontal and posterior regions. Sixteen high-functioning adults with ASD and sixteen neurotypical control participants were trained on and performed an implicit dot pattern prototype learning task in a functional magnetic resonance imaging (fMRI) session. During the preliminary exposure to the type of implicit prototype learning task later to be used in the scanner, the ASD participants took longer than the neurotypical group to learn the task, demonstrating altered implicit learning in ASD. After equating task structure learning, the two groups’ brain activation differed during their learning of a new prototype in the subsequent scanning session. The main findings indicated that neural adaptations in a distributed task network were reduced in the ASD group, relative to the neurotypical group, and were related to ASD symptom severity. Functional connectivity was reduced and did not change as much during learning for the ASD group, and was related to ASD symptom severity. These findings suggest that individuals with ASD show altered neural adaptations during learning, as seen in both activation and functional connectivity measures. This finding suggests why many real-world implicit learning situations may pose special challenges for ASD. PMID:26484826

Absolute Equilibrium Entropy

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1997-01-01

The entropy associated with absolute equilibrium ensemble theories of ideal, homogeneous, fluid and magneto-fluid turbulence is discussed and the three-dimensional fluid case is examined in detail. A sigma-function is defined, whose minimum value with respect to global parameters is the entropy. A comparison is made between the use of global functions sigma and phase functions H (associated with the development of various H-theorems of ideal turbulence). It is shown that the two approaches are complimentary though conceptually different: H-theorems show that an isolated system tends to equilibrium while sigma-functions allow the demonstration that entropy never decreases when two previously isolated systems are combined. This provides a more complete picture of entropy in the statistical mechanics of ideal fluids.

Behavioral measures of implicit theory of mind in adults with high functioning autism.

PubMed

Deschrijver, Eliane; Bardi, Lara; Wiersema, Jan R; Brass, Marcel

2016-01-01

Theory of mind (ToM) research has shown that adults with high functioning autism (HFA) demonstrate typical performance on tasks that require explicit belief reasoning, despite clear social difficulties in everyday life situations. In the current study, we used implicit belief manipulations that are task-irrelevant and therefore less susceptible to strategies. In a ball-detection task, it was shown that neurotypical individuals detect a ball faster if an agent believed the ball was present. We predicted that adults with high functioning autism (HFA) would not show this effect. While we found a numerical difference in the hypothesized direction, we did not find a reliable group effect. Interestingly, the implicit ToM-index showed a strong negative correlation with both self-reported and observational measures of social difficulties in the HFA group. This suggests that the relationship between implicit ToM reasoning and the symptomatology of HFA might be subtler than assumed.

Task-Driven Tube Current Modulation and Regularization Design in Computed Tomography with Penalized-Likelihood Reconstruction.

PubMed

Gang, G J; Siewerdsen, J H; Stayman, J W

2016-02-01

This work applies task-driven optimization to design CT tube current modulation and directional regularization in penalized-likelihood (PL) reconstruction. The relative performance of modulation schemes commonly adopted for filtered-backprojection (FBP) reconstruction were also evaluated for PL in comparison. We adopt a task-driven imaging framework that utilizes a patient-specific anatomical model and information of the imaging task to optimize imaging performance in terms of detectability index ( d' ). This framework leverages a theoretical model based on implicit function theorem and Fourier approximations to predict local spatial resolution and noise characteristics of PL reconstruction as a function of the imaging parameters to be optimized. Tube current modulation was parameterized as a linear combination of Gaussian basis functions, and regularization was based on the design of (directional) pairwise penalty weights for the 8 in-plane neighboring voxels. Detectability was optimized using a covariance matrix adaptation evolutionary strategy algorithm. Task-driven designs were compared to conventional tube current modulation strategies for a Gaussian detection task in an abdomen phantom. The task-driven design yielded the best performance, improving d' by ~20% over an unmodulated acquisition. Contrary to FBP, PL reconstruction using automatic exposure control and modulation based on minimum variance (in FBP) performed worse than the unmodulated case, decreasing d' by 16% and 9%, respectively. This work shows that conventional tube current modulation schemes suitable for FBP can be suboptimal for PL reconstruction. Thus, the proposed task-driven optimization provides additional opportunities for improved imaging performance and dose reduction beyond that achievable with conventional acquisition and reconstruction.

How to choose a subset of frequencies in frequency-domain finite-difference migration

NASA Astrophysics Data System (ADS)

Mulder, W. A.; Plessix, R.-E.

2004-09-01

Finite-difference migration with the two-way wave equation can be accelerated by an order of magnitude if the frequency domain rather than the time domain is used. This gain is mainly accomplished by using a subset of the available frequencies. The implicit assumption is that the data have a certain amount of redundancy in the frequency domain. The choice of frequencies cannot be arbitrary. If the frequencies are chosen with a constant increment and their spacing is too large, the well-known wrap-around that occurs when transforming back to the time domain will also show up in the migration to the depth domain, albeit in a more subtle way. Because migration involves propagation in a given background velocity model and summation over shots and receivers, the effects of wrap-around may disappear even when the Nyquist theorem is not obeyed. We have studied these effects analytically for the constant-velocity case and determined sampling conditions that avoid wrap-around artefacts. The conditions depend on the velocity, depth of the migration grid and offset range. They show that the spacing between subsequent frequencies can be larger than the inverse of the time range prescribed by the Nyquist theorem. A 2-D example has been used to test the validity of these conditions for a more realistic velocity model. Finite-difference migration with the one-way wave equation shows a similar behaviour.

Factorization and resummation of Higgs boson differential distributions in soft-collinear effective theory

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

Mantry, Sonny; Petriello, Frank

We derive a factorization theorem for the Higgs boson transverse momentum (p{sub T}) and rapidity (Y) distributions at hadron colliders, using the soft-collinear effective theory (SCET), for m{sub h}>>p{sub T}>>{Lambda}{sub QCD}, where m{sub h} denotes the Higgs mass. In addition to the factorization of the various scales involved, the perturbative physics at the p{sub T} scale is further factorized into two collinear impact-parameter beam functions (IBFs) and an inverse soft function (ISF). These newly defined functions are of a universal nature for the study of differential distributions at hadron colliders. The additional factorization of the p{sub T}-scale physics simplifies themore » implementation of higher order radiative corrections in {alpha}{sub s}(p{sub T}). We derive formulas for factorization in both momentum and impact parameter space and discuss the relationship between them. Large logarithms of the relevant scales in the problem are summed using the renormalization group equations of the effective theories. Power corrections to the factorization theorem in p{sub T}/m{sub h} and {Lambda}{sub QCD}/p{sub T} can be systematically derived. We perform multiple consistency checks on our factorization theorem including a comparison with known fixed-order QCD results. We compare the SCET factorization theorem with the Collins-Soper-Sterman approach to low-p{sub T} resummation.« less

Implicit and Explicit Memory in Autism: Is Autism an Amnesic Disorder?

ERIC Educational Resources Information Center

Renner, Peggy; Klinger, Laura Grofer; Klinger, Mark R.

2000-01-01

This study examined whether children with high-functioning autism have a dissociation between explicit and implicit memory abilities characteristic of medial temporal lobe amnesic disorder. Children (N=14 and ages 6-14) with autism showed intact implicit and explicit memory abilities but did not show typical memory patterns, suggesting they used…

Dissipative controller designs for second-order dynamic systems

NASA Technical Reports Server (NTRS)

Morris, K. A.; Juang, J. N.

1990-01-01

The passivity theorem may be used to design robust controllers for structures with positive transfer functions. This result is extended to more general configurations using dissipative system theory. A stability theorem for robust, model-independent controllers of structures which lack collocated rate sensors and actuators is given. The theory is illustrated for non-square systems and systems with displacement sensors.

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

Flego, S.P.; Plastino, A.; Universitat de les Illes Balears and IFISC-CSIC, 07122 Palma de Mallorca

We explore intriguing links connecting Hellmann-Feynman's theorem to a thermodynamics information-optimizing principle based on Fisher's information measure. - Highlights: > We link a purely quantum mechanical result, the Hellmann-Feynman theorem, with Jaynes' information theoretical reciprocity relations. > These relations involve the coefficients of a series expansion of the potential function. > We suggest the existence of a Legendre transform structure behind Schroedinger's equation, akin to the one characterizing thermodynamics.

The spectral method and the central limit theorem for general Markov chains

NASA Astrophysics Data System (ADS)

Nagaev, S. V.

2017-12-01

We consider Markov chains with an arbitrary phase space and develop a modification of the spectral method that enables us to prove the central limit theorem (CLT) for non-uniformly ergodic Markov chains. The conditions imposed on the transition function are more general than those by Athreya-Ney and Nummelin. Our proof of the CLT is purely analytical.

Comparative functional neuroanatomy between implicit and explicit memory tasks under negative emotional condition in schizophrenia.

PubMed

Song, Xiao-Li; Kim, Gwang-Won; Moon, Chung-Man; Jeong, Gwang-Woo

To evaluate the brain activation patterns in response to negative emotion during implicit and explicit memory in patients with schizophrenia. Fourteen patients with schizophrenia and 14 healthy controls were included in this study. The 3.0T fMRI was obtained while the subjects performed the implicit and explicit retrievals with unpleasant words. The different predominant brain activation areas were observed during the implicit retrieval and explicit with unpleasant words. The differential neural mechanisms between implicit and explicit memory tasks associated with negative emotional processing in schizophrenia. Copyright © 2017. Published by Elsevier Inc.

Evasion of No-Hair Theorems and Novel Black-Hole Solutions in Gauss-Bonnet Theories

NASA Astrophysics Data System (ADS)

Antoniou, G.; Bakopoulos, A.; Kanti, P.

2018-03-01

We consider a general Einstein-scalar-Gauss-Bonnet theory with a coupling function f (ϕ ) . We demonstrate that black-hole solutions appear as a generic feature of this theory since a regular horizon and an asymptotically flat solution may be easily constructed under mild assumptions for f (ϕ ). We show that the existing no-hair theorems are easily evaded, and a large number of regular black-hole solutions with scalar hair are then presented for a plethora of coupling functions f (ϕ ).

Compact exponential product formulas and operator functional derivative

NASA Astrophysics Data System (ADS)

Suzuki, Masuo

1997-02-01

A new scheme for deriving compact expressions of the logarithm of the exponential product is proposed and it is applied to several exponential product formulas. A generalization of the Dynkin-Specht-Wever (DSW) theorem on free Lie elements is given, and it is used to study the relation between the traditional method (based on the DSW theorem) and the present new scheme. The concept of the operator functional derivative is also proposed, and it is applied to ordered exponentials, such as time-evolution operators for time-dependent Hamiltonians.

Geometry and physics of pseudodifferential operators on manifolds

NASA Astrophysics Data System (ADS)

Esposito, Giampiero; Napolitano, George M.

2016-09-01

A review is made of the basic tools used in mathematics to define a calculus for pseudodifferential operators on Riemannian manifolds endowed with a connection: existence theorem for the function that generalizes the phase; analogue of Taylor's theorem; torsion and curvature terms in the symbolic calculus; the two kinds of derivative acting on smooth sections of the cotangent bundle of the Riemannian manifold; the concept of symbol as an equivalence class. Physical motivations and applications are then outlined, with emphasis on Green functions of quantum field theory and Parker's evaluation of Hawking radiation.

Evasion of No-Hair Theorems and Novel Black-Hole Solutions in Gauss-Bonnet Theories.

PubMed

Antoniou, G; Bakopoulos, A; Kanti, P

2018-03-30

We consider a general Einstein-scalar-Gauss-Bonnet theory with a coupling function f(ϕ). We demonstrate that black-hole solutions appear as a generic feature of this theory since a regular horizon and an asymptotically flat solution may be easily constructed under mild assumptions for f(ϕ). We show that the existing no-hair theorems are easily evaded, and a large number of regular black-hole solutions with scalar hair are then presented for a plethora of coupling functions f(ϕ).

A point implicit time integration technique for slow transient flow problems

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

Kadioglu, Samet Y.; Berry, Ray A.; Martineau, Richard C.

2015-05-01

We introduce a point implicit time integration technique for slow transient flow problems. The method treats the solution variables of interest (that can be located at cell centers, cell edges, or cell nodes) implicitly and the rest of the information related to same or other variables are handled explicitly. The method does not require implicit iteration; instead it time advances the solutions in a similar spirit to explicit methods, except it involves a few additional function(s) evaluation steps. Moreover, the method is unconditionally stable, as a fully implicit method would be. This new approach exhibits the simplicity of implementation ofmore » explicit methods and the stability of implicit methods. It is specifically designed for slow transient flow problems of long duration wherein one would like to perform time integrations with very large time steps. Because the method can be time inaccurate for fast transient problems, particularly with larger time steps, an appropriate solution strategy for a problem that evolves from a fast to a slow transient would be to integrate the fast transient with an explicit or semi-implicit technique and then switch to this point implicit method as soon as the time variation slows sufficiently. We have solved several test problems that result from scalar or systems of flow equations. Our findings indicate the new method can integrate slow transient problems very efficiently; and its implementation is very robust.« less

Entropy Inequalities for Stable Densities and Strengthened Central Limit Theorems

NASA Astrophysics Data System (ADS)

Toscani, Giuseppe

2016-10-01

We consider the central limit theorem for stable laws in the case of the standardized sum of independent and identically distributed random variables with regular probability density function. By showing decay of different entropy functionals along the sequence we prove convergence with explicit rate in various norms to a Lévy centered density of parameter λ >1 . This introduces a new information-theoretic approach to the central limit theorem for stable laws, in which the main argument is shown to be the relative fractional Fisher information, recently introduced in Toscani (Ricerche Mat 65(1):71-91, 2016). In particular, it is proven that, with respect to the relative fractional Fisher information, the Lévy density satisfies an analogous of the logarithmic Sobolev inequality, which allows to pass from the monotonicity and decay to zero of the relative fractional Fisher information in the standardized sum to the decay to zero in relative entropy with an explicit decay rate.

Newton Algorithms for Analytic Rotation: An Implicit Function Approach

ERIC Educational Resources Information Center

Boik, Robert J.

2008-01-01

In this paper implicit function-based parameterizations for orthogonal and oblique rotation matrices are proposed. The parameterizations are used to construct Newton algorithms for minimizing differentiable rotation criteria applied to "m" factors and "p" variables. The speed of the new algorithms is compared to that of existing algorithms and to…

Final Report on Scientific Activities Pursuant to the Provisions of AFOSR Grant 79-0018-A during the Period November 1, 1982 to October 31, 1983.

DTIC Science & Technology

1983-10-31

nonparallel line segments, itand it2’ with unit exterior normals vIand v 2- Proceeding as before we can show, applying the Rolmgren theorem together...application of (2.7) readily shows that z) le -tg(t) , Re(z) > P. (2.9) Re(z)-A L 2 [0 0) Let rr,p denote the positively oriented D-shaped contour consisting of...dedness of p in strips I le (z) 4- p . Proof of Theorem 4.6. From Theorem 4.3 the functions ezkt form a Schauder basis for L2 [-,wJ; equivalently, the

Testing ground for fluctuation theorems: The one-dimensional Ising model

NASA Astrophysics Data System (ADS)

Lemos, C. G. O.; Santos, M.; Ferreira, A. L.; Figueiredo, W.

2018-04-01

In this paper we determine the nonequilibrium magnetic work performed on a Ising model and relate it to the fluctuation theorem derived some years ago by Jarzynski. The basic idea behind this theorem is the relationship connecting the free energy difference between two thermodynamic states of a system and the average work performed by an external agent, in a finite time, through nonequilibrium paths between the same thermodynamic states. We test the validity of this theorem by considering the one-dimensional Ising model where the free energy is exactly determined as a function of temperature and magnetic field. We have found that the Jarzynski theorem remains valid for all the values of the rate of variation of the magnetic field applied to the system. We have also determined the probability distribution function for the work performed on the system for the forward and reverse processes and verified that predictions based on the Crooks relation are equally correct. We also propose a method to calculate the lag between the current state of the system and that of the equilibrium based on macroscopic variables. We have shown that the lag increases with the sweeping rate of the field at its final value for the reverse process, while it decreases in the case of the forward process. The lag increases linearly with the size of the chain and with a slope decreasing with the inverse of the rate of variation of the field.

Uncertainty in sample estimates and the implicit loss function for soil information.

NASA Astrophysics Data System (ADS)

Lark, Murray

2015-04-01

One significant challenge in the communication of uncertain information is how to enable the sponsors of sampling exercises to make a rational choice of sample size. One way to do this is to compute the value of additional information given the loss function for errors. The loss function expresses the costs that result from decisions made using erroneous information. In certain circumstances, such as remediation of contaminated land prior to development, loss functions can be computed and used to guide rational decision making on the amount of resource to spend on sampling to collect soil information. In many circumstances the loss function cannot be obtained prior to decision making. This may be the case when multiple decisions may be based on the soil information and the costs of errors are hard to predict. The implicit loss function is proposed as a tool to aid decision making in these circumstances. Conditional on a logistical model which expresses costs of soil sampling as a function of effort, and statistical information from which the error of estimates can be modelled as a function of effort, the implicit loss function is the loss function which makes a particular decision on effort rational. In this presentation the loss function is defined and computed for a number of arbitrary decisions on sampling effort for a hypothetical soil monitoring problem. This is based on a logistical model of sampling cost parameterized from a recent geochemical survey of soil in Donegal, Ireland and on statistical parameters estimated with the aid of a process model for change in soil organic carbon. It is shown how the implicit loss function might provide a basis for reflection on a particular choice of sample size by comparing it with the values attributed to soil properties and functions. Scope for further research to develop and apply the implicit loss function to help decision making by policy makers and regulators is then discussed.

Heuristic analogy in Ars Conjectandi: From Archimedes' De Circuli Dimensione to Bernoulli's theorem.

PubMed

Campos, Daniel G

2018-02-01

This article investigates the way in which Jacob Bernoulli proved the main mathematical theorem that undergirds his art of conjecturing-the theorem that founded, historically, the field of mathematical probability. It aims to contribute a perspective into the question of problem-solving methods in mathematics while also contributing to the comprehension of the historical development of mathematical probability. It argues that Bernoulli proved his theorem by a process of mathematical experimentation in which the central heuristic strategy was analogy. In this context, the analogy functioned as an experimental hypothesis. The article expounds, first, Bernoulli's reasoning for proving his theorem, describing it as a process of experimentation in which hypothesis-making is crucial. Next, it investigates the analogy between his reasoning and Archimedes' approximation of the value of π, by clarifying both Archimedes' own experimental approach to the said approximation and its heuristic influence on Bernoulli's problem-solving strategy. The discussion includes some general considerations about analogy as a heuristic technique to make experimental hypotheses in mathematics. Copyright © 2018 Elsevier Ltd. All rights reserved.

Reconstruction of fluorescence molecular tomography with a cosinoidal level set method.

PubMed

Zhang, Xuanxuan; Cao, Xu; Zhu, Shouping

2017-06-27

Implicit shape-based reconstruction method in fluorescence molecular tomography (FMT) is capable of achieving higher image clarity than image-based reconstruction method. However, the implicit shape method suffers from a low convergence speed and performs unstably due to the utilization of gradient-based optimization methods. Moreover, the implicit shape method requires priori information about the number of targets. A shape-based reconstruction scheme of FMT with a cosinoidal level set method is proposed in this paper. The Heaviside function in the classical implicit shape method is replaced with a cosine function, and then the reconstruction can be accomplished with the Levenberg-Marquardt method rather than gradient-based methods. As a result, the priori information about the number of targets is not required anymore and the choice of step length is avoided. Numerical simulations and phantom experiments were carried out to validate the proposed method. Results of the proposed method show higher contrast to noise ratios and Pearson correlations than the implicit shape method and image-based reconstruction method. Moreover, the number of iterations required in the proposed method is much less than the implicit shape method. The proposed method performs more stably, provides a faster convergence speed than the implicit shape method, and achieves higher image clarity than the image-based reconstruction method.

Aspects of AdS/CFT: Conformal Deformations and the Goldstone Equivalence Theorem

NASA Astrophysics Data System (ADS)

Cantrell, Sean Andrew

The AdS/CFT correspondence provides a map from the states of theories situated in AdSd+1 to those in dual conformal theories in a d-dimensional space. The correspondence can be used to establish certain universal properties of some theories in one space by examining the behave of general objects in the other. In this thesis, we develop various formal aspects of AdS/CFT. Conformal deformations manifest in the AdS/CFT correspondence as boundary conditions on the AdS field. Heretofore, double-trace deformations have been the primary focus in this context. To better understand multitrace deformations, we revisit the relationship between the generating AdS partition function for a free bulk theory and the boundary CFT partition function subject to arbitrary conformal deformations. The procedure leads us to a formalism that constructs bulk fields from boundary operators. We independently replicate the holographic RG flow narrative to go on to interpret the brane used to regulate the AdS theory as a renormalization scale. The scale-dependence of the dilatation spectrum of a boundary theory in the presence of general deformations can be thus understood on the AdS side using this formalism. The Goldstone equivalence theorem allows one to relate scattering amplitudes of massive gauge fields to those of scalar fields in the limit of large scattering energies. We generalize this theorem under the framework of the AdS/CFT correspondence. First, we obtain an expression of the equivalence theorem in terms of correlation functions of creation and annihilation operators by using an AdS wave function approach to the AdS/CFT dictionary. It is shown that the divergence of the non-conserved conformal current dual to the bulk gauge field is approximately primary when computing correlators for theories in which the masses of all the exchanged particles are sufficiently large. The results are then generalized to higher spin fields. We then go on to generalize the theorem using conformal blocks in two and four-dimensional CFTs. We show that when the scaling dimensions of the exchanged operators are large compared to both their spins and the dimension of the current, the conformal blocks satisfy an equivalence theorem.

More on Weinberg's no-go theorem in quantum gravity

NASA Astrophysics Data System (ADS)

Nagahama, Munehiro; Oda, Ichiro

2018-05-01

We complement Weinberg's no-go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the G L (4 ) symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.

The Riesz-Radon-Fréchet problem of characterization of integrals

NASA Astrophysics Data System (ADS)

Zakharov, Valerii K.; Mikhalev, Aleksandr V.; Rodionov, Timofey V.

2010-11-01

This paper is a survey of results on characterizing integrals as linear functionals. It starts from the familiar result of F. Riesz (1909) on integral representation of bounded linear functionals by Riemann-Stieltjes integrals on a closed interval, and is directly connected with Radon's famous theorem (1913) on integral representation of bounded linear functionals by Lebesgue integrals on a compact subset of {R}^n. After the works of Radon, Fréchet, and Hausdorff, the problem of characterizing integrals as linear functionals took the particular form of the problem of extending Radon's theorem from {R}^n to more general topological spaces with Radon measures. This problem turned out to be difficult, and its solution has a long and rich history. Therefore, it is natural to call it the Riesz-Radon-Fréchet problem of characterization of integrals. Important stages of its solution are associated with such eminent mathematicians as Banach (1937-1938), Saks (1937-1938), Kakutani (1941), Halmos (1950), Hewitt (1952), Edwards (1953), Prokhorov (1956), Bourbaki (1969), and others. Essential ideas and technical tools were developed by A.D. Alexandrov (1940-1943), Stone (1948-1949), Fremlin (1974), and others. Most of this paper is devoted to the contemporary stage of the solution of the problem, connected with papers of König (1995-2008), Zakharov and Mikhalev (1997-2009), and others. The general solution of the problem is presented in the form of a parametric theorem on characterization of integrals which directly implies the characterization theorems of the indicated authors. Bibliography: 60 titles.

TASK-RELATED FUNCTIONAL CONNECTIVITY OF THE CAUDATE MEDIATES THE ASSOCIATION BETWEEN TRAIT MINDFULNESS AND IMPLICIT LEARNING IN OLDER ADULTS

PubMed Central

Stillman, Chelsea M.; You, Xiaozhen; Seaman, Kendra L.; Vaidya, Chandan J.; Howard, James H.; Howard, Darlene V.

2016-01-01

Accumulating evidence shows a positive relationship between mindfulness and explicit cognitive functioning, i.e., that which occurs with conscious intent and awareness. However, recent evidence suggests that there may be a negative relationship between mindfulness and implicit types of learning, or those that occur without conscious awareness or intent. Here we examined the neural mechanisms underlying the recently reported negative relationship between dispositional mindfulness and implicit probabilistic sequence learning in both younger and older adults. We tested the hypothesis that the relationship is mediated by communication, or functional connectivity, of brain regions once traditionally considered to be central to dissociable learning systems: the caudate, medial temporal lobe (MTL), and prefrontal cortex (PFC). We first replicated the negative relationship between mindfulness and implicit learning in a sample of healthy older adults (60–90 years old) who completed three event-related runs of an implicit sequence learning task. Then, using a seed-based connectivity approach, we identified task-related connectivity associated with individual differences in both learning and mindfulness. The main finding was that caudate-MTL connectivity (bilaterally) was positively correlated with learning and negatively correlated with mindfulness. Further, the strength of task-related connectivity between these regions mediated the negative relationship between mindfulness and learning. This pattern of results was limited to the older adults. Thus, at least in healthy older adults, the functional communication between two interactive learning-relevant systems can account for the relationship between mindfulness and implicit probabilistic sequence learning. PMID:27121302

The distribution of the zeros of the Hermite-Padé polynomials for a pair of functions forming a Nikishin system

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

Rakhmanov, E A; Suetin, S P

2013-09-30

The distribution of the zeros of the Hermite-Padé polynomials of the first kind for a pair of functions with an arbitrary even number of common branch points lying on the real axis is investigated under the assumption that this pair of functions forms a generalized complex Nikishin system. It is proved (Theorem 1) that the zeros have a limiting distribution, which coincides with the equilibrium measure of a certain compact set having the S-property in a harmonic external field. The existence problem for S-compact sets is solved in Theorem 2. The main idea of the proof of Theorem 1 consists in replacing a vector equilibrium problem in potentialmore » theory by a scalar problem with an external field and then using the general Gonchar-Rakhmanov method, which was worked out in the solution of the '1/9'-conjecture. The relation of the result obtained here to some results and conjectures due to Nuttall is discussed. Bibliography: 51 titles.« less

Quantum Field Theory on Spacetimes with a Compactly Generated Cauchy Horizon

NASA Astrophysics Data System (ADS)

Kay, Bernard S.; Radzikowski, Marek J.; Wald, Robert M.

1997-02-01

We prove two theorems which concern difficulties in the formulation of the quantum theory of a linear scalar field on a spacetime, (M,g_{ab}), with a compactly generated Cauchy horizon. These theorems demonstrate the breakdown of the theory at certain base points of the Cauchy horizon, which are defined as 'past terminal accumulation points' of the horizon generators. Thus, the theorems may be interpreted as giving support to Hawking's 'Chronology Protection Conjecture', according to which the laws of physics prevent one from manufacturing a 'time machine'. Specifically, we prove: Theorem 1. There is no extension to (M,g_{ab}) of the usual field algebra on the initial globally hyperbolic region which satisfies the condition of F-locality at any base point. In other words, any extension of the field algebra must, in any globally hyperbolic neighbourhood of any base point, differ from the algebra one would define on that neighbourhood according to the rules for globally hyperbolic spacetimes. Theorem 2. The two-point distribution for any Hadamard state defined on the initial globally hyperbolic region must (when extended to a distributional bisolution of the covariant Klein-Gordon equation on the full spacetime) be singular at every base point x in the sense that the difference between this two point distribution and a local Hadamard distribution cannot be given by a bounded function in any neighbourhood (in M 2 M) of (x,x). In consequence of Theorem 2, quantities such as the renormalized expectation value of J2 or of the stress-energy tensor are necessarily ill-defined or singular at any base point. The proof of these theorems relies on the 'Propagation of Singularities' theorems of Duistermaat and Hörmander.

The neural basis of implicit learning and memory: a review of neuropsychological and neuroimaging research.

PubMed

Reber, Paul J

2013-08-01

Memory systems research has typically described the different types of long-term memory in the brain as either declarative versus non-declarative or implicit versus explicit. These descriptions reflect the difference between declarative, conscious, and explicit memory that is dependent on the medial temporal lobe (MTL) memory system, and all other expressions of learning and memory. The other type of memory is generally defined by an absence: either the lack of dependence on the MTL memory system (nondeclarative) or the lack of conscious awareness of the information acquired (implicit). However, definition by absence is inherently underspecified and leaves open questions of how this type of memory operates, its neural basis, and how it differs from explicit, declarative memory. Drawing on a variety of studies of implicit learning that have attempted to identify the neural correlates of implicit learning using functional neuroimaging and neuropsychology, a theory of implicit memory is presented that describes it as a form of general plasticity within processing networks that adaptively improve function via experience. Under this model, implicit memory will not appear as a single, coherent, alternative memory system but will instead be manifested as a principle of improvement from experience based on widespread mechanisms of cortical plasticity. The implications of this characterization for understanding the role of implicit learning in complex cognitive processes and the effects of interactions between types of memory will be discussed for examples within and outside the psychology laboratory. Copyright © 2013 Elsevier Ltd. All rights reserved.

Implicit memory. Retention without remembering.

PubMed

Roediger, H L

1990-09-01

Explicit measures of human memory, such as recall or recognition, reflect conscious recollection of the past. Implicit tests of retention measure transfer (or priming) from past experience on tasks that do not require conscious recollection of recent experiences for their performance. The article reviews research on the relation between explicit and implicit memory. The evidence points to substantial differences between standard explicit and implicit tests, because many variables create dissociations between these tests. For example, although pictures are remembered better than words on explicit tests, words produce more priming than do pictures on several implicit tests. These dissociations may implicate different memory systems that subserve distinct memorial functions, but the present argument is that many dissociations can be understood by appealing to general principles that apply to both explicit and implicit tests. Phenomena studied under the rubric of implicit memory may have important implications in many other fields, including social cognition, problem solving, and cognitive development.

Physical Activity Is Associated with Reduced Implicit Learning but Enhanced Relational Memory and Executive Functioning in Young Adults

PubMed Central

Watt, Jennifer C.; Grove, George A.; Wollam, Mariegold E.; Uyar, Fatma; Mataro, Maria; Cohen, Neal J.; Howard, Darlene V.; Howard, James H.; Erickson, Kirk I.

2016-01-01

Accumulating evidence suggests that physical activity improves explicit memory and executive cognitive functioning at the extreme ends of the lifespan (i.e., in older adults and children). However, it is unknown whether these associations hold for younger adults who are considered to be in their cognitive prime, or for implicit cognitive functions that do not depend on motor sequencing. Here we report the results of a study in which we examine the relationship between objectively measured physical activity and (1) explicit relational memory, (2) executive control, and (3) implicit probabilistic sequence learning in a sample of healthy, college-aged adults. The main finding was that physical activity was positively associated with explicit relational memory and executive control (replicating previous research), but negatively associated with implicit learning, particularly in females. These results raise the intriguing possibility that physical activity upregulates some cognitive processes, but downregulates others. Possible implications of this pattern of results for physical health and health habits are discussed. PMID:27584059

Compact exponential product formulas and operator functional derivative

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

Suzuki, M.

1997-02-01

A new scheme for deriving compact expressions of the logarithm of the exponential product is proposed and it is applied to several exponential product formulas. A generalization of the Dynkin{endash}Specht{endash}Wever (DSW) theorem on free Lie elements is given, and it is used to study the relation between the traditional method (based on the DSW theorem) and the present new scheme. The concept of the operator functional derivative is also proposed, and it is applied to ordered exponentials, such as time-evolution operators for time-dependent Hamiltonians. {copyright} {ital 1997 American Institute of Physics.}

Implicit measures: A normative analysis and review.

PubMed

De Houwer, Jan; Teige-Mocigemba, Sarah; Spruyt, Adriaan; Moors, Agnes

2009-05-01

Implicit measures can be defined as outcomes of measurement procedures that are caused in an automatic manner by psychological attributes. To establish that a measurement outcome is an implicit measure, one should examine (a) whether the outcome is causally produced by the psychological attribute it was designed to measure, (b) the nature of the processes by which the attribute causes the outcome, and (c) whether these processes operate automatically. This normative analysis provides a heuristic framework for organizing past and future research on implicit measures. The authors illustrate the heuristic function of their framework by using it to review past research on the 2 implicit measures that are currently most popular: effects in implicit association tests and affective priming tasks. (PsycINFO Database Record (c) 2009 APA, all rights reserved).

The Holographic F Theorem

NASA Astrophysics Data System (ADS)

Taylor, Marika; Woodhead, William

2017-12-01

The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension between 3/2 and 5/2. Therefore the strongest version of the F theorem is in general violated.

An efficient method for solving the steady Euler equations

NASA Technical Reports Server (NTRS)

Liou, M. S.

1986-01-01

An efficient numerical procedure for solving a set of nonlinear partial differential equations is given, specifically for the steady Euler equations. Solutions of the equations were obtained by Newton's linearization procedure, commonly used to solve the roots of nonlinear algebraic equations. In application of the same procedure for solving a set of differential equations we give a theorem showing that a quadratic convergence rate can be achieved. While the domain of quadratic convergence depends on the problems studied and is unknown a priori, we show that firstand second-order derivatives of flux vectors determine whether the condition for quadratic convergence is satisfied. The first derivatives enter as an implicit operator for yielding new iterates and the second derivatives indicates smoothness of the flows considered. Consequently flows involving shocks are expected to require larger number of iterations. First-order upwind discretization in conjunction with the Steger-Warming flux-vector splitting is employed on the implicit operator and a diagonal dominant matrix results. However the explicit operator is represented by first- and seond-order upwind differencings, using both Steger-Warming's and van Leer's splittings. We discuss treatment of boundary conditions and solution procedures for solving the resulting block matrix system. With a set of test problems for one- and two-dimensional flows, we show detailed study as to the efficiency, accuracy, and convergence of the present method.

Review of incursive, hyperincursive and anticipatory systems-foundation of anticipation in electromagnetism

NASA Astrophysics Data System (ADS)

Dubois, Daniel M.

2000-05-01

The main purpose of this paper is to show that anticipation is not only a property of biosystems but is also a fundamental property of physical systems. In electromagnetism, the anticipation is related to the Lorentz transform. In this framework the anticipation is a strong anticipation because it is not based on a prediction from a model of the physical system but is embedded in the fundamental system. So, Robert Rosen's anticipatory systems deal with weak anticipation. Contrary to Robert Rosen's affirmation, anticipation is thus not a characteristic of living systems. Finality is implicitly embedded in any system and thus the final cause of Aristotle is implicitly embedded in any physical and biological systems, contrary to what Robert Rosen argued. This paper will review some incursive and hyperincursive systems giving rise to strong anticipation. Space-time incursive parabolic systems show non-local properties. Hyperincursive crisp systems are related to catastrophe theory. Finally it will be shown that incursive and hyperincursive anticipatory systems could model properties of biosystems like free will, game strategy, theorem creation, etc. Anticipation is not only related to predictions but to decisions: hyperincursive systems create multiple choices and a decision process selects one choice. So, anticipation is not a final goal, like in cybernetics and system science, but is a fundamental property of physical and biological systems.

Viewing the Roots of Polynomial Functions in Complex Variable: The Use of Geogebra and the CAS Maple

ERIC Educational Resources Information Center

Alves, Francisco Regis Vieira

2013-01-01

Admittedly, the Fundamental Theorem of Calculus-TFA holds an important role in the Complex Analysis-CA, as well as in other mathematical branches. In this article, we bring a discussion about the TFA, the Rouché's theorem and the winding number with the intention to analyze the roots of a polynomial equation. We propose also a description for a…

On direct theorems for best polynomial approximation

NASA Astrophysics Data System (ADS)

Auad, A. A.; AbdulJabbar, R. S.

2018-05-01

This paper is to obtain similarity for the best approximation degree of functions, which are unbounded in L p,α (A = [0,1]), which called weighted space by algebraic polynomials. {E}nH{(f)}p,α and the best approximation degree in the same space on the interval [0,2π] by trigonometric polynomials {E}nT{(f)}p,α of direct wellknown theorems in forms the average modules.

Implicit Self-Importance in an Interpersonal Pronoun Categorization Task.

PubMed

Fetterman, Adam K; Robinson, Michael D; Gilbertson, Elizabeth P

2014-06-01

Object relations theories emphasize the manner in which the salience/importance of implicit representations of self and other guide interpersonal functioning. Two studies and a pilot test (total N = 304) sought to model such representations. In dyadic contexts, the self is a "you" and the other is a "me", as verified in a pilot test. Study 1 then used a simple categorization task and found evidence for implicit self-importance: The pronoun "you" was categorized more quickly and accurately when presented in a larger font size, whereas the pronoun "me" was categorized more quickly and accurately when presented in a smaller font size. Study 2 showed that this pattern possesses value in understanding individual differences in interpersonal functioning. As predicted, arrogant people scored higher in implicit self-importance in the paradigm. Findings are discussed from the perspective of dyadic interpersonal dynamics.

Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

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

Woolgar, Eric, E-mail: ewoolgar@ualberta.ca; Wylie, William, E-mail: wwylie@syr.edu

We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able tomore » extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.« less

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

Venkatesan, R.C., E-mail: ravi@systemsresearchcorp.com; Plastino, A., E-mail: plastino@fisica.unlp.edu.ar

The (i) reciprocity relations for the relative Fisher information (RFI, hereafter) and (ii) a generalized RFI–Euler theorem are self-consistently derived from the Hellmann–Feynman theorem. These new reciprocity relations generalize the RFI–Euler theorem and constitute the basis for building up a mathematical Legendre transform structure (LTS, hereafter), akin to that of thermodynamics, that underlies the RFI scenario. This demonstrates the possibility of translating the entire mathematical structure of thermodynamics into a RFI-based theoretical framework. Virial theorems play a prominent role in this endeavor, as a Schrödinger-like equation can be associated to the RFI. Lagrange multipliers are determined invoking the RFI–LTS linkmore » and the quantum mechanical virial theorem. An appropriate ansatz allows for the inference of probability density functions (pdf’s, hereafter) and energy-eigenvalues of the above mentioned Schrödinger-like equation. The energy-eigenvalues obtained here via inference are benchmarked against established theoretical and numerical results. A principled theoretical basis to reconstruct the RFI-framework from the FIM framework is established. Numerical examples for exemplary cases are provided. - Highlights: • Legendre transform structure for the RFI is obtained with the Hellmann–Feynman theorem. • Inference of the energy-eigenvalues of the SWE-like equation for the RFI is accomplished. • Basis for reconstruction of the RFI framework from the FIM-case is established. • Substantial qualitative and quantitative distinctions with prior studies are discussed.« less

Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

NASA Astrophysics Data System (ADS)

Woolgar, Eric; Wylie, William

2016-02-01

We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the "pure Bakry-Émery" N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (-∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (-∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.

Stable sequential Kuhn-Tucker theorem in iterative form or a regularized Uzawa algorithm in a regular nonlinear programming problem

NASA Astrophysics Data System (ADS)

Sumin, M. I.

2015-06-01

A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fréchet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.

Voluntary Explicit versus Involuntary Conceptual Memory Are Associated with Dissociable fMRI Responses in Hippocampus, Amygdala, and Parietal Cortex for Emotional and Neutral Word Pairs

ERIC Educational Resources Information Center

Ramponi, Cristina; Barnard, Philip J.; Kherif, Ferath; Henson, Richard N.

2011-01-01

Although functional neuroimaging studies have supported the distinction between explicit and implicit forms of memory, few have matched explicit and implicit tests closely, and most of these tested perceptual rather than conceptual implicit memory. We compared event-related fMRI responses during an intentional test, in which a group of…

Application of the Yoshida-Ruth Techniques to Implicit Integration and Multi-Map Explicit Integration

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

Forest, E.; Bengtsson, J.; Reusch, M.F.

1991-04-01

The full power of Yoshida's technique is exploited to produce an arbitrary order implicit symplectic integrator and multi-map explicit integrator. This implicit integrator uses a characteristic function involving the force term alone. Also we point out the usefulness of the plain Ruth algorithm in computing Taylor series map using the techniques first introduced by Berz in his 'COSY-INFINITY' code.

Autonomous quantum to classical transitions and the generalized imaging theorem

NASA Astrophysics Data System (ADS)

Briggs, John S.; Feagin, James M.

2016-03-01

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. Here we prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Currently, the quantum to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.

Autonomous quantum to classical transitions and the generalized imaging theorem

DOE PAGES

Briggs, John S.; Feagin, James M.

2016-03-16

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. We prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Now, the quantummore » to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.« less

About the best approximations with trigonometric polynomials on the class W0Hω¯ of the space L, part I

NASA Astrophysics Data System (ADS)

Nikolova, Yanka

2012-11-01

In this paper we obtain estimation for the best approximation En(W0Hω)¯ in the L-metric, where W0Hω¯ is the conjugate of the class W0Hω, i.e. W0Hω¯def = {f¯,f∈W0Hω}. Our results concern evaluations of the function Φ(Ḡ; x) where Φ(G; x) is the so-called Σ-representation of the function G, as defined in [2, p. 144], and Ḡ(x) denotes the conjugate of the function G(x). We prove three theorems, necessary for the estimation of the functional Fω(ḡ) = sup/f∈Hω ∫ 02πf(t).ḡ(t)dt. Specially, in Theorem 4 we prove an inequality for this functional and show that estimation is exact, i.e. the inequality becomes equality for some specific conjugate functions.

The Coast Artillery Journal. Volume 57, Number 6, December 1922

DTIC Science & Technology

1922-12-01

theorems ; Chapter III, to application; Chapters IV, V and VI, to infinitesimals and differentials, trigonometric functions, and logarithms and...taneously." There are chapters on complex numbers with simple and direct discussion of the roots of unity; on elementary theorems on the roots of an...through the centuries from the time of Pythagoras , an interest shared on the one extreme by nearly every noted mathematician and on the other extreme by

Boundedness and almost Periodicity in Time of Solutions of Evolutionary Variational Inequalities

NASA Astrophysics Data System (ADS)

Pankov, A. A.

1983-04-01

In this paper existence theorems are obtained for the solutions of abstract parabolic variational inequalities, which are bounded with respect to time (in the Stepanov and L^\\infty norms). The regularity and almost periodicity properties of such solutions are studied. Theorems are also established concerning their solvability in spaces of Besicovitch almost periodic functions. The majority of the results are obtained without any compactness assumptions. Bibliography: 30 titles.

Automated Real Proving in PVS via MetiTarski

NASA Technical Reports Server (NTRS)

Denman, William; Munoz, Cesar

2014-01-01

This paper reports the development of a proof strategy that integrates the MetiTarski theorem prover as a trusted external decision procedure into the PVS theorem prover. The strategy automatically discharges PVS sequents containing real-valued formulas, including transcendental and special functions, by translating the sequents into first order formulas and submitting them to MetiTarski. The new strategy is considerably faster and more powerful than other strategies for nonlinear arithmetic available to PVS.

Generalized Optical Theorem Detection in Random and Complex Media

NASA Astrophysics Data System (ADS)

Tu, Jing

The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar optical theorem theory applies to arbitrary lossless backgrounds and quite general probing fields including near fields which play a key role in super-resolution imaging. The derived formulation holds for arbitrary passive scatterers, which can be dissipative, as well as for the more general class of active scatterers which are composed of a (passive) scatterer component and an active, radiating (antenna) component. Furthermore, the generalization of the optical theorem to active scatterers is relevant to many applications such as surveillance of active targets including certain cloaks, invisible scatterers, and wireless communications. The latter developments have important military applications. The derived theoretical framework includes the familiar real power optical theorem describing power extinction due to both dissipation and scattering as well as a reactive optical theorem related to the reactive power changes. Meanwhile, the developed approach naturally leads to three optical theorem indicators or statistics, which can be used to detect changes or targets in unknown complex media. In addition, the optical theorem theory is generalized in the time domain so that it applies to arbitrary full vector fields, and arbitrary media including anisotropic media, nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The second component of this Ph.D. research program focuses on the application of the optical theorem to change detection. Three different forms of indicators or statistics are developed for change detection in unknown background media: a real power optical theorem detector, a reactive power optical theorem detector, and a total apparent power optical theorem detector. No prior knowledge is required of the background or the change or target. The performance of the three proposed optical theorem detectors is compared with the classical energy detector approach for change detection. The latter uses a mathematical or functional energy while the optical theorem detectors are based on real physical energy. For reference, the optical theorem detectors are also compared with the matched filter approach which (unlike the optical theorem detectors) assumes perfect target and medium information. The practical implementation of the optical theorem detectors is based for certain random and complex media on the exploitation of time reversal focusing ideas developed in the past 20 years in electromagnetics and acoustics. In the final part of the dissertation, we also discuss the implementation of the optical theorem sensors for one-dimensional propagation systems such as transmission lines. We also present a new generalized likelihood ratio test for detection that exploits a prior data constraint based on the optical theorem. Finally, we also address the practical implementation of the optical theorem sensors for optical imaging systems, by means of holography. The later is the first holographic implementation the optical theorem for arbitrary scenes and targets.

Implicit Theories of Intelligence and Personality, Self-Efficacy in Problem Solving, and the Perception of Skills and Competences in High School Students in Sicily, Italy

ERIC Educational Resources Information Center

Pirrone, Concetta; Commodari, Elena

2013-01-01

Various theories of intelligence and personality (TIP) help explain the implicit beliefs that an individual develops about the functioning of his intelligence and personality. Such beliefs are defined "implicit" because the individual might not be fully aware of his or her belief system. The results from scientific research on the TIP…

Singlet-triplet splittings from the virial theorem and single-particle excitation energies

NASA Astrophysics Data System (ADS)

Becke, Axel D.

2018-01-01

The zeroth-order (uncorrelated) singlet-triplet energy difference in single-particle excited configurations is 2Kif, where Kif is the Coulomb self-energy of the product of the transition orbitals. Here we present a non-empirical, virial-theorem argument that the correlated singlet-triplet energy difference should be half of this, namely, Kif. This incredibly simple result gives vertical HOMO-LUMO excitation energies in small-molecule benchmarks as good as the popular TD-B3LYP time-dependent approach to excited states. For linear acenes and nonlinear polycyclic aromatic hydrocarbons, the performance is significantly better than TD-B3LYP. In addition to the virial theorem, the derivation borrows intuitive pair-density concepts from density-functional theory.

A Geometrical Approach to Bell's Theorem

NASA Technical Reports Server (NTRS)

Rubincam, David Parry

2000-01-01

Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.

Implicit Memory in Korsakoff’s Syndrome: A Review of Procedural Learning and Priming Studies

PubMed Central

Hayes, Scott M.; Fortier, Catherine B.; Levine, Andrea; Milberg, William P.; McGlinchey, Regina

2013-01-01

Korsakoff’s syndrome (KS) is characterized by dense anterograde amnesia resulting from damage to the diencephalon region, typically resulting from chronic alcohol abuse and thiamine deficiency. This review assesses the integrity of the implicit memory system in KS, focusing on studies of procedural learning and priming. KS patients are impaired on several measures of procedural memory, most likely due to impairment in cognitive functions associated with alcohol-related neural damage outside of the diencephalon. The pattern of performance on tasks of implicit priming suggests reliance on a residual, non-flexible memory operating more or less in an automatic fashion. Our review concludes that whether measures of implicit memory reveal intact or impaired performance in individuals with KS depends heavily on specific task parameters and demands, including timing between stimuli, the specific nature of the stimuli used in a task, and the integrity of supportive cognitive functions necessary for performance. PMID:22592661

Implicit Self-Importance in an Interpersonal Pronoun Categorization Task

PubMed Central

Fetterman, Adam K.; Robinson, Michael D.; Gilbertson, Elizabeth P.

2014-01-01

Object relations theories emphasize the manner in which the salience/importance of implicit representations of self and other guide interpersonal functioning. Two studies and a pilot test (total N = 304) sought to model such representations. In dyadic contexts, the self is a “you” and the other is a “me”, as verified in a pilot test. Study 1 then used a simple categorization task and found evidence for implicit self-importance: The pronoun “you” was categorized more quickly and accurately when presented in a larger font size, whereas the pronoun “me” was categorized more quickly and accurately when presented in a smaller font size. Study 2 showed that this pattern possesses value in understanding individual differences in interpersonal functioning. As predicted, arrogant people scored higher in implicit self-importance in the paradigm. Findings are discussed from the perspective of dyadic interpersonal dynamics. PMID:25419089

Stability of and Changes in Implicit Motives. A Narrative Review of Empirical Studies

PubMed Central

Denzinger, Ferdinand; Brandstätter, Veronika

2018-01-01

Although growing research indicates that certain personality traits change over the lifespan, implicit motives are often deemed to be rather stable personality characteristics. Researchers have been interested in implicit motives for several decades, but our understanding of how these dispositions change still lacks clarity. This article gives an overview and a discussion of the current evidence for the stability of and the changes in implicit motives. After elaborating on the theoretical background of the motive construct and its measurement, we present an overview of studies that have investigated the trainability of implicit motives and their dispositional stability and changes using cross-sectional and longitudinal methods. Although the results are inconclusive concerning the direction of change, the reviewed studies suggest that implicit motives adapt to life circumstances much like other personality traits. This review sets out to contribute to a better understanding of the functioning of implicit motives and to present a roadmap for further research. PMID:29887818

A theorem regarding roots of the zero-order Bessel function of the first kind

NASA Technical Reports Server (NTRS)

Lin, X.-A.; Agrawal, O. P.

1993-01-01

This paper investigates a problem on the steady-state, conduction-convection heat transfer process in cylindrical porous heat exchangers. The governing partial differential equations for the system are obtained using the energy conservation law. Solution of these equations and the concept of enthalpy lead to a new approach to prove a theorem that the sum of inverse squares of all the positive roots of the zero order Bessel function of the first kind equals to one-forth. As a corollary, it is shown that the sum of one over pth power (p greater than or equal to 2) of the roots converges to some constant.

Cancellation of spurious arrivals in Green's function extraction and the generalized optical theorem

USGS Publications Warehouse

Snieder, R.; Van Wijk, K.; Haney, M.; Calvert, R.

2008-01-01

The extraction of the Green's function by cross correlation of waves recorded at two receivers nowadays finds much application. We show that for an arbitrary small scatterer, the cross terms of scattered waves give an unphysical wave with an arrival time that is independent of the source position. This constitutes an apparent inconsistency because theory predicts that such spurious arrivals do not arise, after integration over a complete source aperture. This puzzling inconsistency can be resolved for an arbitrary scatterer by integrating the contribution of all sources in the stationary phase approximation to show that the stationary phase contributions to the source integral cancel the spurious arrival by virtue of the generalized optical theorem. This work constitutes an alternative derivation of this theorem. When the source aperture is incomplete, the spurious arrival is not canceled and could be misinterpreted to be part of the Green's function. We give an example of how spurious arrivals provide information about the medium complementary to that given by the direct and scattered waves; the spurious waves can thus potentially be used to better constrain the medium. ?? 2008 The American Physical Society.

Towards an explicit account of implicit learning.

PubMed

Forkstam, Christian; Petersson, Karl Magnus

2005-08-01

The human brain supports acquisition mechanisms that can extract structural regularities implicitly from experience without the induction of an explicit model. Reber defined the process by which an individual comes to respond appropriately to the statistical structure of the input ensemble as implicit learning. He argued that the capacity to generalize to new input is based on the acquisition of abstract representations that reflect underlying structural regularities in the acquisition input. We focus this review of the implicit learning literature on studies published during 2004 and 2005. We will not review studies of repetition priming ('implicit memory'). Instead we focus on two commonly used experimental paradigms: the serial reaction time task and artificial grammar learning. Previous comprehensive reviews can be found in Seger's 1994 article and the Handbook of Implicit Learning. Emerging themes include the interaction between implicit and explicit processes, the role of the medial temporal lobe, developmental aspects of implicit learning, age-dependence, the role of sleep and consolidation. The attempts to characterize the interaction between implicit and explicit learning are promising although not well understood. The same can be said about the role of sleep and consolidation. Despite the fact that lesion studies have relatively consistently suggested that the medial temporal lobe memory system is not necessary for implicit learning, a number of functional magnetic resonance studies have reported medial temporal lobe activation in implicit learning. This issue merits further research. Finally, the clinical relevance of implicit learning remains to be determined.

What do we know about implicit false-belief tracking?

PubMed

Schneider, Dana; Slaughter, Virginia P; Dux, Paul E

2015-02-01

There is now considerable evidence that neurotypical individuals track the internal cognitions of others, even in the absence of instructions to do so. This finding has prompted the suggestion that humans possess an implicit mental state tracking system (implicit Theory of Mind, ToM) that exists alongside a system that allows the deliberate and explicit analysis of the mental states of others (explicit ToM). Here we evaluate the evidence for this hypothesis and assess the extent to which implicit and explicit ToM operations are distinct. We review evidence showing that adults can indeed engage in ToM processing even without being conscious of doing so. However, at the same time, there is evidence that explicit and implicit ToM operations share some functional features, including drawing on executive resources. Based on the available evidence, we propose that implicit and explicit ToM operations overlap and should only be considered partially distinct.

Implicit Social Biases in People with Autism

PubMed Central

Birmingham, Elina; Stanley, Damian; Nair, Remya; Adolphs, Ralph

2015-01-01

Implicit social biases are ubiquitous and are known to influence social behavior. A core diagnostic criterion of Autism Spectrum Disorder (ASD) is abnormal social behavior. Here we investigated the extent to which individuals with ASD might show a specific attenuation of implicit social biases, using the Implicit Association Test (IAT) across Social (gender, race) and Nonsocial (flowers/insect, shoes) categories. High-functioning adults with ASD showed intact but reduced IAT effects relative to healthy controls. Importantly, we observed no selective attenuation of implicit social (vs. nonsocial) biases in our ASD population. To extend these results, we collected data from a large online sample of the general population, and explored correlations between autistic traits and IAT effects. No associations were found between autistic traits and IAT effects for any of the categories tested in our online sample. Taken together, these results suggest that implicit social biases, as measured by the IAT, are largely intact in ASD. PMID:26386014

Two-time correlation function of an open quantum system in contact with a Gaussian reservoir

NASA Astrophysics Data System (ADS)

Ban, Masashi; Kitajima, Sachiko; Shibata, Fumiaki

2018-05-01

An exact formula of a two-time correlation function is derived for an open quantum system which interacts with a Gaussian thermal reservoir. It is provided in terms of functional derivative with respect to fictitious fields. A perturbative expansion and its diagrammatic representation are developed, where the small expansion parameter is related to a correlation time of the Gaussian thermal reservoir. The two-time correlation function of the lowest order is equivalent to that calculated by means of the quantum regression theorem. The result clearly shows that the violation of the quantum regression theorem is caused by a finiteness of the reservoir correlation time. By making use of an exactly solvable model consisting of a two-level system and a set of harmonic oscillators, it is shown that the two-time correlation function up to the first order is a good approximation to the exact one.

An introduction to generalized functions with some applications in aerodynamics and aeroacoustics

NASA Technical Reports Server (NTRS)

Farassat, F.

1994-01-01

In this paper, we start with the definition of generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support. The concept of generalization differentiation is introduced next. This is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some of the results of classical analysis, such as Leibniz rule of differentiation under the integral sign and the divergence theorem, are derived using the generalized function theory. It is shown that the divergence theorem remains valid for discontinuous vector fields provided that the derivatives are all viewed as generalized derivatives. This implies that all conservation laws of fluid mechanics are valid as they stand for discontinuous fields with all derivatives treated as generalized deriatives. Once these derivatives are written as ordinary derivatives and jumps in the field parameters across discontinuities, the jump conditions can be easily found. For example, the unsteady shock jump conditions can be derived from mass and momentum conservation laws. By using a generalized function theory, this derivative becomes trivial. Other applications of the generalized function theory in aerodynamics discussed in this paper are derivation of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of finite part of divergent integrals, derivation of Oswatiitsch integral equation of transonic flow, and analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics presented here include the derivation of the Kirchoff formula for moving surfaces,the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation.

Shrunk loop theorem for the topology probabilities of closed Brownian (or Feynman) paths on the twice punctured plane

NASA Astrophysics Data System (ADS)

Giraud, O.; Thain, A.; Hannay, J. H.

2004-02-01

The shrunk loop theorem proved here is an integral identity which facilitates the calculation of the relative probability (or probability amplitude) of any given topology that a free, closed Brownian (or Feynman) path of a given 'duration' might have on the twice punctured plane (plane with two marked points). The result is expressed as a 'scattering' series of integrals of increasing dimensionality based on the maximally shrunk version of the path. Physically, this applies in different contexts: (i) the topology probability of a closed ideal polymer chain on a plane with two impassable points, (ii) the trace of the Schrödinger Green function, and thence spectral information, in the presence of two Aharonov-Bohm fluxes and (iii) the same with two branch points of a Riemann surface instead of fluxes. Our theorem starts from the Stovicek scattering expansion for the Green function in the presence of two Aharonov-Bohm flux lines, which itself is based on the famous Sommerfeld one puncture point solution of 1896 (the one puncture case has much easier topology, just one winding number). Stovicek's expansion itself can supply the results at the expense of choosing a base point on the loop and then integrating it away. The shrunk loop theorem eliminates this extra two-dimensional integration, distilling the topology from the geometry.

Implicit unified gas-kinetic scheme for steady state solutions in all flow regimes

NASA Astrophysics Data System (ADS)

Zhu, Yajun; Zhong, Chengwen; Xu, Kun

2016-06-01

This paper presents an implicit unified gas-kinetic scheme (UGKS) for non-equilibrium steady state flow computation. The UGKS is a direct modeling method for flow simulation in all regimes with the updates of both macroscopic flow variables and microscopic gas distribution function. By solving the macroscopic equations implicitly, a predicted equilibrium state can be obtained first through iterations. With the newly predicted equilibrium state, the evolution equation of the gas distribution function and the corresponding collision term can be discretized in a fully implicit way for fast convergence through iterations as well. The lower-upper symmetric Gauss-Seidel (LU-SGS) factorization method is implemented to solve both macroscopic and microscopic equations, which improves the efficiency of the scheme. Since the UGKS is a direct modeling method and its physical solution depends on the mesh resolution and the local time step, a physical time step needs to be fixed before using an implicit iterative technique with a pseudo-time marching step. Therefore, the physical time step in the current implicit scheme is determined by the same way as that in the explicit UGKS for capturing the physical solution in all flow regimes, but the convergence to a steady state speeds up through the adoption of a numerical time step with large CFL number. Many numerical test cases in different flow regimes from low speed to hypersonic ones, such as the Couette flow, cavity flow, and the flow passing over a cylinder, are computed to validate the current implicit method. The overall efficiency of the implicit UGKS can be improved by one or two orders of magnitude in comparison with the explicit one.

Generalized quantum no-go theorems of pure states

NASA Astrophysics Data System (ADS)

Li, Hui-Ran; Luo, Ming-Xing; Lai, Hong

2018-07-01

Various results of the no-cloning theorem, no-deleting theorem and no-superposing theorem in quantum mechanics have been proved using the superposition principle and the linearity of quantum operations. In this paper, we investigate general transformations forbidden by quantum mechanics in order to unify these theorems. First, we prove that any useful information cannot be created from an unknown pure state which is randomly chosen from a Hilbert space according to the Harr measure. And then, we propose a unified no-go theorem based on a generalized no-superposing result. The new theorem includes the no-cloning theorem, no-anticloning theorem, no-partial-erasure theorem, no-splitting theorem, no-superposing theorem or no-encoding theorem as a special case. Moreover, it implies various new results. Third, we extend the new theorem into another form that includes the no-deleting theorem as a special case.

Discrimination of Native-like States of Membrane Proteins with Implicit Membrane-based Scoring Functions.

PubMed

Dutagaci, Bercem; Wittayanarakul, Kitiyaporn; Mori, Takaharu; Feig, Michael

2017-06-13

A scoring protocol based on implicit membrane-based scoring functions and a new protocol for optimizing the positioning of proteins inside the membrane was evaluated for its capacity to discriminate native-like states from misfolded decoys. A decoy set previously established by the Baker lab (Proteins: Struct., Funct., Genet. 2006, 62, 1010-1025) was used along with a second set that was generated to cover higher resolution models. The Implicit Membrane Model 1 (IMM1), IMM1 model with CHARMM 36 parameters (IMM1-p36), generalized Born with simple switching (GBSW), and heterogeneous dielectric generalized Born versions 2 (HDGBv2) and 3 (HDGBv3) were tested along with the new HDGB van der Waals (HDGBvdW) model that adds implicit van der Waals contributions to the solvation free energy. For comparison, scores were also calculated with the distance-scaled finite ideal-gas reference (DFIRE) scoring function. Z-scores for native state discrimination, energy vs root-mean-square deviation (RMSD) correlations, and the ability to select the most native-like structures as top-scoring decoys were evaluated to assess the performance of the scoring functions. Ranking of the decoys in the Baker set that were relatively far from the native state was challenging and dominated largely by packing interactions that were captured best by DFIRE with less benefit of the implicit membrane-based models. Accounting for the membrane environment was much more important in the second decoy set where especially the HDGB-based scoring functions performed very well in ranking decoys and providing significant correlations between scores and RMSD, which shows promise for improving membrane protein structure prediction and refinement applications. The new membrane structure scoring protocol was implemented in the MEMScore web server ( http://feiglab.org/memscore ).

Optical theorem for two-dimensional (2D) scalar monochromatic acoustical beams in cylindrical coordinates.

PubMed

Mitri, F G

2015-09-01

The optical theorem for plane waves is recognized as one of the fundamental theorems in optical, acoustical and quantum wave scattering theory as it relates the extinction cross-section to the forward scattering complex amplitude function. Here, the optical theorem is extended and generalized in a cylindrical coordinates system for the case of 2D beams of arbitrary character as opposed to plane waves of infinite extent. The case of scalar monochromatic acoustical wavefronts is considered, and generalized analytical expressions for the extinction, absorption and scattering cross-sections are derived and extended in the framework of the scalar resonance scattering theory. The analysis reveals the presence of an interference scattering cross-section term describing the interaction between the diffracted Franz waves with the resonance elastic waves. The extended optical theorem in cylindrical coordinates is applicable to any object of arbitrary geometry in 2D located arbitrarily in the beam's path. Related investigations in optics, acoustics and quantum mechanics will benefit from this analysis in the context of wave scattering theory and other phenomena closely connected to it, such as the multiple scattering by a cloud of particles, as well as the resulting radiation force and torque. Copyright © 2015 Elsevier B.V. All rights reserved.

Defensive function of persecutory delusion and discrepancy between explicit and implicit self-esteem in schizophrenia: study using the Brief Implicit Association Test

PubMed Central

Nakamura, Mitsuo; Hayakawa, Tomomi; Okamura, Aiko; Kohigashi, Mutsumi; Fukui, Kenji; Narumoto, Jin

2015-01-01

Background If delusions serve as a defense mechanism in schizophrenia patients with paranoia, then they should show normal or high explicit self-esteem and low implicit self-esteem. However, the results of previous studies are inconsistent. One possible explanation for this inconsistency is that there are two types of paranoia, “bad me” (self-blaming) paranoia and “poor me” (non-self-blaming) paranoia. We thus examined implicit and explicit self-esteem and self-blaming tendency in patients with schizophrenia and schizoaffective disorder. We hypothesized that patients with paranoia would show lower implicit self-esteem and only those with non-self-blaming paranoia would experience a discrepancy between explicit and implicit self-esteem. Methods Participants consisted of patients with schizophrenia and schizoaffective disorder recruited from a day hospital (N=71). Participants were assessed for psychotic symptoms, using the Brief Psychiatric Rating Scale (BPRS), and self-blaming tendency, using the brief COPE. We also assessed explicit self-esteem, using the Rosenberg Self-Esteem Scale (RSES), implicit self-esteem, using Brief Implicit Association Test (BIAT), and discrepancy between explicit and implicit self-esteem. Results Contrary to our hypothesis, implicit self-esteem in paranoia and nonparanoia showed no statistical difference. As expected, only patients with non-self-blaming paranoia experienced a discrepancy between explicit and implicit self-esteem; other groups showed no such discrepancy. Conclusion These results suggest that persecutory delusion plays a defensive role in non-self-blaming paranoia. PMID:25565849

A new approach for describing glass transition kinetics.

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

Vasin, N. M.; Shchelkachev, M. G.; Vinokur, V. M.

2010-04-01

We use a functional integral technique generalizing the Keldysh diagram technique to describe glass transition kinetics. We show that the Keldysh functional approach takes the dynamical determinant arising in the glass dynamics into account exactly and generalizes the traditional approach based on using the supersymmetric dynamic generating functional method. In contrast to the supersymmetric method, this approach allows avoiding additional Grassmannian fields and tracking the violation of the fluctuation-dissipation theorem explicitly. We use this method to describe the dynamics of an Edwards-Anderson soft spin-glass-type model near the paramagnet-glass transition. We show that a Vogel-Fulcher-type dynamics arises in the fluctuation regionmore » only if the fluctuation-dissipation theorem is violated in the process of dynamical renormalization of the Keldysh action in the replica space.« less

Implicit Plasma Kinetic Simulation Using The Jacobian-Free Newton-Krylov Method

NASA Astrophysics Data System (ADS)

Taitano, William; Knoll, Dana; Chacon, Luis

2009-11-01

The use of fully implicit time integration methods in kinetic simulation is still area of algorithmic research. A brute-force approach to simultaneously including the field equations and the particle distribution function would result in an intractable linear algebra problem. A number of algorithms have been put forward which rely on an extrapolation in time. They can be thought of as linearly implicit methods or one-step Newton methods. However, issues related to time accuracy of these methods still remain. We are pursuing a route to implicit plasma kinetic simulation which eliminates extrapolation, eliminates phase-space from the linear algebra problem, and converges the entire nonlinear system within a time step. We accomplish all this using the Jacobian-Free Newton-Krylov algorithm. The original research along these lines considered particle methods to advance the distribution function [1]. In the current research we are advancing the Vlasov equations on a grid. Results will be presented which highlight algorithmic details for single species electrostatic problems and coupled ion-electron electrostatic problems. [4pt] [1] H. J. Kim, L. Chac'on, G. Lapenta, ``Fully implicit particle in cell algorithm,'' 47th Annual Meeting of the Division of Plasma Physics, Oct. 24-28, 2005, Denver, CO

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

Meadows, B.T.; /Cincinnati U.

A new approach to the analysis of three body decays is presented. Model-independent results are obtained for the S-wave K{pi} amplitude as a function of K{pi} invariant mass. These are compared with results from K{sup -}{pi}{sup +} elastic scattering, and the prediction of the Watson theorem, that the phase behavior be the same below K{eta}' threshold, is tested. Contributions from I = 1/2 and I = 3/2 are not resolved in this study. If I = 1/2 dominates, however, the Watson theorem does not describe these data well.

Monterey Bay Geoid

DTIC Science & Technology

1994-03-01

thought to be a flat disk. The first scientific hypothesis that the earth was spherical is credited to Thales of Milet in 600 B.C. or Pythagoras in 550...acceleration can be integrated over the surface, by Gauss’s theorem and gives: 35 v1 Wv2 <v3 Figure 12. Equipotential Surfaces and Gravity: V,, V2, V3 are...continuous derivatives where they satisfy Laplace’s equation. Stokes’ theorem states that a harmonic function outside a surface is uniquely determined by

On Leighton's comparison theorem

NASA Astrophysics Data System (ADS)

Ghatasheh, Ahmed; Weikard, Rudi

2017-06-01

We give a simple proof of a fairly flexible comparison theorem for equations of the type -(p (u‧ + su)) ‧ + rp (u‧ + su) + qu = 0 on a finite interval where 1 / p, r, s, and q are real and integrable. Flexibility is provided by two functions which may be chosen freely (within limits) according to the situation at hand. We illustrate this by presenting some examples and special cases which include Schrödinger equations with distributional potentials as well as Jacobi difference equations.

Implicit perceptual-motor skill learning in mild cognitive impairment and Parkinson's disease.

PubMed

Gobel, Eric W; Blomeke, Kelsey; Zadikoff, Cindy; Simuni, Tanya; Weintraub, Sandra; Reber, Paul J

2013-05-01

Implicit skill learning is hypothesized to depend on nondeclarative memory that operates independent of the medial temporal lobe (MTL) memory system and instead depends on cortico striatal circuits between the basal ganglia and cortical areas supporting motor function and planning. Research with the Serial Reaction Time (SRT) task suggests that patients with memory disorders due to MTL damage exhibit normal implicit sequence learning. However, reports of intact learning rely on observations of no group differences, leading to speculation as to whether implicit sequence learning is fully intact in these patients. Patients with Parkinson's disease (PD) often exhibit impaired sequence learning, but this impairment is not universally observed. Implicit perceptual-motor sequence learning was examined using the Serial Interception Sequence Learning (SISL) task in patients with amnestic Mild Cognitive Impairment (MCI; n = 11) and patients with PD (n = 15). Sequence learning in SISL is resistant to explicit learning and individually adapted task difficulty controls for baseline performance differences. Patients with MCI exhibited robust sequence learning, equivalent to healthy older adults (n = 20), supporting the hypothesis that the MTL does not contribute to learning in this task. In contrast, the majority of patients with PD exhibited no sequence-specific learning in spite of matched overall task performance. Two patients with PD exhibited performance indicative of an explicit compensatory strategy suggesting that impaired implicit learning may lead to greater reliance on explicit memory in some individuals. The differences in learning between patient groups provides strong evidence in favor of implicit sequence learning depending solely on intact basal ganglia function with no contribution from the MTL memory system.

Separated-pair independent particle model and the generalized Brillouin theorem: ab initio calculations on the dissociation of polyatomic molecules

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

Sundberg, Kenneth Randall

1976-01-01

A method is developed to optimize the separated-pair independent particle (SPIP) wave function; it is a special case of the separated-pair theory obtained by using two-term natural expansions of the geminals. The orbitals are optimized by a theory based on the generalized Brillouin theorem and iterative configuration interaction (CI) calculations in the space of the SPIP function and its single excitations. The geminal expansion coefficients are optimized by serial 2 x 2 CI calculations. Formulas are derived for the matrix elements. An algorithm to implement the method is presented, and the work needed to evaluate the molecular integrals is discussed.

Uniqueness and characterization theorems for generalized entropies

NASA Astrophysics Data System (ADS)

Enciso, Alberto; Tempesta, Piergiulio

2017-12-01

The requirement that an entropy function be composable is key: it means that the entropy of a compound system can be calculated in terms of the entropy of its independent components. We prove that, under mild regularity assumptions, the only composable generalized entropy in trace form is the Tsallis one-parameter family (which contains Boltzmann-Gibbs as a particular case). This result leads to the use of generalized entropies that are not of trace form, such as Rényi’s entropy, in the study of complex systems. In this direction, we also present a characterization theorem for a large class of composable non-trace-form entropy functions with features akin to those of Rényi’s entropy.

Calculational Schemes in GUTs

NASA Astrophysics Data System (ADS)

Kounnas, Costas

The following sections are included: * Introduction * Mass Spectrum in a Spontaneously Broken-Theory SU(5) - Minimal Model * Renormalization and Renormalization Group Equation (R.G.E.) * Step Approximation and Decoupling Theorem * Notion of the Effective Coupling Constant * First Estimation of MX, α(MX) and sin2θ(MW) * Renormalization Properties and Photon-Z Mixing * β-Function Definitions * Threshold Functions and Decoupling Theorem * MX-Determination * Proton Lifetime * sin2θ(μ)-Determination * Quark-Lepton Mass Relations (mb/mτ) * Overview of the Conventional GUTs - Hierarchy Problem * Stability of Hierarchy - Supersymmetric GUTS * Cosmologically Acceptable SUSY GUT Models * Radiative Breaking of SU(2) × U(1) — MW/MX Hierarchy Generation * No Scale Supergravity Models^{56,57} Dynamical Determination of M_{B}-M_{F} * Conclusion * References

On the Maxwellian distribution, symmetric form, and entropy conservation for the Euler equations

NASA Technical Reports Server (NTRS)

Deshpande, S. M.

1986-01-01

The Euler equations of gas dynamics have some very interesting properties in that the flux vector is a homogeneous function of the unknowns and the equations can be cast in symmetric hyperbolic form and satisfy the entropy conservation. The Euler equations are the moments of the Boltzmann equation of the kinetic theory of gases when the velocity distribution function is a Maxwellian. The present paper shows the relationship between the symmetrizability and the Maxwellian velocity distribution. The entropy conservation is in terms of the H-function, which is a slight modification of the H-function first introduced by Boltzmann in his famous H-theorem. In view of the H-theorem, it is suggested that the development of total H-diminishing (THD) numerical methods may be more profitable than the usual total variation diminishing (TVD) methods for obtaining wiggle-free solutions.

A brief history of partitions of numbers, partition functions and their modern applications

NASA Astrophysics Data System (ADS)

Debnath, Lokenath

2016-04-01

'Number rules the universe.' The Pythagoras 'If you wish to forsee the future of mathematics our course is to study the history and present conditions of the science.' Henri Poincaré 'The primary source (Urqell) of all mathematics are integers.' Hermann Minkowski This paper is written to commemorate the centennial anniversary of the Mathematical Association of America. It deals with a short history of different kinds of natural numbers including triangular, square, pentagonal, hexagonal and k-gonal numbers, and their simple properties and their geometrical representations. Included are Euclid's and Pythagorean's main contributions to elementary number theory with the main contents of the Euclid Elements of the 13-volume masterpiece of mathematical work. This is followed by Euler's new discovery of the additive number theory based on partitions of numbers. Special attention is given to many examples, Euler's theorems on partitions of numbers with geometrical representations of Ferrers' graphs, Young's diagrams, Lagrange's four-square theorem and the celebrated Waring problem. Included are Euler's generating functions for the partitions of numbers, Euler's pentagonal number theorem, Gauss' triangular and square number theorems and the Jacobi triple product identity. Applications of the theory of partitions of numbers to different statistics such as the Bose- Einstein, Fermi- Dirac, Gentile, and Maxwell- Boltzmann statistics are briefly discussed. Special attention is given to pedagogical information through historical approach to number theory so that students and teachers at the school, college and university levels can become familiar with the basic concepts of partitions of numbers, partition functions and their modern applications, and can pursue advanced study and research in analytical and computational number theory.

Applying the multivariate time-rescaling theorem to neural population models

PubMed Central

Gerhard, Felipe; Haslinger, Robert; Pipa, Gordon

2011-01-01

Statistical models of neural activity are integral to modern neuroscience. Recently, interest has grown in modeling the spiking activity of populations of simultaneously recorded neurons to study the effects of correlations and functional connectivity on neural information processing. However any statistical model must be validated by an appropriate goodness-of-fit test. Kolmogorov-Smirnov tests based upon the time-rescaling theorem have proven to be useful for evaluating point-process-based statistical models of single-neuron spike trains. Here we discuss the extension of the time-rescaling theorem to the multivariate (neural population) case. We show that even in the presence of strong correlations between spike trains, models which neglect couplings between neurons can be erroneously passed by the univariate time-rescaling test. We present the multivariate version of the time-rescaling theorem, and provide a practical step-by-step procedure for applying it towards testing the sufficiency of neural population models. Using several simple analytically tractable models and also more complex simulated and real data sets, we demonstrate that important features of the population activity can only be detected using the multivariate extension of the test. PMID:21395436

Propofol and memory: a study using a process dissociation procedure and functional magnetic resonance imaging.

PubMed

Quan, X; Yi, J; Ye, T H; Tian, S Y; Zou, L; Yu, X R; Huang, Y G

2013-04-01

Thirty volunteers randomly received either mild or deep propofol sedation, to assess its effect on explicit and implicit memory. Blood oxygen level-dependent functional magnetic resonance during sedation examined brain activation by auditory word stimulus and a process dissociation procedure was performed 4 h after scanning. Explicit memory formation did not occur in either group. Implicit memories were formed during mild but not deep sedation (p = 0.04). Mild propofol sedation inhibited superior temporal gyrus activation (Z value 4.37, voxel 167). Deep propofol sedation inhibited superior temporal gyrus (Z value 4.25, voxel 351), middle temporal gyrus (Z value 4.39, voxel 351) and inferior parietal lobule (Z value 5.06, voxel 239) activation. Propofol only abolishes implicit memory during deep sedation. The superior temporal gyrus is associated with explicit memory processing, while the formation of both implicit and explicit memories is associated with superior and middle temporal gyri and inferior parietal lobule activation. Anaesthesia © 2013 The Association of Anaesthetists of Great Britain and Ireland.

Time Asymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

Bohm, Arno R.; Gadella, Manuel; Kielanowski, Piotr

2011-09-01

The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.

The role of expression and race in weapons identification.

PubMed

Kubota, Jennifer T; Ito, Tiffany A

2014-12-01

Emotional expressions can signal intentions and so possess the power to moderate social inferences. Here, we test whether stereotypes implicitly elicited by a stigmatized racial outgroup member are moderated by facial expression. Participants classified pictures of guns and tools that were primed with pictures of Black and White male faces posing angry, happy, and neutral expressions. Across the 3 measures examined--response latencies, error rates, and automatic processing, facial expression modulated implicit stereotyping (Study 1, n = 71; Study 2, n = 166). A Black angry prime elicited implicit stereotyping, while a Black happy prime diminished implicit stereotyping. Responding after neutral primes varied as a function of the expression context. When viewed alongside more threatening expressions (Study 1), neutral Black targets no longer elicited implicit stereotyping, but when viewed alongside more threatening expressions (Study 2), neutral Black targets primed crime and danger-relevant stereotypes. These results demonstrate that an individual can activate different associations based on changes in emotional expression and that a feature present in many everyday encounters (a smile) attenuates implicit racial stereotyping.

Intact implicit statistical learning in borderline personality disorder.

PubMed

Unoka, Zsolt; Vizin, Gabriella; Bjelik, Anna; Radics, Dóra; Nemeth, Dezso; Janacsek, Karolina

2017-09-01

Wide-spread neuropsychological deficits have been identified in borderline personality disorder (BPD). Previous research found impairments in decision making, declarative memory, working memory and executive functions; however, no studies have focused on implicit learning in BPD yet. The aim of our study was to investigate implicit statistical learning by comparing learning performance of 19 BPD patients and 19 healthy, age-, education- and gender-matched controls on a probabilistic sequence learning task. Moreover, we also tested whether participants retain the acquired knowledge after a delay period. To this end, participants were retested on a shorter version of the same task 24h after the learning phase. We found intact implicit statistical learning as well as retention of the acquired knowledge in this personality disorder. BPD patients seem to be able to extract and represent regularities implicitly, which is in line with the notion that implicit learning is less susceptible to illness compared to the more explicit processes. Copyright © 2017 Elsevier Ireland Ltd. All rights reserved.

Implicit solvation model for density-functional study of nanocrystal surfaces and reaction pathways

NASA Astrophysics Data System (ADS)

Mathew, Kiran; Sundararaman, Ravishankar; Letchworth-Weaver, Kendra; Arias, T. A.; Hennig, Richard G.

2014-02-01

Solid-liquid interfaces are at the heart of many modern-day technologies and provide a challenge to many materials simulation methods. A realistic first-principles computational study of such systems entails the inclusion of solvent effects. In this work, we implement an implicit solvation model that has a firm theoretical foundation into the widely used density-functional code Vienna ab initio Software Package. The implicit solvation model follows the framework of joint density functional theory. We describe the framework, our algorithm and implementation, and benchmarks for small molecular systems. We apply the solvation model to study the surface energies of different facets of semiconducting and metallic nanocrystals and the SN2 reaction pathway. We find that solvation reduces the surface energies of the nanocrystals, especially for the semiconducting ones and increases the energy barrier of the SN2 reaction.

The hormonal correlates of implicit power motivation

PubMed Central

Stanton, Steven J.; Schultheiss, Oliver C.

2009-01-01

Attempts to link testosterone to dominance dispositions using self-report measures of dominance have yielded inconsistent findings. Similarly, attempts to link testosterone changes to a situational outcome like winning or losing a dominance contest have yielded inconsistent findings. However, research has consistently shown that an indirect measure of an individual’s dominance disposition, implicit power motivation, is positively related to baseline testosterone levels and, in interaction with situational outcomes, predicts testosterone changes. We propose a hormonal model of implicit power motivation that describes how testosterone levels change as an interactive function of individuals’ implicit power motivation and dominance situations. We also propose that estradiol, and not testosterone, plays a key role in dominance motivation in women. PMID:20161646

A semi-implicit level set method for multiphase flows and fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Cottet, Georges-Henri; Maitre, Emmanuel

2016-06-01

In this paper we present a novel semi-implicit time-discretization of the level set method introduced in [8] for fluid-structure interaction problems. The idea stems from a linear stability analysis derived on a simplified one-dimensional problem. The semi-implicit scheme relies on a simple filter operating as a pre-processing on the level set function. It applies to multiphase flows driven by surface tension as well as to fluid-structure interaction problems. The semi-implicit scheme avoids the stability constraints that explicit scheme need to satisfy and reduces significantly the computational cost. It is validated through comparisons with the original explicit scheme and refinement studies on two-dimensional benchmarks.

Quantum identities for the action

NASA Astrophysics Data System (ADS)

Gozzi, E.

2018-04-01

In this paper we derive various identities involving the action functional which enters the path-integral formulation of quantum mechanics. They provide some kind of generalisations of the Ehrenfest theorem giving correlations between powers of the action and its functional derivatives.

Quantum computing without wavefunctions: time-dependent density functional theory for universal quantum computation.

PubMed

Tempel, David G; Aspuru-Guzik, Alán

2012-01-01

We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms.

The Law of Self-Acting Machines and Irreversible Processes with Reversible Replicas

NASA Astrophysics Data System (ADS)

Valev, Pentcho

2002-11-01

Clausius and Kelvin saved Carnot theorem and developed the second law by assuming that Carnot machines can work in the absence of an operator and that all the irreversible processes have reversible replicas. The former assumption restored Carnot theorem as an experience of mankind whereas the latter generated "the law of ever increasing entropy". Both assumptions are wrong so it makes sense to return to Carnot theorem (or some equivalent) and test it experimentally. Two testable paradigms - the system performing two types of reversible work and the system in dynamical equilibrium - suggest that perpetuum mobile of the second kind in the presence of an operator is possible. The deviation from the second law prediction, expressed as difference between partial derivatives in a Maxwell relation, measures the degree of structural-functional evolution for the respective system.

The extinction properties of forest components

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.; Blanchard, A. J.; Nance, C. E.

1988-01-01

The effect of each forest component on the extinction of electromagnetic waves is investigated by modeling the branches with finite cylinders, deciduous leaves with elliptic disks, and coniferous leaves with needles. The inner field is estimated by the field inside an infinitely long cylinder of similar properties for the branches, and by the Shifrin approximation for the leaves. For each forest component analytic expressions were derived for the extinction cross section via the forward scattering theorem and for ohmic and scattered losses. For branches, the variation of the extinction cross section obtained via the forward scattering theorem is illustrated numerically as a function of the branch radius and the imaginery part of its dielectric constant. It is compared with the measurements from a single branch. For the leaves, the forward scattering theorem gives value for the extinction cross section equal to the ohmic cross section.

Elementary solutions of coupled model equations in the kinetic theory of gases

NASA Technical Reports Server (NTRS)

Kriese, J. T.; Siewert, C. E.; Chang, T. S.

1974-01-01

The method of elementary solutions is employed to solve two coupled integrodifferential equations sufficient for determining temperature-density effects in a linearized BGK model in the kinetic theory of gases. Full-range completeness and orthogonality theorems are proved for the developed normal modes and the infinite-medium Green's function is constructed as an illustration of the full-range formalism. The appropriate homogeneous matrix Riemann problem is discussed, and half-range completeness and orthogonality theorems are proved for a certain subset of the normal modes. The required existence and uniqueness theorems relevant to the H matrix, basic to the half-range analysis, are proved, and an accurate and efficient computational method is discussed. The half-space temperature-slip problem is solved analytically, and a highly accurate value of the temperature-slip coefficient is reported.

A harbinger of plate tectonics: a commentary on Bullard, Everett and Smith (1965) 'The fit of the continents around the Atlantic'.

PubMed

Dewey, John F

2015-04-13

In the 1960s, geology was transformed by the paradigm of plate tectonics. The 1965 paper of Bullard, Everett and Smith was a linking transition between the theories of continental drift and plate tectonics. They showed, conclusively, that the continents around the Atlantic were once contiguous and that the Atlantic Ocean had grown at rates of a few centimetres per year since the Early Jurassic, about 160 Ma. They achieved fits of the continental margins at the 500 fathom line (approx. 900 m), not the shorelines, by minimizing misfits between conjugate margins and finding axes, poles and angles of rotation, using Euler's theorem, that defined the unique single finite difference rotation that carried congruent continents from contiguity to their present positions, recognizing that the real motion may have been more complex around a number of finite motion poles. Critically, they were concerned only with kinematic reality and were not restricted by considerations of the mechanism by which continents split and oceans grow. Many of the defining features of plate tectonics were explicit or implicit in their reconstructions, such as the torsional rigidity of continents, Euler's theorem, closure of the Tethyan ocean(s), major continental margin shear zones, the rapid rotation of small continental blocks (Iberia) around nearby poles, the consequent opening of small wedge-shaped oceans (Bay of Biscay), and misfit overlaps (deltas and volcanic piles) and underlaps (stretched continental edges). This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

A harbinger of plate tectonics: a commentary on Bullard, Everett and Smith (1965) ‘The fit of the continents around the Atlantic’

PubMed Central

Dewey, John F.

2015-01-01

In the 1960s, geology was transformed by the paradigm of plate tectonics. The 1965 paper of Bullard, Everett and Smith was a linking transition between the theories of continental drift and plate tectonics. They showed, conclusively, that the continents around the Atlantic were once contiguous and that the Atlantic Ocean had grown at rates of a few centimetres per year since the Early Jurassic, about 160 Ma. They achieved fits of the continental margins at the 500 fathom line (approx. 900 m), not the shorelines, by minimizing misfits between conjugate margins and finding axes, poles and angles of rotation, using Euler's theorem, that defined the unique single finite difference rotation that carried congruent continents from contiguity to their present positions, recognizing that the real motion may have been more complex around a number of finite motion poles. Critically, they were concerned only with kinematic reality and were not restricted by considerations of the mechanism by which continents split and oceans grow. Many of the defining features of plate tectonics were explicit or implicit in their reconstructions, such as the torsional rigidity of continents, Euler's theorem, closure of the Tethyan ocean(s), major continental margin shear zones, the rapid rotation of small continental blocks (Iberia) around nearby poles, the consequent opening of small wedge-shaped oceans (Bay of Biscay), and misfit overlaps (deltas and volcanic piles) and underlaps (stretched continental edges). This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society. PMID:25750142

An Implicit Measure of Associations with Mental Illness versus Physical Illness: Response Latency Decomposition and Stimuli Differential Functioning in Relation to IAT Order of Associative Conditions and Accuracy

PubMed Central

Mannarini, Stefania; Boffo, Marilisa

2014-01-01

The present study aimed at the definition of a latent measurement dimension underlying an implicit measure of automatic associations between the concept of mental illness and the psychosocial and biogenetic causal explanatory attributes. To this end, an Implicit Association Test (IAT) assessing the association between the Mental Illness and Physical Illness target categories to the Psychological and Biologic attribute categories, representative of the causal explanation domains, was developed. The IAT presented 22 stimuli (words and pictures) to be categorized into the four categories. After 360 university students completed the IAT, a Many-Facet Rasch Measurement (MFRM) modelling approach was applied. The model specified a person latency parameter and a stimulus latency parameter. Two additional parameters were introduced to denote the order of presentation of the task associative conditions and the general response accuracy. Beyond the overall definition of the latent measurement dimension, the MFRM was also applied to disentangle the effect of the task block order and the general response accuracy on the stimuli response latency. Further, the MFRM allowed detecting any differential functioning of each stimulus in relation to both block ordering and accuracy. The results evidenced: a) the existence of a latency measurement dimension underlying the Mental Illness versus Physical Illness - Implicit Association Test; b) significant effects of block order and accuracy on the overall latency; c) a differential functioning of specific stimuli. The results of the present study can contribute to a better understanding of the functioning of an implicit measure of semantic associations with mental illness and give a first blueprint for the examination of relevant issues in the development of an IAT. PMID:25000406

An implicit measure of associations with mental illness versus physical illness: response latency decomposition and stimuli differential functioning in relation to IAT order of associative conditions and accuracy.

PubMed

Mannarini, Stefania; Boffo, Marilisa

2014-01-01

The present study aimed at the definition of a latent measurement dimension underlying an implicit measure of automatic associations between the concept of mental illness and the psychosocial and biogenetic causal explanatory attributes. To this end, an Implicit Association Test (IAT) assessing the association between the Mental Illness and Physical Illness target categories to the Psychological and Biologic attribute categories, representative of the causal explanation domains, was developed. The IAT presented 22 stimuli (words and pictures) to be categorized into the four categories. After 360 university students completed the IAT, a Many-Facet Rasch Measurement (MFRM) modelling approach was applied. The model specified a person latency parameter and a stimulus latency parameter. Two additional parameters were introduced to denote the order of presentation of the task associative conditions and the general response accuracy. Beyond the overall definition of the latent measurement dimension, the MFRM was also applied to disentangle the effect of the task block order and the general response accuracy on the stimuli response latency. Further, the MFRM allowed detecting any differential functioning of each stimulus in relation to both block ordering and accuracy. The results evidenced: a) the existence of a latency measurement dimension underlying the Mental Illness versus Physical Illness - Implicit Association Test; b) significant effects of block order and accuracy on the overall latency; c) a differential functioning of specific stimuli. The results of the present study can contribute to a better understanding of the functioning of an implicit measure of semantic associations with mental illness and give a first blueprint for the examination of relevant issues in the development of an IAT.

On deriving the Maxwell stress tensor method for calculating the optical force and torque on an object in harmonic electromagnetic fields

NASA Astrophysics Data System (ADS)

Ye, Qian; Lin, Haoze

2017-07-01

Though extensively used in calculating optical force and torque acting on a material object illuminated by laser, the Maxwell stress tensor (MST) method follows the electromagnetic linear and angular momentum balance that is usually derived in most textbooks for a continuous volume charge distribution in free space, if not resorting to the application of Noether’s theorem in electrodynamics. To cast the conservation laws into a physically appealing form involving the current densities of linear and angular momentum, on which the MST method is based, the divergence theorem is employed to transform a volume integral into a surface integral. When a material object of finite volume is put into the field, it brings about a discontinuity of field across its surface, due to the presence of induced surface charge and surface current. Ambiguity arises among students in whether the divergence theorem can still be directly used without any justification. By taking into account the effect of the induced surface charge and current, we present a simple pedagogical derivation for the MST method for calculating the optical force and torque on an object immersed in monochromatic optical field, without resorting to Noether’s theorem. Although the results turn out to be identical to those given in the standard textbooks, our derivation avoids the direct use of the divergence theorem on a discontinuous function.

Walking Speed Influences the Effects of Implicit Visual Feedback Distortion on Modulation of Gait Symmetry

PubMed Central

Maestas, Gabrielle; Hu, Jiyao; Trevino, Jessica; Chunduru, Pranathi; Kim, Seung-Jae; Lee, Hyunglae

2018-01-01

The use of visual feedback in gait rehabilitation has been suggested to promote recovery of locomotor function by incorporating interactive visual components. Our prior work demonstrated that visual feedback distortion of changes in step length symmetry entails an implicit or unconscious adaptive process in the subjects’ spatial gait patterns. We investigated whether the effect of the implicit visual feedback distortion would persist at three different walking speeds (slow, self-preferred and fast speeds) and how different walking speeds would affect the amount of adaption. In the visual feedback distortion paradigm, visual vertical bars portraying subjects’ step lengths were distorted so that subjects perceived their step lengths to be asymmetric during testing. Measuring the adjustments in step length during the experiment showed that healthy subjects made spontaneous modulations away from actual symmetry in response to the implicit visual distortion, no matter the walking speed. In all walking scenarios, the effects of implicit distortion became more significant at higher distortion levels. In addition, the amount of adaptation induced by the visual distortion was significantly greater during walking at preferred or slow speed than at the fast speed. These findings indicate that although a link exists between supraspinal function through visual system and human locomotion, sensory feedback control for locomotion is speed-dependent. Ultimately, our results support the concept that implicit visual feedback can act as a dominant form of feedback in gait modulation, regardless of speed. PMID:29632481

Toward a Comprehensive Understanding of Executive Cognitive Function in Implicit Racial Bias

PubMed Central

Ito, Tiffany A.; Friedman, Naomi P.; Bartholow, Bruce D.; Correll, Joshua; Loersch, Chris; Altamirano, Lee J.; Miyake, Akira

2014-01-01

Although performance on laboratory-based implicit bias tasks often is interpreted strictly in terms of the strength of automatic associations, recent evidence suggests that such tasks are influenced by higher-order cognitive control processes, so-called executive functions (EFs). However, extant work in this area has been limited by failure to account for the unity and diversity of EFs, focus on only a single measure of bias and/or EF, and relatively small sample sizes. The current study sought to comprehensively model the relation between individual differences in EFs and the expression of racial bias in three commonly used laboratory measures. Participants (N=485) completed a battery of EF tasks (session 1) and three racial bias tasks (session 2), along with numerous individual difference questionnaires. The main findings were as follows: (1) measures of implicit bias were only weakly intercorrelated; (2) EF and estimates of automatic processes both predicted implicit bias and also interacted, such that the relation between automatic processes and bias expression was reduced at higher levels of EF; (3) specific facets of EF were differentially associated with overall task performance and controlled processing estimates across different bias tasks; (4) EF did not moderate associations between implicit and explicit measures of bias; and (5) external, but not internal, motivation to control prejudice depended on EF to reduce bias expression. Findings are discussed in terms of the importance of global and specific EF abilities in determining expression of implicit racial bias. PMID:25603372

Implicit Perceptual-Motor Skill Learning in Mild Cognitive Impairment and Parkinson's Disease

PubMed Central

Gobel, Eric W.; Blomeke, Kelsey; Zadikoff, Cindy; Simuni, Tanya; Weintraub, Sandy; Reber, Paul J.

2015-01-01

Objective Implicit skill learning is hypothesized to depend on nondeclarative memory that operates independent of the medial temporal lobe (MTL) memory system and instead depends on cortico-striatal circuits between the basal ganglia and cortical areas supporting motor function and planning. Research with the Serial Reaction Time (SRT) task suggests that patients with memory-disorders due to MTL damage exhibit normal implicit sequence learning. However, reports of intact learning rely on observations of no group differences, leading to speculation whether implicit sequence learning is fully intact in these patients. Patients with Parkinson's Disease (PD) often exhibit impaired sequence learning, but this impairment is not universally observed. Method Implicit perceptual-motor sequence learning was examined using the Serial Interception Sequence Learning (SISL) task in patients with amnestic Mild Cognitive Impairment (MCI; n=11) and patients with PD (n=15). Sequence learning in SISL is resistant to explicit learning and individually adapted task difficulty controls for baseline performance differences. Results Patients with MCI exhibited robust sequence learning, equivalent to healthy older adults (n=20), supporting the hypothesis that the MTL does not contribute to learning in this task. In contrast, the majority of patients with PD exhibited no sequence-specific learning in spite of matched overall task performance. Two patients with PD exhibited performance indicative of an explicit compensatory strategy suggesting that impaired implicit learning may lead to greater reliance on explicit memory in some individuals. Conclusion The differences in learning between patient groups provides strong evidence in favor of implicit sequence learning depending solely on intact basal ganglia function with no contribution from the MTL memory system. PMID:23688213

Completeness of the Coulomb Wave Functions in Quantum Mechanics

ERIC Educational Resources Information Center

Mukunda, N.

1978-01-01

Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)

Homoclinic orbits and critical points of barrier functions

NASA Astrophysics Data System (ADS)

Cannarsa, Piermarco; Cheng, Wei

2015-06-01

We interpret the close link between the critical points of Mather's barrier functions and minimal homoclinic orbits with respect to the Aubry sets on {{T}}n . We also prove a critical point theorem for barrier functions and the existence of such homoclinic orbits on {{T}}2 as an application.

Moderators of the Relationship between Implicit and Explicit Evaluation

PubMed Central

Nosek, Brian A.

2005-01-01

Automatic and controlled modes of evaluation sometimes provide conflicting reports of the quality of social objects. This paper presents evidence for four moderators of the relationship between automatic (implicit) and controlled (explicit) evaluations. Implicit and explicit preferences were measured for a variety of object pairs using a large sample. The average correlation was r = .36, and 52 of the 57 object pairs showed a significant positive correlation. Results of multilevel modeling analyses suggested that: (a) implicit and explicit preferences are related, (b) the relationship varies as a function of the objects assessed, and (c) at least four variables moderate the relationship – self-presentation, evaluative strength, dimensionality, and distinctiveness. The variables moderated implicit-explicit correspondence across individuals and accounted for much of the observed variation across content domains. The resulting model of the relationship between automatic and controlled evaluative processes is grounded in personal experience with the targets of evaluation. PMID:16316292

Implicit self-esteem compensation: automatic threat defense.

PubMed

Rudman, Laurie A; Dohn, Matthew C; Fairchild, Kimberly

2007-11-01

Four experiments demonstrated implicit self-esteem compensation (ISEC) in response to threats involving gender identity (Experiment 1), implicit racism (Experiment 2), and social rejection (Experiments 3-4). Under conditions in which people might be expected to suffer a blow to self-worth, they instead showed high scores on 2 implicit self-esteem measures. There was no comparable effect on explicit self-esteem. However, ISEC was eliminated following self-affirmation (Experiment 3). Furthermore, threat manipulations increased automatic intergroup bias, but ISEC mediated these relationships (Experiments 2-3). Thus, a process that serves as damage control for the self may have negative social consequences. Finally, pretest anxiety mediated the relationship between threat and ISEC (Experiment 3), whereas ISEC negatively predicted anxiety among high-threat participants (Experiment 4), suggesting that ISEC may function to regulate anxiety. The implications of these findings for automatic emotion regulation, intergroup bias, and implicit self-esteem measures are discussed. (c) 2007 APA, all rights reserved.

Medial temporal lobe-dependent repetition suppression and enhancement due to implicit vs. explicit processing of individual repeated search displays

PubMed Central

Geyer, Thomas; Baumgartner, Florian; Müller, Hermann J.; Pollmann, Stefan

2012-01-01

Using visual search, functional magnetic resonance imaging (fMRI) and patient studies have demonstrated that medial temporal lobe (MTL) structures differentiate repeated from novel displays—even when observers are unaware of display repetitions. This suggests a role for MTL in both explicit and, importantly, implicit learning of repeated sensory information (Greene et al., 2007). However, recent behavioral studies suggest, by examining visual search and recognition performance concurrently, that observers have explicit knowledge of at least some of the repeated displays (Geyer et al., 2010). The aim of the present fMRI study was thus to contribute new evidence regarding the contribution of MTL structures to explicit vs. implicit learning in visual search. It was found that MTL activation was increased for explicit and, respectively, decreased for implicit relative to baseline displays. These activation differences were most pronounced in left anterior parahippocampal cortex (aPHC), especially when observers were highly trained on the repeated displays. The data are taken to suggest that explicit and implicit memory processes are linked within MTL structures, but expressed via functionally separable mechanisms (repetition-enhancement vs. -suppression). They further show that repetition effects in visual search would have to be investigated at the display level. PMID:23060776

Altered Medial Frontal and Superior Temporal Response to Implicit Processing of Emotions in Autism.

PubMed

Kana, Rajesh K; Patriquin, Michelle A; Black, Briley S; Channell, Marie M; Wicker, Bruno

2016-01-01

Interpreting emotional expressions appropriately poses a challenge for individuals with autism spectrum disorder (ASD). In particular, difficulties with emotional processing in ASD are more pronounced in contexts where emotional expressions are subtle, automatic, and reflexive-that is, implicit. In contrast, explicit emotional processing, which requires the cognitive evaluation of an emotional experience, appears to be relatively intact in individuals with ASD. In the present study, we examined the brain activation and functional connectivity differences underlying explicit and implicit emotional processing in age- and IQ-matched adults with (n = 17) and without (n = 15) ASD. Results indicated: (1) significantly reduced levels of brain activation in participants with ASD in medial prefrontal cortex (MPFC) and superior temporal gyrus (STG) during implicit emotion processing; (2) significantly weaker functional connectivity in the ASD group in connections of the MPFC with the amygdala, temporal lobe, parietal lobe, and fusiform gyrus; (3) No group difference in performance accuracy or reaction time; and (4) Significant positive relationship between empathizing ability and STG activity in ASD but not in typically developing participants. These findings suggest that the neural mechanisms underlying implicit, but not explicit, emotion processing may be altered at multiple levels in individuals with ASD. © 2015 International Society for Autism Research, Wiley Periodicals, Inc.

Double-time correlation functions of two quantum operations in open systems

NASA Astrophysics Data System (ADS)

Ban, Masashi

2017-10-01

A double-time correlation function of arbitrary two quantum operations is studied for a nonstationary open quantum system which is in contact with a thermal reservoir. It includes a usual correlation function, a linear response function, and a weak value of an observable. Time evolution of the correlation function can be derived by means of the time-convolution and time-convolutionless projection operator techniques. For this purpose, a quasidensity operator accompanied by a fictitious field is introduced, which makes it possible to derive explicit formulas for calculating a double-time correlation function in the second-order approximation with respect to a system-reservoir interaction. The derived formula explicitly shows that the quantum regression theorem for calculating the double-time correlation function cannot be used if a thermal reservoir has a finite correlation time. Furthermore, the formula is applied for a pure dephasing process and a linear dissipative process. The quantum regression theorem and the the Leggett-Garg inequality are investigated for an open two-level system. The results are compared with those obtained by exact calculation to examine whether the formula is a good approximation.

Thermal transport in the Falicov-Kimball model

NASA Astrophysics Data System (ADS)

Freericks, J. K.; Zlatić, V.

2001-12-01

We prove the Jonson-Mahan theorem for the thermopower of the Falicov-Kimball model by solving explicitly for correlation functions in the large dimensional limit. We prove a similar result for the thermal conductivity. We separate the results for thermal transport into the pieces of the heat current that arise from the kinetic energy and those that arise from the potential energy. Our method of proof is specific to the Falicov-Kimball model, but illustrates the near cancellations between the kinetic- and potential-energy pieces of the heat current implied by the Jonson-Mahan theorem.

Memory-less response and violation of the fluctuation-dissipation theorem in colloids suspended in an active bath.

PubMed

Maggi, Claudio; Paoluzzi, Matteo; Angelani, Luca; Di Leonardo, Roberto

2017-12-14

We investigate experimentally and numerically the stochastic dynamics and the time-dependent response of colloids subject to a small external perturbation in a dense bath of motile E. coli bacteria. The external field is a magnetic field acting on a superparamagnetic microbead suspended in an active medium. The measured linear response reveals an instantaneous friction kernel despite the complexity of the bacterial bath. By comparing the mean squared displacement and the response function we detect a clear violation of the fluctuation dissipation theorem.

Power-law exponent of the Bouchaud-Mézard model on regular random networks

NASA Astrophysics Data System (ADS)

Ichinomiya, Takashi

2013-07-01

We study the Bouchaud-Mézard model on a regular random network. By assuming adiabaticity and independency, and utilizing the generalized central limit theorem and the Tauberian theorem, we derive an equation that determines the exponent of the probability distribution function of the wealth as x→∞. The analysis shows that the exponent can be smaller than 2, while a mean-field analysis always gives the exponent as being larger than 2. The results of our analysis are shown to be in good agreement with those of the numerical simulations.

Diagrams for the Free Energy and Density Weight Factors of the Ising Models.

DTIC Science & Technology

1983-01-01

sum to zero . The associated R. A. Farrell, T. Morita, and P. H. E. Meijer, "Cluster Expan- also, "_ ratum: New Generating Functions and Results for the...given for the cubic lattices. We employ a theorem that states that a certain sum of diagrams is zero in order to obtain the density-dependent weight...these diagrams are given for the cubic lattices. We employ a theorem that states that a certain sum of diagrams is zero in order to obtain the density

Generalization of the quasi-geostrophic Eliassen-Palm flux to include eddy forcing of condensation heating

NASA Technical Reports Server (NTRS)

Stone, P. H.; Salustri, G.

1984-01-01

A modified Eulerian form of the Eliassen-Palm flux which includes the effect of eddy forcing on condensation heating is defined. With the two-dimensional vector flux in the meridional plane which is a function of the zonal mean eddy fluxes replaced by the modified flux, both the Eliassen-Palm theorem and a modified but more general form of the nonacceleration theorem for quasi-geostrophic motion still hold. Calculations of the divergence of the modified flux and of the eddy forcing of the moisture field are presented.

The mere exposure effect in patients with schizophrenia.

PubMed

Marie, A; Gabrieli, J D; Vaidya, C; Brown, B; Pratto, F; Zajonc, R B; Shaw, R J

2001-01-01

The mere exposure effect refers to the development of an emotional preference for previously unfamiliar material because of frequent exposure to that material. This study compared schizophrenia subjects (n = 20) to normal controls (n = 21) to determine whether implicit memory, as demonstrated by the mere exposure effect, was intact. Patients with schizophrenia demonstrated a normal preference for both verbal and visual materials seen earlier relative to novel materials, despite impaired performance on a recognition task for explicit memory using similar materials. Previous studies of schizophrenia subjects have shown a dissociation between implicit and explicit memory on verbal tasks. We found a similar dissociation demonstrated by normal functioning on an implicit memory task and impaired functioning on an explicit memory task. Potential implications of these findings are discussed with regard to treatment and rehabilitation.

A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations

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

Carrie, Michael; Shadwick, B. A.

2016-01-04

Here, we present a time-implicit numerical method to solve the relativistic Vlasov–Ampere system of equations on a two dimensional phase space grid. The time-splitting algorithm we use allows the generalization of the work presented here to higher dimensions keeping the linear aspect of the resulting discrete set of equations. The implicit method is benchmarked against linear theory results for the relativistic Landau damping for which analytical expressions using the Maxwell-Juttner distribution function are derived. We note that, independently from the shape of the distribution function, the relativistic treatment features collective behaviors that do not exist in the non relativistic case.more » The numerical study of the relativistic two-stream instability completes the set of benchmarking tests.« less

A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations

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

Carrié, Michael, E-mail: mcarrie2@unl.edu; Shadwick, B. A., E-mail: shadwick@mailaps.org

2016-01-15

We present a time-implicit numerical method to solve the relativistic Vlasov–Ampere system of equations on a two dimensional phase space grid. The time-splitting algorithm we use allows the generalization of the work presented here to higher dimensions keeping the linear aspect of the resulting discrete set of equations. The implicit method is benchmarked against linear theory results for the relativistic Landau damping for which analytical expressions using the Maxwell-Jüttner distribution function are derived. We note that, independently from the shape of the distribution function, the relativistic treatment features collective behaviours that do not exist in the nonrelativistic case. The numericalmore » study of the relativistic two-stream instability completes the set of benchmarking tests.« less

The Role of Expression and Race in Weapons Identification

PubMed Central

Kubota, Jennifer T.; Ito, Tiffany A.

2014-01-01

Emotional expressions can signal intentions and so possess the power to moderate social inferences. Here we test whether stereotypes implicitly elicited by a stigmatized racial outgroup member are moderated by facial expression. Participants classified pictures of guns and tools that were primed with pictures of Black and White male faces posing angry, happy, and neutral expressions. Across the three measures examined—response latencies, error rates, and automatic processing— facial expression modulated implicit stereotyping (study 1, n=71; study 2, n=166). A Black angry prime elicited implicit stereotyping while a Black happy prime diminished implicit stereotyping. Responding after neutral primes varied as a function of the expression context. When viewed alongside more threatening expressions (study 1), neutral Black targets no longer elicited implicit stereotyping; but when viewed alongside more threatening expressions (study 2), neutral Black targets primed crime and danger-relevant stereotypes. These results demonstrate that an individual can activate different associations based on changes in emotional expression, and that a feature present in many everyday encounters (a smile) attenuates implicit racial stereotyping. PMID:25401289

Stokes' theorem, gauge symmetry and the time-dependent Aharonov-Bohm effect

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

Macdougall, James, E-mail: jbm34@mail.fresnostate.edu; Singleton, Douglas, E-mail: dougs@csufresno.edu

2014-04-15

Stokes' theorem is investigated in the context of the time-dependent Aharonov-Bohm effect—the two-slit quantum interference experiment with a time varying solenoid between the slits. The time varying solenoid produces an electric field which leads to an additional phase shift which is found to exactly cancel the time-dependent part of the usual magnetic Aharonov-Bohm phase shift. This electric field arises from a combination of a non-single valued scalar potential and/or a 3-vector potential. The gauge transformation which leads to the scalar and 3-vector potentials for the electric field is non-single valued. This feature is connected with the non-simply connected topology ofmore » the Aharonov-Bohm set-up. The non-single valued nature of the gauge transformation function has interesting consequences for the 4-dimensional Stokes' theorem for the time-dependent Aharonov-Bohm effect. An experimental test of these conclusions is proposed.« less

Implicit and Explicit Olfactory Memory in People with and without Down Syndrome

ERIC Educational Resources Information Center

Johns, Adam; Homewood, Judi; Stevenson, Richard; Taylor, Alan

2012-01-01

This study examined differences in implicit and explicit memory performance between people with Down syndrome (DS), their siblings, children matched on mental age, and university undergraduates, using olfactory stimuli. The DS and mental-age matched participants were also compared on two tasks of executive function. The data revealed implicit…

Accurate image-charge method by the use of the residue theorem for core-shell dielectric sphere

NASA Astrophysics Data System (ADS)

Fu, Jing; Xu, Zhenli

2018-02-01

An accurate image-charge method (ICM) is developed for ionic interactions outside a core-shell structured dielectric sphere. Core-shell particles have wide applications for which the theoretical investigation requires efficient methods for the Green's function used to calculate pairwise interactions of ions. The ICM is based on an inverse Mellin transform from the coefficients of spherical harmonic series of the Green's function such that the polarization charge due to dielectric boundaries is represented by a series of image point charges and an image line charge. The residue theorem is used to accurately calculate the density of the line charge. Numerical results show that the ICM is promising in fast evaluation of the Green's function, and thus it is useful for theoretical investigations of core-shell particles. This routine can also be applicable for solving other problems with spherical dielectric interfaces such as multilayered media and Debye-Hückel equations.

Symmetry for the duration of entropy-consuming intervals.

PubMed

García-García, Reinaldo; Domínguez, Daniel

2014-05-01

We introduce the violation fraction υ as the cumulative fraction of time that a mesoscopic system spends consuming entropy at a single trajectory in phase space. We show that the fluctuations of this quantity are described in terms of a symmetry relation reminiscent of fluctuation theorems, which involve a function Φ, which can be interpreted as an entropy associated with the fluctuations of the violation fraction. The function Φ, when evaluated for arbitrary stochastic realizations of the violation fraction, is odd upon the symmetry transformations that are relevant for the associated stochastic entropy production. This fact leads to a detailed fluctuation theorem for the probability density function of Φ. We study the steady-state limit of this symmetry in the paradigmatic case of a colloidal particle dragged by optical tweezers through an aqueous solution. Finally, we briefly discuss possible applications of our results for the estimation of free-energy differences from single-molecule experiments.

The Great Emch Closure Theorem and a combinatorial proof of Poncelet's Theorem

NASA Astrophysics Data System (ADS)

Avksentyev, E. A.

2015-11-01

The relations between the classical closure theorems (Poncelet's, Steiner's, Emch's, and the zigzag theorems) and some of their generalizations are discussed. It is known that Emch's Theorem is the most general of these, while the others follow as special cases. A generalization of Emch's Theorem to pencils of circles is proved, which (by analogy with the Great Poncelet Theorem) can be called the Great Emch Theorem. It is shown that the Great Emch and Great Poncelet Theorems are equivalent and can be derived one from the other using elementary geometry, and also that both hold in the Lobachevsky plane as well. A new closure theorem is also obtained, in which the construction of closure is slightly more involved: closure occurs on a variable circle which is tangent to a fixed pair of circles. In conclusion, a combinatorial proof of Poncelet's Theorem is given, which deduces the closure principle for an arbitrary number of steps from the principle for three steps using combinatorics and number theory. Bibliography: 20 titles.

Toward a comprehensive understanding of executive cognitive function in implicit racial bias.

PubMed

Ito, Tiffany A; Friedman, Naomi P; Bartholow, Bruce D; Correll, Joshua; Loersch, Chris; Altamirano, Lee J; Miyake, Akira

2015-02-01

Although performance on laboratory-based implicit bias tasks often is interpreted strictly in terms of the strength of automatic associations, recent evidence suggests that such tasks are influenced by higher-order cognitive control processes, so-called executive functions (EFs). However, extant work in this area has been limited by failure to account for the unity and diversity of EFs, focus on only a single measure of bias and/or EF, and relatively small sample sizes. The current study sought to comprehensively model the relation between individual differences in EFs and the expression of racial bias in 3 commonly used laboratory measures. Participants (N = 485) completed a battery of EF tasks (Session 1) and 3 racial bias tasks (Session 2), along with numerous individual difference questionnaires. The main findings were as follows: (a) measures of implicit bias were only weakly intercorrelated; (b) EF and estimates of automatic processes both predicted implicit bias and also interacted, such that the relation between automatic processes and bias expression was reduced at higher levels of EF; (c) specific facets of EF were differentially associated with overall task performance and controlled processing estimates across different bias tasks; (d) EF did not moderate associations between implicit and explicit measures of bias; and (e) external, but not internal, motivation to control prejudice depended on EF to reduce bias expression. Findings are discussed in terms of the importance of global and specific EF abilities in determining expression of implicit racial bias. PsycINFO Database Record (c) 2015 APA, all rights reserved.

Dual-modality impairment of implicit learning of letter-strings versus color-patterns in patients with schizophrenia.

PubMed

Chiu, Ming-Jang; Liu, Kristina; Hsieh, Ming H; Hwu, Hai-Gwo

2005-12-12

Implicit learning was reported to be intact in schizophrenia using artificial grammar learning. However, emerging evidence indicates that artificial grammar learning is not a unitary process. The authors used dual coding stimuli and schizophrenia clinical symptom dimensions to re-evaluate the effect of schizophrenia on various components of artificial grammar learning. Letter string and color pattern artificial grammar learning performances were compared between 63 schizophrenic patients and 27 comparison subjects. Four symptom dimensions derived from a Chinese Positive and Negative Symptom Scale ratings were correlated with patients' artificial grammar implicit learning performances along the two stimulus dimensions. Patients' explicit memory performances were assessed by verbal paired associates and visual reproduction subtests of the Wechsler Memory Scales Revised Version to provide a contrast to their implicit memory function. Schizophrenia severely hindered color pattern artificial grammar learning while the disease affected lexical string artificial grammar learning to a lesser degree after correcting the influences from age, education and the performance of explicit memory function of both verbal and visual modalities. Both learning performances correlated significantly with the severity of patients' schizophrenic clinical symptom dimensions that reflect poor abstract thinking, disorganized thinking, and stereotyped thinking. The results of this study suggested that schizophrenia affects various mechanisms of artificial grammar learning differently. Implicit learning, knowledge acquisition in the absence of conscious awareness, is not entirely intact in patients with schizophrenia. Schizophrenia affects implicit learning through an impairment of the ability of making abstractions from rules and at least in part decreasing the capacity for perceptual learning.

Implicit Coupling Approach for Simulation of Charring Carbon Ablators

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Gokcen, Tahir

2013-01-01

This study demonstrates that coupling of a material thermal response code and a flow solver with nonequilibrium gas/surface interaction for simulation of charring carbon ablators can be performed using an implicit approach. The material thermal response code used in this study is the three-dimensional version of Fully Implicit Ablation and Thermal response program, which predicts charring material thermal response and shape change on hypersonic space vehicles. The flow code solves the reacting Navier-Stokes equations using Data Parallel Line Relaxation method. Coupling between the material response and flow codes is performed by solving the surface mass balance in flow solver and the surface energy balance in material response code. Thus, the material surface recession is predicted in flow code, and the surface temperature and pyrolysis gas injection rate are computed in material response code. It is demonstrated that the time-lagged explicit approach is sufficient for simulations at low surface heating conditions, in which the surface ablation rate is not a strong function of the surface temperature. At elevated surface heating conditions, the implicit approach has to be taken, because the carbon ablation rate becomes a stiff function of the surface temperature, and thus the explicit approach appears to be inappropriate resulting in severe numerical oscillations of predicted surface temperature. Implicit coupling for simulation of arc-jet models is performed, and the predictions are compared with measured data. Implicit coupling for trajectory based simulation of Stardust fore-body heat shield is also conducted. The predicted stagnation point total recession is compared with that predicted using the chemical equilibrium surface assumption

Analyticity without Differentiability

ERIC Educational Resources Information Center

Kirillova, Evgenia; Spindler, Karlheinz

2008-01-01

In this article we derive all salient properties of analytic functions, including the analytic version of the inverse function theorem, using only the most elementary convergence properties of series. Not even the notion of differentiability is required to do so. Instead, analytical arguments are replaced by combinatorial arguments exhibiting…

Production Functions for Water Delivery Systems: Analysis and Estimation Using Dual Cost Function and Implicit Price Specifications

NASA Astrophysics Data System (ADS)

Teeples, Ronald; Glyer, David

1987-05-01

Both policy and technical analysis of water delivery systems have been based on cost functions that are inconsistent with or are incomplete representations of the neoclassical production functions of economics. We present a full-featured production function model of water delivery which can be estimated from a multiproduct, dual cost function. The model features implicit prices for own-water inputs and is implemented as a jointly estimated system of input share equations and a translog cost function. Likelihood ratio tests are performed showing that a minimally constrained, full-featured production function is a necessary specification of the water delivery operations in our sample. This, plus the model's highly efficient and economically correct parameter estimates, confirms the usefulness of a production function approach to modeling the economic activities of water delivery systems.

KAM tori and whiskered invariant tori for non-autonomous systems

NASA Astrophysics Data System (ADS)

Canadell, Marta; de la Llave, Rafael

2015-08-01

We consider non-autonomous dynamical systems which converge to autonomous (or periodic) systems exponentially fast in time. Such systems appear naturally as models of many physical processes affected by external pulses. We introduce definitions of non-autonomous invariant tori and non-autonomous whiskered tori and their invariant manifolds and we prove their persistence under small perturbations, smooth dependence on parameters and several geometric properties (if the systems are Hamiltonian, the tori are Lagrangian manifolds). We note that such definitions are problematic for general time-dependent systems, but we show that they are unambiguous for systems converging exponentially fast to autonomous. The proof of persistence relies only on a standard Implicit Function Theorem in Banach spaces and it does not require that the rotations in the tori are Diophantine nor that the systems we consider preserve any geometric structure. We only require that the autonomous system preserves these objects. In particular, when the autonomous system is integrable, we obtain the persistence of tori with rational rotational. We also discuss fast and efficient algorithms for their computation. The method also applies to infinite dimensional systems which define a good evolution, e.g. PDE's. When the systems considered are Hamiltonian, we show that the time dependent invariant tori are isotropic. Hence, the invariant tori of maximal dimension are Lagrangian manifolds. We also obtain that the (un)stable manifolds of whiskered tori are Lagrangian manifolds. We also include a comparison with the more global theory developed in Blazevski and de la Llave (2011).

Making Temporal Logic Calculational: A Tool for Unification and Discovery

NASA Astrophysics Data System (ADS)

Boute, Raymond

In temporal logic, calculational proofs beyond simple cases are often seen as challenging. The situation is reversed by making temporal logic calculational, yielding shorter and clearer proofs than traditional ones, and serving as a (mental) tool for unification and discovery. A side-effect of unifying theories is easier access by practicians. The starting point is a simple generic (software tool independent) Functional Temporal Calculus (FTC). Specific temporal logics are then captured via endosemantic functions. This concept reflects tacit conventions throughout mathematics and, once identified, is general and useful. FTC also yields a reasoning style that helps discovering theorems by calculation rather than just proving given facts. This is illustrated by deriving various theorems, most related to liveness issues in TLA+, and finding strengthenings of known results. Educational issues are addressed in passing.

Spheres, charges, instantons, and bootstrap: A five-dimensional odyssey

NASA Astrophysics Data System (ADS)

Chang, Chi-Ming; Fluder, Martin; Lin, Ying-Hsuan; Wang, Yifan

2018-03-01

We combine supersymmetric localization and the conformal bootstrap to study five-dimensional superconformal field theories. To begin, we classify the admissible counter-terms and derive a general relation between the five-sphere partition function and the conformal and flavor central charges. Along the way, we discover a new superconformal anomaly in five dimensions. We then propose a precise triple factorization formula for the five-sphere partition function, that incorporates instantons and is consistent with flavor symmetry enhancement. We numerically evaluate the central charges for the rank-one Seiberg and Morrison-Seiberg theories, and find strong evidence for their saturation of bootstrap bounds, thereby determining the spectra of long multiplets in these theories. Lastly, our results provide new evidence for the F-theorem and possibly a C-theorem in five-dimensional superconformal theories.

Implicit and Explicit Sexual Attitudes: How Are They Related to Sexual Desire and Sexual Satisfaction in Men and Women?

PubMed

Dosch, Alessandra; Belayachi, Sanaâ; Van der Linden, Martial

2016-01-01

This article examines individual variability in sexual desire and sexual satisfaction by exploring the relation between these sexual aspects and sexual attitudes (implicit and explicit) and by taking gender into account, as this has been shown to be an influential factor. A total of 28 men and 33 women living in heterosexual relationships completed questionnaires assessing sexual desire (dyadic, solitary), sexual satisfaction, and explicit sexual attitudes. An adapted version of the Affect Misattribution Procedure was used to assess implicit sexual attitudes. Results showed higher levels of dyadic and solitary sexual desire in men than in women. No gender differences were found regarding sexual satisfaction or sexual attitudes. High dyadic sexual desire was associated with positive implicit and explicit sexual attitudes, regardless of gender. However, solitary sexual desire was significantly higher in men than women and was associated, in women only, with positive implicit sexual attitudes, suggesting that solitary sexual desire may fulfill different functions in men and women. Finally, sexual satisfaction depended on the combination of explicit and implicit sexual attitudes in both men and women. This study highlights the importance of considering both implicit and explicit sexual attitudes to better understand the mechanisms underlying individual variability in sexual desire and satisfaction.

Functional differences between statistical learning with and without explicit training

PubMed Central

Reber, Paul J.; Paller, Ken A.

2015-01-01

Humans are capable of rapidly extracting regularities from environmental input, a process known as statistical learning. This type of learning typically occurs automatically, through passive exposure to environmental input. The presumed function of statistical learning is to optimize processing, allowing the brain to more accurately predict and prepare for incoming input. In this study, we ask whether the function of statistical learning may be enhanced through supplementary explicit training, in which underlying regularities are explicitly taught rather than simply abstracted through exposure. Learners were randomly assigned either to an explicit group or an implicit group. All learners were exposed to a continuous stream of repeating nonsense words. Prior to this implicit training, learners in the explicit group received supplementary explicit training on the nonsense words. Statistical learning was assessed through a speeded reaction-time (RT) task, which measured the extent to which learners used acquired statistical knowledge to optimize online processing. Both RTs and brain potentials revealed significant differences in online processing as a function of training condition. RTs showed a crossover interaction; responses in the explicit group were faster to predictable targets and marginally slower to less predictable targets relative to responses in the implicit group. P300 potentials to predictable targets were larger in the explicit group than in the implicit group, suggesting greater recruitment of controlled, effortful processes. Taken together, these results suggest that information abstracted through passive exposure during statistical learning may be processed more automatically and with less effort than information that is acquired explicitly. PMID:26472644

A Theory Upon Origin of Implicit Musical Language.

PubMed

Vas József, P

2015-11-30

The author suggests that the origin of musicality is implied in an implicit musical language every human being possesses in uterus due to a resonance and attunement with prenatal environment, mainly the mother. It is emphasized that ego-development and evolving implicit musical language can be regarded as parallel processes. To support this idea a lot of examples of musical representations are demonstrated by the author. Music is viewed as a tone of ego-functioning involving the musical representations of bodily and visceral senses, cross-modal perception, unity of sense of self, individual fate of ego, and tripolar and bipolar musical coping codes. Finally, a special form of music therapy is shown to illustrate how can implicit musical language be transformed into explicit language by virtue of participants' spontaneity, creativity, and playfulness.

A Theory Upon Origin of Implicit Musical Language

PubMed Central

Vas József, P.

2015-01-01

The author suggests that the origin of musicality is implied in an implicit musical language every human being possesses in uterus due to a resonance and attunement with prenatal environment, mainly the mother. It is emphasized that ego-development and evolving implicit musical language can be regarded as parallel processes. To support this idea a lot of examples of musical representations are demonstrated by the author. Music is viewed as a tone of ego-functioning involving the musical representations of bodily and visceral senses, cross-modal perception, unity of sense of self, individual fate of ego, and tripolar and bipolar musical coping codes. Finally, a special form of music therapy is shown to illustrate how can implicit musical language be transformed into explicit language by virtue of participants’ spontaneity, creativity, and playfulness. PMID:26973966

Variational Implicit Solvation with Solute Molecular Mechanics: From Diffuse-Interface to Sharp-Interface Models.

PubMed

Li, Bo; Zhao, Yanxiang

2013-01-01

Central in a variational implicit-solvent description of biomolecular solvation is an effective free-energy functional of the solute atomic positions and the solute-solvent interface (i.e., the dielectric boundary). The free-energy functional couples together the solute molecular mechanical interaction energy, the solute-solvent interfacial energy, the solute-solvent van der Waals interaction energy, and the electrostatic energy. In recent years, the sharp-interface version of the variational implicit-solvent model has been developed and used for numerical computations of molecular solvation. In this work, we propose a diffuse-interface version of the variational implicit-solvent model with solute molecular mechanics. We also analyze both the sharp-interface and diffuse-interface models. We prove the existence of free-energy minimizers and obtain their bounds. We also prove the convergence of the diffuse-interface model to the sharp-interface model in the sense of Γ-convergence. We further discuss properties of sharp-interface free-energy minimizers, the boundary conditions and the coupling of the Poisson-Boltzmann equation in the diffuse-interface model, and the convergence of forces from diffuse-interface to sharp-interface descriptions. Our analysis relies on the previous works on the problem of minimizing surface areas and on our observations on the coupling between solute molecular mechanical interactions with the continuum solvent. Our studies justify rigorously the self consistency of the proposed diffuse-interface variational models of implicit solvation.

Primary motor cortex contributes to the implementation of implicit value-based rules during motor decisions.

PubMed

Derosiere, Gerard; Zénon, Alexandre; Alamia, Andrea; Duque, Julie

2017-02-01

In the present study, we investigated the functional contribution of the human primary motor cortex (M1) to motor decisions. Continuous theta burst stimulation (cTBS) was used to alter M1 activity while participants performed a decision-making task in which the reward associated with the subjects' responses (right hand finger movements) depended on explicit and implicit value-based rules. Subjects performed the task over two consecutive days and cTBS occurred in the middle of Day 2, once the subjects were just about to implement implicit rules, in addition to the explicit instructions, to choose their responses, as evident in the control group (cTBS over the right somatosensory cortex). Interestingly, cTBS over the left M1 prevented subjects from implementing the implicit value-based rule while its implementation was enhanced in the group receiving cTBS over the right M1. Hence, cTBS had opposite effects depending on whether it was applied on the contralateral or ipsilateral M1. The use of the explicit value-based rule was unaffected by cTBS in the three groups of subject. Overall, the present study provides evidence for a functional contribution of M1 to the implementation of freshly acquired implicit rules, possibly through its involvement in a cortico-subcortical network controlling value-based motor decisions. Copyright © 2016 Elsevier Inc. All rights reserved.

On a theorem of existence for scaling problems

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

Osmolovskii, V.G.

1995-12-05

The authors study the question of the existence of the global minimum of the functional over the set of functions where {Omega} {contained_in} R{sup n} is a bounded domain, and a fixed function K (x,y) = K (y,x) belongs to L{sub 2} ({Omega} x {Omega}). Such functionals arise in some mathematical models of economics and sociology.

The Relevance of the Nature of Learned Associations for the Differentiation of Human Memory Systems

ERIC Educational Resources Information Center

Rose, Michael; Haider, Hilde; Weiller, Cornelius; Buchel, Christian

2004-01-01

In a previous functional magnetic resonance imaging (fMRI) study we demonstrated an involvement of the medial temporal lobe (MTL) during an implicit learning task. We concluded that the MTL was engaged because of the complex contingencies that were implicitly learned. In addition, the basal ganglia demonstrated effects of a paralleled…

Implicit learning deficit in children with Duchenne muscular dystrophy: Evidence for a cerebellar cognitive impairment?

PubMed

Vicari, Stefano; Piccini, Giorgia; Mercuri, Eugenio; Battini, Roberta; Chieffo, Daniela; Bulgheroni, Sara; Pecini, Chiara; Lucibello, Simona; Lenzi, Sara; Moriconi, Federica; Pane, Marika; D'Amico, Adele; Astrea, Guja; Baranello, Giovanni; Riva, Daria; Cioni, Giovanni; Alfieri, Paolo

2018-01-01

This study aimed at comparing implicit sequence learning in individuals affected by Duchenne Muscular Dystrophy without intellectual disability and age-matched typically developing children. A modified version of the Serial Reaction Time task was administered to 32 Duchenne children and 37 controls of comparable chronological age. The Duchenne group showed a reduced rate of implicit learning even if in the absence of global intellectual disability. This finding provides further evidence of the involvement of specific aspects of cognitive function in Duchenne muscular dystrophy and on its possible neurobiological substrate.

Implicit and Explicit Illusory Correlation as a Function of Political Ideology

PubMed Central

Carraro, Luciana; Negri, Paolo; Castelli, Luigi; Pastore, Massimiliano

2014-01-01

Research has demonstrated that people who embrace different ideological orientations often show differences at the level of basic cognitive processes. For instance, conservatives (vs. liberals) display an automatic selective attention for negative (vs. positive) stimuli, and tend to more easily form illusory correlations between negative information and minority groups. In the present work, we further explored this latter effect by examining whether it only involves the formation of explicit attitudes or it extends to implicit attitudes. To this end, following the typical illusory correlation paradigm, participants were presented with members of two numerically different groups (majority and minority) each performing either a positive or negative behaviour. Negative behaviors were relatively infrequent, and the proportion of positive and negative behaviors within each group was the same. Next, explicit and implicit (i.e., IAT-measured) attitudes were assessed. Results showed that conservatives (vs. liberals) displayed stronger explicit as well as implicit illusory correlations effects, forming more negative attitudes toward the minority (vs. majority) group at both the explicit and implicit level. PMID:24820311

Fanning the flames of prejudice: the influence of specific incidental emotions on implicit prejudice.

PubMed

Dasgupta, Nilanjana; Desteno, David; Williams, Lisa A; Hunsinger, Matthew

2009-08-01

Three experiments examined the impact of incidental emotions on implicit intergroup evaluations. Experiment 1 demonstrated that for unknown social groups, two negative emotions that are broadly applicable to intergroup conflict (anger and disgust) both created implicit bias where none had existed before. However, for known groups about which perceivers had prior knowledge, emotions increased implicit prejudice only if the induced emotion was applicable to the outgroup stereotype. Disgust increased bias against disgust-relevant groups (e.g., homosexuals) but anger did not (Experiment 2); anger increased bias against anger-relevant groups (e.g., Arabs) but disgust did not (Experiment 3). Consistent with functional theories of emotion, these findings suggest that negative intergroup emotions signal specific types of threat. If the emotion-specific threat is applicable to prior expectations of a group, the emotion ratchets up implicit prejudice toward that group. However, if the emotion-specific threat is not applicable to the target group, evaluations remain unchanged. 2009 APA, all rights reserved.

Implicit Learning of Viewpoint-Independent Spatial Layouts

PubMed Central

Tsuchiai, Taiga; Matsumiya, Kazumichi; Kuriki, Ichiro; Shioiri, Satoshi

2012-01-01

We usually perceive things in our surroundings as unchanged despite viewpoint changes caused by self-motion. The visual system therefore must have a function to process objects independently of viewpoint. In this study, we examined whether viewpoint-independent spatial layout can be obtained implicitly. For this purpose, we used a contextual cueing effect, a learning effect of spatial layout in visual search displays known to be an implicit effect. We investigated the transfer of the contextual cueing effect to images from a different viewpoint by using visual search displays of 3D objects. For images from a different viewpoint, the contextual cueing effect was maintained with self-motion but disappeared when the display changed without self-motion. This indicates that there is an implicit learning effect in environment-centered coordinates and suggests that the spatial representation of object layouts can be obtained and updated implicitly. We also showed that binocular disparity plays an important role in the layout representations. PMID:22740837

An implicit time-marching method for studying unsteady flow with massive separation

NASA Technical Reports Server (NTRS)

Osswald, G. A.; Ghia, K. N.; Chia, U.

1985-01-01

A fully implicit time-marching method is developed such that all spatial derivatives are approximated using central differences, but no use is made of any artificial dissipation. The numerical method solves the discretized equations using Alternating Direction Implicit-Block Gaussian Elimination technique. The method is implemented in the unsteady analysis, which solves the incompressible Navier-Stokes equations in terms of vorticity and stream function in generalized orthogonal coordinates. A clustered conformal C-grid is employed, and every effort is made to resolve the various length scales in the flow problem. The metric discontinuity at the branch-cut is treated appropriately using analytic continuation. Introduction of the BGE reordering permits implicit treatment of the branch cut in the numerical method. The vorticity singularity at the cusped trailing edge is also appropriately treated. This accurate and efficient implicit method is used to study flow at Re = 1000, past a 12-percent thick symmetric Joukowski airfoil at high angle of attack 30 and 53 deg.

Implicit and explicit illusory correlation as a function of political ideology.

PubMed

Carraro, Luciana; Negri, Paolo; Castelli, Luigi; Pastore, Massimiliano

2014-01-01

Research has demonstrated that people who embrace different ideological orientations often show differences at the level of basic cognitive processes. For instance, conservatives (vs. liberals) display an automatic selective attention for negative (vs. positive) stimuli, and tend to more easily form illusory correlations between negative information and minority groups. In the present work, we further explored this latter effect by examining whether it only involves the formation of explicit attitudes or it extends to implicit attitudes. To this end, following the typical illusory correlation paradigm, participants were presented with members of two numerically different groups (majority and minority) each performing either a positive or negative behaviour. Negative behaviors were relatively infrequent, and the proportion of positive and negative behaviors within each group was the same. Next, explicit and implicit (i.e., IAT-measured) attitudes were assessed. Results showed that conservatives (vs. liberals) displayed stronger explicit as well as implicit illusory correlations effects, forming more negative attitudes toward the minority (vs. majority) group at both the explicit and implicit level.

Implicit recognition based on lateralized perceptual fluency.

PubMed

Vargas, Iliana M; Voss, Joel L; Paller, Ken A

2012-02-06

In some circumstances, accurate recognition of repeated images in an explicit memory test is driven by implicit memory. We propose that this "implicit recognition" results from perceptual fluency that influences responding without awareness of memory retrieval. Here we examined whether recognition would vary if images appeared in the same or different visual hemifield during learning and testing. Kaleidoscope images were briefly presented left or right of fixation during divided-attention encoding. Presentation in the same visual hemifield at test produced higher recognition accuracy than presentation in the opposite visual hemifield, but only for guess responses. These correct guesses likely reflect a contribution from implicit recognition, given that when the stimulated visual hemifield was the same at study and test, recognition accuracy was higher for guess responses than for responses with any level of confidence. The dramatic difference in guessing accuracy as a function of lateralized perceptual overlap between study and test suggests that implicit recognition arises from memory storage in visual cortical networks that mediate repetition-induced fluency increments.

An asymptotic formula for polynomials orthonormal with respect to a varying weight. II

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

Komlov, A V; Suetin, S P

2014-09-30

This paper gives a proof of the theorem announced by the authors in the preceding paper with the same title. The theorem states that asymptotically the behaviour of the polynomials which are orthonormal with respect to the varying weight e{sup −2nQ(x)}p{sub g}(x)/√(∏{sub j=1}{sup 2p}(x−e{sub j})) coincides with the asymptotic behaviour of the Nuttall psi-function, which solves a special boundary-value problem on the relevant hyperelliptic Riemann surface of genus g=p−1. Here e{sub 1}

Certain approximation problems for functions on the infinite-dimensional torus: Lipschitz spaces

NASA Astrophysics Data System (ADS)

Platonov, S. S.

2018-02-01

We consider some questions about the approximation of functions on the infinite-dimensional torus by trigonometric polynomials. Our main results are analogues of the direct and inverse theorems in the classical theory of approximation of periodic functions and a description of the Lipschitz spaces on the infinite-dimensional torus in terms of the best approximation.

Frontostriatal and Mediotemporal Lobe Contributions to Implicit Higher-Order Spatial Sequence Learning Declines in Aging and Parkinson’s Disease

PubMed Central

Schendan, Haline E.; Tinaz, Sule; Maher, Stephen M.; Stern, Chantal E.

2015-01-01

Sequence learning depends on the striatal system, but recent findings also implicate the mediotemporal lobe (MTL) system. Schendan, Searl, Melrose, & Stern (2003) found higher-order associative, learning-related activation in the striatum, dorsolateral prefrontal cortex, and the MTL during the early acquisition phase of both implicit and explicit variants of a serial response time task. This functional magnetic resonance imaging (fMRI) study capitalized on this task to determine how changes in MTL function observed in aging and compromised frontostriatal function characteristic of Parkinson’s disease (PD) patients impacts sequence learning and memory under implicit instructions. Brain activity was compared between “Sequence” and “Random” conditions in 12 non-demented PD patients and education and gender matched healthy control participants of whom 12 were age matched (MC) and 14 were younger (YC). Behaviorally, sequence-specific learning of higher-order associations was reduced with aging and changed further with PD and resulted primarily in implicit knowledge in the older participants. FMRI revealed reduced intensity and extent of sequence learning-related activation in older relative to younger people in frontostriatal circuits and the MTL. This was because signal was greater for the Sequence than Random condition in younger people, whereas older people, especially those with PD, showed the opposite pattern. Both older groups also showed increased activation to the task itself relative to baseline fixation. In addition, right MTL showed hypoactivation and left MTL hyperactivation in PD relative to the MC group. The results suggest changes in frontostriatal and MTL activity occur during aging that affect task-related activity and the initial acquisition phase of implicit higher-order sequence learning. In addition, the results suggest that Parkinson’s disease adversely affects processes in the MTL including sequence learning and memory. PMID:23565935

Unified gas-kinetic scheme with multigrid convergence for rarefied flow study

NASA Astrophysics Data System (ADS)

Zhu, Yajun; Zhong, Chengwen; Xu, Kun

2017-09-01

The unified gas kinetic scheme (UGKS) is based on direct modeling of gas dynamics on the mesh size and time step scales. With the modeling of particle transport and collision in a time-dependent flux function in a finite volume framework, the UGKS can connect the flow physics smoothly from the kinetic particle transport to the hydrodynamic wave propagation. In comparison with the direct simulation Monte Carlo (DSMC) method, the current equation-based UGKS can implement implicit techniques in the updates of macroscopic conservative variables and microscopic distribution functions. The implicit UGKS significantly increases the convergence speed for steady flow computations, especially in the highly rarefied and near continuum regimes. In order to further improve the computational efficiency, for the first time, a geometric multigrid technique is introduced into the implicit UGKS, where the prediction step for the equilibrium state and the evolution step for the distribution function are both treated with multigrid acceleration. More specifically, a full approximate nonlinear system is employed in the prediction step for fast evaluation of the equilibrium state, and a correction linear equation is solved in the evolution step for the update of the gas distribution function. As a result, convergent speed has been greatly improved in all flow regimes from rarefied to the continuum ones. The multigrid implicit UGKS (MIUGKS) is used in the non-equilibrium flow study, which includes microflow, such as lid-driven cavity flow and the flow passing through a finite-length flat plate, and high speed one, such as supersonic flow over a square cylinder. The MIUGKS shows 5-9 times efficiency increase over the previous implicit scheme. For the low speed microflow, the efficiency of MIUGKS is several orders of magnitude higher than the DSMC. Even for the hypersonic flow at Mach number 5 and Knudsen number 0.1, the MIUGKS is still more than 100 times faster than the DSMC method for obtaining a convergent steady state solution.

The super-indeterminism in orthodox quantum mechanics does not implicate the reality of experimenter free will

NASA Astrophysics Data System (ADS)

Walleczek, J.

2016-03-01

The concept of ‘super-indeterminism’ captures the notion that the free choice assumption of orthodox quantum mechanics necessitates only the following requirement: an agent's free-choice performance in the selection of measurement settings must not represent an exception to the rule of irreducible quantum indeterminism in the physical universe (i.e, “universal indeterminism”). Any additional metaphysical speculation, such as to whether quantum indeterminism, i.e., intrinsic randomness, implicates the reality of experimenter “freedom”, “free will”, or “free choice”, is redundant in relation to the predictive success of orthodox quantum mechanics. Accordingly, super-indeterminism views as redundant also, from a technical standpoint, whether an affirmative or a negative answer is claimed in reference to universal indeterminism as a necessary precondition for experimenter freedom. Super-indeterminism accounts, for example, for the circular reasoning which is implicit in the free will theorem by Conway and Kochen [1,2]. The concept of super-indeterminism is of great assistance in clarifying the often misunderstood meaning of the concept of “free variables” as used by John Bell [3]. The present work argues that Bell sought an operational, effective free will theorem, one based upon the notion of “determinism without predetermination”, i.e., one wherein “free variables” represent universally uncomputable variables. In conclusion, the standard interpretation of quantum theory does not answer, and does not need to answer in order to ensure the predictive success of orthodox theory, the question of whether either incompatibilism or compatibilism is valid in relation to free-will metaphysics and to the free-will phenomenology of experimenter agents in quantum mechanics.

Accelerating NLTE radiative transfer by means of the Forth-and-Back Implicit Lambda Iteration: A two-level atom line formation in 2D Cartesian coordinates

NASA Astrophysics Data System (ADS)

Milić, Ivan; Atanacković, Olga

2014-10-01

State-of-the-art methods in multidimensional NLTE radiative transfer are based on the use of local approximate lambda operator within either Jacobi or Gauss-Seidel iterative schemes. Here we propose another approach to the solution of 2D NLTE RT problems, Forth-and-Back Implicit Lambda Iteration (FBILI), developed earlier for 1D geometry. In order to present the method and examine its convergence properties we use the well-known instance of the two-level atom line formation with complete frequency redistribution. In the formal solution of the RT equation we employ short characteristics with two-point algorithm. Using an implicit representation of the source function in the computation of the specific intensities, we compute and store the coefficients of the linear relations J=a+bS between the mean intensity J and the corresponding source function S. The use of iteration factors in the ‘local’ coefficients of these implicit relations in two ‘inward’ sweeps of 2D grid, along with the update of the source function in other two ‘outward’ sweeps leads to four times faster solution than the Jacobi’s one. Moreover, the update made in all four consecutive sweeps of the grid leads to an acceleration by a factor of 6-7 compared to the Jacobi iterative scheme.

Implicit contextual learning in prodromal and early stage Huntington's disease patients.

PubMed

van Asselen, Marieke; Almeida, Inês; Júlio, Filipa; Januário, Cristina; Campos, Elzbieta Bobrowicz; Simões, Mário; Castelo-Branco, Miguel

2012-07-01

Huntington's disease (HD) is a genetic neurodegenerative disorder affecting the basal ganglia. These subcortical structures are particularly important for motor functions, response selection and implicit learning. In the current study, we have assessed prodromal and symptomatic HD participants with an implicit contextual learning task that is not based on motor learning, but on a purely visual implicit learning mechanism. We used an implicit contextual learning task in which subjects need to locate a target among several distractors. In half of the trials, the positions of the distractors and target stimuli were repeated. By memorizing this contextual information, attention can be guided faster to the target stimulus. Nine symptomatic HD participants, 16 prodromal HD participants and 22 control subjects were included. We found that the responses of the control subjects were faster for the repeated trials than for the new trials, indicating that their visual search was facilitated when repeated contextual information was present. In contrast, no difference in response times between the repeated and new trials was found for the symptomatic and prodromal HD participants. The results of the current study indicate that both prodromal and symptomatic HD participants are impaired on an implicit contextual learning task.

Connection of Scattering Principles: A Visual and Mathematical Tour

ERIC Educational Resources Information Center

Broggini, Filippo; Snieder, Roel

2012-01-01

Inverse scattering, Green's function reconstruction, focusing, imaging and the optical theorem are subjects usually studied as separate problems in different research areas. We show a physical connection between the principles because the equations that rule these "scattering principles" have a similar functional form. We first lead the reader…

Illustrating the Central Limit Theorem through Microsoft Excel Simulations

ERIC Educational Resources Information Center

Moen, David H.; Powell, John E.

2005-01-01

Using Microsoft Excel, several interactive, computerized learning modules are developed to demonstrate the Central Limit Theorem. These modules are used in the classroom to enhance the comprehension of this theorem. The Central Limit Theorem is a very important theorem in statistics, and yet because it is not intuitively obvious, statistics…

Unified quantum no-go theorems and transforming of quantum pure states in a restricted set

NASA Astrophysics Data System (ADS)

Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun

2017-12-01

The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed pure state in Hilbert space of a finite dimension. The new theorem is further extended for multiple copies of an unknown state as input states. These generalized results of the no-encoding theorem include the no-cloning theorem, the no-deleting theorem and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may lead to fruitful results that are completely characterized with the linear independence of the representative vectors of input pure states. The upper bounds of the efficiency are also proved. Third, we generalize a recent superposing scheme of unknown states with a fixed overlap into new schemes when multiple copies of an unknown state are as input states.

Global Similarity Predicts Dissociation of Classification and Recognition: Evidence Questioning the Implicit-Explicit Learning Distinction in Amnesia

ERIC Educational Resources Information Center

Jamieson, Randall K.; Holmes, Signy; Mewhort, D. J. K.

2010-01-01

Dissociation of classification and recognition in amnesia is widely taken to imply 2 functional systems: an implicit procedural-learning system that is spared in amnesia and an explicit episodic-learning system that is compromised. We argue that both tasks reflect the global similarity of probes to memory. In classification, subjects sort…

Age Differences and Cognitive Aptitudes for Implicit and Explicit Learning in Ultimate Second Language Attainment

ERIC Educational Resources Information Center

Granena, Gisela

2012-01-01

Very high-level, functional ability in foreign languages is increasingly important in many walks of life. It is also very rare, and likely requires an early start and/or a special aptitude. This study investigated the extent to which aptitude for explicit learning, defined as "analytic ability" and aptitude for implicit learning, defined…

Machine Understanding of Human Implicit Intention

DTIC Science & Technology

2013-05-18

Cognitive Neurodynamics , Hokkaido, Japan, June 2011, Hokkaido, Japan (Plenary Talk) - Soo-Young Lee, Implicit Intention Recognition and Hierarchical...subject’s response with the accuracy of about 80% by SVM. 15. SUBJECT TERMS Brain Science and Engineering; Cognitive Neuroscience; Human-Computer...oscillations have been related to a variety of functions such as perception, cognition , sleep, etc. For a long time, researchers have found the sensory and

Exact Dynamics via Poisson Process: a unifying Monte Carlo paradigm

NASA Astrophysics Data System (ADS)

Gubernatis, James

2014-03-01

A common computational task is solving a set of ordinary differential equations (o.d.e.'s). A little known theorem says that the solution of any set of o.d.e.'s is exactly solved by the expectation value over a set of arbitary Poisson processes of a particular function of the elements of the matrix that defines the o.d.e.'s. The theorem thus provides a new starting point to develop real and imaginary-time continous-time solvers for quantum Monte Carlo algorithms, and several simple observations enable various quantum Monte Carlo techniques and variance reduction methods to transfer to a new context. I will state the theorem, note a transformation to a very simple computational scheme, and illustrate the use of some techniques from the directed-loop algorithm in context of the wavefunction Monte Carlo method that is used to solve the Lindblad master equation for the dynamics of open quantum systems. I will end by noting that as the theorem does not depend on the source of the o.d.e.'s coming from quantum mechanics, it also enables the transfer of continuous-time methods from quantum Monte Carlo to the simulation of various classical equations of motion heretofore only solved deterministically.

Comments on Musha's theorem that an evanescent photon in the microtubule is a superluminal particle.

PubMed

Hari, Syamala D

2014-07-01

Takaaki Musha's research of high performance quantum computation in living systems is motivated by the theories of Penrose and Hameroff that microtubules in the brain function as quantum computers, and by those of Jibu and Yasue that the quantum states of microtubules depend upon boson condensates of evanescent photons. His work is based on the assumption that the evanescent photons described by Jibu et al. are superluminal and that they are tachyons defined and discussed by well-known physicists such as Sudarshan, Feinberg and Recami. Musha gives a brief justification for the assumption and sometimes calls it a theorem. However, the assumption is not valid because Jibu et al. stated that the evanescent photons have transmission speed smaller than that of light and that their mass is real and momentum is imaginary whereas a tachyon's mass is imaginary and momentum is real. We show here that Musha's proof of the "theorem" has errors and hence his theorem/assumption is not valid. This article is not meant to further discuss any biological aspects of the brain but only to comment on the consistency of the quantum-physical aspects of earlier work by Musha et al. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Large deviation theory for the kinetics and energetics of turnover of enzyme catalysis in a chemiostatic flow.

PubMed

Das, Biswajit; Gangopadhyay, Gautam

2018-05-07

In the framework of large deviation theory, we have characterized nonequilibrium turnover statistics of enzyme catalysis in a chemiostatic flow with externally controllable parameters, like substrate injection rate and mechanical force. In the kinetics of the process, we have shown the fluctuation theorems in terms of the symmetry of the scaled cumulant generating function (SCGF) in the transient and steady state regime and a similar symmetry rule is reflected in a large deviation rate function (LDRF) as a property of the dissipation rate through boundaries. Large deviation theory also gives the thermodynamic force of a nonequilibrium steady state, as is usually recorded experimentally by a single molecule technique, which plays a key role responsible for the dynamical symmetry of the SCGF and LDRF. Using some special properties of the Legendre transformation, here, we have provided a relation between the fluctuations of fluxes and dissipation rates, and among them, the fluctuation of the turnover rate is routinely estimated but the fluctuation in the dissipation rate is yet to be characterized for small systems. Such an enzymatic reaction flow system can be a very good testing ground to systematically understand the rare events from the large deviation theory which is beyond fluctuation theorem and central limit theorem.

Fractional cable model for signal conduction in spiny neuronal dendrites

NASA Astrophysics Data System (ADS)

Vitali, Silvia; Mainardi, Francesco

2017-06-01

The cable model is widely used in several fields of science to describe the propagation of signals. A relevant medical and biological example is the anomalous subdiffusion in spiny neuronal dendrites observed in several studies of the last decade. Anomalous subdiffusion can be modelled in several ways introducing some fractional component into the classical cable model. The Chauchy problem associated to these kind of models has been investigated by many authors, but up to our knowledge an explicit solution for the signalling problem has not yet been published. Here we propose how this solution can be derived applying the generalized convolution theorem (known as Efros theorem) for Laplace transforms. The fractional cable model considered in this paper is defined by replacing the first order time derivative with a fractional derivative of order α ∈ (0, 1) of Caputo type. The signalling problem is solved for any input function applied to the accessible end of a semi-infinite cable, which satisfies the requirements of the Efros theorem. The solutions corresponding to the simple cases of impulsive and step inputs are explicitly calculated in integral form containing Wright functions. Thanks to the variability of the parameter α, the corresponding solutions are expected to adapt to the qualitative behaviour of the membrane potential observed in experiments better than in the standard case α = 1.

Large deviation theory for the kinetics and energetics of turnover of enzyme catalysis in a chemiostatic flow

NASA Astrophysics Data System (ADS)

Das, Biswajit; Gangopadhyay, Gautam

2018-05-01

In the framework of large deviation theory, we have characterized nonequilibrium turnover statistics of enzyme catalysis in a chemiostatic flow with externally controllable parameters, like substrate injection rate and mechanical force. In the kinetics of the process, we have shown the fluctuation theorems in terms of the symmetry of the scaled cumulant generating function (SCGF) in the transient and steady state regime and a similar symmetry rule is reflected in a large deviation rate function (LDRF) as a property of the dissipation rate through boundaries. Large deviation theory also gives the thermodynamic force of a nonequilibrium steady state, as is usually recorded experimentally by a single molecule technique, which plays a key role responsible for the dynamical symmetry of the SCGF and LDRF. Using some special properties of the Legendre transformation, here, we have provided a relation between the fluctuations of fluxes and dissipation rates, and among them, the fluctuation of the turnover rate is routinely estimated but the fluctuation in the dissipation rate is yet to be characterized for small systems. Such an enzymatic reaction flow system can be a very good testing ground to systematically understand the rare events from the large deviation theory which is beyond fluctuation theorem and central limit theorem.

The Lyapunov-Krasovskii theorem and a sufficient criterion for local stability of isochronal synchronization in networks of delay-coupled oscillators

NASA Astrophysics Data System (ADS)

Grzybowski, J. M. V.; Macau, E. E. N.; Yoneyama, T.

2017-05-01

This paper presents a self-contained framework for the stability assessment of isochronal synchronization in networks of chaotic and limit-cycle oscillators. The results were based on the Lyapunov-Krasovskii theorem and they establish a sufficient condition for local synchronization stability of as a function of the system and network parameters. With this in mind, a network of mutually delay-coupled oscillators subject to direct self-coupling is considered and then the resulting error equations are block-diagonalized for the purpose of studying their stability. These error equations are evaluated by means of analytical stability results derived from the Lyapunov-Krasovskii theorem. The proposed approach is shown to be a feasible option for the investigation of local stability of isochronal synchronization for a variety of oscillators coupled through linear functions of the state variables under a given undirected graph structure. This ultimately permits the systematic identification of stability regions within the high-dimensionality of the network parameter space. Examples of applications of the results to a number of networks of delay-coupled chaotic and limit-cycle oscillators are provided, such as Lorenz, Rössler, Cubic Chua's circuit, Van der Pol oscillator and the Hindmarsh-Rose neuron.

Neural activity in the reward-related brain regions predicts implicit self-esteem: A novel validity test of psychological measures using neuroimaging.

PubMed

Izuma, Keise; Kennedy, Kate; Fitzjohn, Alexander; Sedikides, Constantine; Shibata, Kazuhisa

2018-03-01

Self-esteem, arguably the most important attitudes an individual possesses, has been a premier research topic in psychology for more than a century. Following a surge of interest in implicit attitude measures in the 90s, researchers have tried to assess self-esteem implicitly to circumvent the influence of biases inherent in explicit measures. However, the validity of implicit self-esteem measures remains elusive. Critical tests are often inconclusive, as the validity of such measures is examined in the backdrop of imperfect behavioral measures. To overcome this serious limitation, we tested the neural validity of the most widely used implicit self-esteem measure, the implicit association test (IAT). Given the conceptualization of self-esteem as attitude toward the self, and neuroscience findings that the reward-related brain regions represent an individual's attitude or preference for an object when viewing its image, individual differences in implicit self-esteem should be associated with neural signals in the reward-related regions during passive-viewing of self-face (the most obvious representation of the self). Using multi-voxel pattern analysis (MVPA) on functional MRI (fMRI) data, we demonstrate that the neural signals in the reward-related regions were robustly associated with implicit (but not explicit) self-esteem, thus providing unique evidence for the neural validity of the self-esteem IAT. In addition, both implicit and explicit self-esteem were related, although differently, to neural signals in regions involved in self-processing. Our finding highlights the utility of neuroscience methods in addressing fundamental psychological questions and providing unique insights into important psychological constructs. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

TESTING THE NO-HAIR THEOREM WITH OBSERVATIONS IN THE ELECTROMAGNETIC SPECTRUM. II. BLACK HOLE IMAGES

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

Johannsen, Tim; Psaltis, Dimitrios, E-mail: timj@physics.arizona.ed, E-mail: dpsaltis@email.arizona.ed

2010-07-20

According to the no-hair theorem, all astrophysical black holes are fully described by their masses and spins. This theorem can be tested observationally by measuring (at least) three different multipole moments of the spacetimes of black holes. In this paper, we analyze images of black holes within a framework that allows us to calculate observables in the electromagnetic spectrum as a function of the mass, spin, and, independently, the quadrupole moment of a black hole. We show that a deviation of the quadrupole moment from the expected Kerr value leads to images of black holes that are either prolate ormore » oblate depending on the sign and magnitude of the deviation. In addition, there is a ring-like structure around the black hole shadow with a diameter of {approx}10 black hole masses that is substantially brighter than the image of the underlying accretion flow and that is independent of the astrophysical details of accretion flow models. We show that the shape of this ring depends directly on the mass, spin, and quadrupole moment of the black hole and can be used for an independent measurement of all three parameters. In particular, we demonstrate that this ring is highly circular for a Kerr black hole with a spin a {approx}< 0.9 M, independent of the observer's inclination, but becomes elliptical and asymmetric if the no-hair theorem is violated. Near-future very long baseline interferometric observations of Sgr A* will image this ring and may allow for an observational test of the no-hair theorem.« less

A sharp interpolation between the Hölder and Gaussian Young inequalities

NASA Astrophysics Data System (ADS)

da Pelo, Paolo; Lanconelli, Alberto; Stan, Aurel I.

2016-03-01

We prove a very general sharp inequality of the Hölder-Young-type for functions defined on infinite dimensional Gaussian spaces. We begin by considering a family of commutative products for functions which interpolates between the pointwise and Wick products; this family arises naturally in the context of stochastic differential equations, through Wong-Zakai-type approximation theorems, and plays a key role in some generalizations of the Beckner-type Poincaré inequality. We then obtain a crucial integral representation for that family of products which is employed, together with a generalization of the classic Young inequality due to Lieb, to prove our main theorem. We stress that our main inequality contains as particular cases the Hölder inequality and Nelson’s hyper-contractive estimate, thus providing a unified framework for two fundamental results of the Gaussian analysis.

An Optimized Multicolor Point-Implicit Solver for Unstructured Grid Applications on Graphics Processing Units

NASA Technical Reports Server (NTRS)

Zubair, Mohammad; Nielsen, Eric; Luitjens, Justin; Hammond, Dana

2016-01-01

In the field of computational fluid dynamics, the Navier-Stokes equations are often solved using an unstructuredgrid approach to accommodate geometric complexity. Implicit solution methodologies for such spatial discretizations generally require frequent solution of large tightly-coupled systems of block-sparse linear equations. The multicolor point-implicit solver used in the current work typically requires a significant fraction of the overall application run time. In this work, an efficient implementation of the solver for graphics processing units is proposed. Several factors present unique challenges to achieving an efficient implementation in this environment. These include the variable amount of parallelism available in different kernel calls, indirect memory access patterns, low arithmetic intensity, and the requirement to support variable block sizes. In this work, the solver is reformulated to use standard sparse and dense Basic Linear Algebra Subprograms (BLAS) functions. However, numerical experiments show that the performance of the BLAS functions available in existing CUDA libraries is suboptimal for matrices representative of those encountered in actual simulations. Instead, optimized versions of these functions are developed. Depending on block size, the new implementations show performance gains of up to 7x over the existing CUDA library functions.

On the Mathematical Modeling of Single and Multiple Scattering of Ultrasonic Guided Waves by Small Scatterers: A Structural Health Monitoring Measurement Model

NASA Astrophysics Data System (ADS)

Strom, Brandon William

In an effort to assist in the paradigm shift from schedule based maintenance to conditioned based maintenance, we derive measurement models to be used within structural health monitoring algorithms. Our models are physics based, and use scattered Lamb waves to detect and quantify pitting corrosion. After covering the basics of Lamb waves and the reciprocity theorem, we develop a technique for the scattered wave solution. The first application is two-dimensional, and is employed in two different ways. The first approach integrates a traction distribution and replaces it by an equivalent force. The second approach is higher order and uses the actual traction distribution. We find that the equivalent force version of the solution technique holds well for small pits at low frequencies. The second application is three-dimensional. The equivalent force caused by the scattered wave of an arbitrary equivalent force is calculated. We obtain functions for the scattered wave displacements as a function of equivalent forces, equivalent forces as a function of incident wave, and scattered wave amplitudes as a function of incident amplitude. The third application uses self-consistency to derive governing equations for the scattered waves due to multiple corrosion pits. We decouple the implicit set of equations and solve explicitly by using a recursive series solution. Alternatively, we solve via an undetermined coefficient method which results in an interaction operator and solution via matrix inversion. The general solution is given for N pits including mode conversion. We show that the two approaches are equivalent, and give a solution for three pits. Various approximations are advanced to simplify the problem while retaining the leading order physics. As a final application, we use the multiple scattering model to investigate resonance of Lamb waves. We begin with a one-dimensional problem and progress to a three-dimensional problem. A directed graph enables interpretation of the interaction operator, and we show that a series solution converges due to loss of energy in the system. We see that there are four causes of resonance and plot the modulation depth as a function of spacing between the pits.

Kinematic Structural Modelling in Bayesian Networks

NASA Astrophysics Data System (ADS)

Schaaf, Alexander; de la Varga, Miguel; Florian Wellmann, J.

2017-04-01

We commonly capture our knowledge about the spatial distribution of distinct geological lithologies in the form of 3-D geological models. Several methods exist to create these models, each with its own strengths and limitations. We present here an approach to combine the functionalities of two modeling approaches - implicit interpolation and kinematic modelling methods - into one framework, while explicitly considering parameter uncertainties and thus model uncertainty. In recent work, we proposed an approach to implement implicit modelling algorithms into Bayesian networks. This was done to address the issues of input data uncertainty and integration of geological information from varying sources in the form of geological likelihood functions. However, one general shortcoming of implicit methods is that they usually do not take any physical constraints into consideration, which can result in unrealistic model outcomes and artifacts. On the other hand, kinematic structural modelling intends to reconstruct the history of a geological system based on physically driven kinematic events. This type of modelling incorporates simplified, physical laws into the model, at the cost of a substantial increment of usable uncertain parameters. In the work presented here, we show an integration of these two different modelling methodologies, taking advantage of the strengths of both of them. First, we treat the two types of models separately, capturing the information contained in the kinematic models and their specific parameters in the form of likelihood functions, in order to use them in the implicit modelling scheme. We then go further and combine the two modelling approaches into one single Bayesian network. This enables the direct flow of information between the parameters of the kinematic modelling step and the implicit modelling step and links the exclusive input data and likelihoods of the two different modelling algorithms into one probabilistic inference framework. In addition, we use the capabilities of Noddy to analyze the topology of structural models to demonstrate how topological information, such as the connectivity of two layers across an unconformity, can be used as a likelihood function. In an application to a synthetic case study, we show that our approach leads to a successful combination of the two different modelling concepts. Specifically, we show that we derive ensemble realizations of implicit models that now incorporate the knowledge of the kinematic aspects, representing an important step forward in the integration of knowledge and a corresponding estimation of uncertainties in structural geological models.

Enabling quaternion derivatives: the generalized HR calculus

PubMed Central

Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C.; Mandic, Danilo P.

2015-01-01

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis. PMID:26361555

Enabling quaternion derivatives: the generalized HR calculus.

PubMed

Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C; Mandic, Danilo P

2015-08-01

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis.

Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods

PubMed Central

Zatsiorsky, Vladimir M.

2011-01-01

One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423–453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem. PMID:21311907

A Decomposition Theorem for Finite Automata.

ERIC Educational Resources Information Center

Santa Coloma, Teresa L.; Tucci, Ralph P.

1990-01-01

Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)

Validity of virial theorem in all-electron mixed basis density functional, Hartree–Fock, and GW calculations

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

Kuwahara, Riichi; Accelrys K. K., Kasumigaseki Tokyu Building 17F, 3-7-1 Kasumigaseki, Chiyoda-ku, Tokyo 100-0013; Tadokoro, Yoichi

In this paper, we calculate kinetic and potential energy contributions to the electronic ground-state total energy of several isolated atoms (He, Be, Ne, Mg, Ar, and Ca) by using the local density approximation (LDA) in density functional theory, the Hartree–Fock approximation (HFA), and the self-consistent GW approximation (GWA). To this end, we have implemented self-consistent HFA and GWA routines in our all-electron mixed basis code, TOMBO. We confirm that virial theorem is fairly well satisfied in all of these approximations, although the resulting eigenvalue of the highest occupied molecular orbital level, i.e., the negative of the ionization potential, is inmore » excellent agreement only in the case of the GWA. We find that the wave function of the lowest unoccupied molecular orbital level of noble gas atoms is a resonating virtual bound state, and that of the GWA spreads wider than that of the LDA and thinner than that of the HFA.« less

An extension of the Laplace transform to Schwartz distributions

NASA Technical Reports Server (NTRS)

Price, D. R.

1974-01-01

A characterization of the Laplace transform is developed which extends the transform to the Schwartz distributions. The class of distributions includes the impulse functions and other singular functions which occur as solutions to ordinary and partial differential equations. The standard theorems on analyticity, uniqueness, and invertibility of the transform are proved by using the characterization as the definition of the Laplace transform. The definition uses sequences of linear transformations on the space of distributions which extends the Laplace transform to another class of generalized functions, the Mikusinski operators. It is shown that the sequential definition of the transform is equivalent to Schwartz' extension of the ordinary Laplace transform to distributions but, in contrast to Schwartz' definition, does not use the distributional Fourier transform. Several theorems concerning the particular linear transformations used to define the Laplace transforms are proved. All the results proved in one dimension are extended to the n-dimensional case, but proofs are presented only for those situations that require methods different from their one-dimensional analogs.

Fuchsian triangle groups and Grothendieck dessins. Variations on a theme of Belyi

NASA Astrophysics Data System (ADS)

Cohen, Paula Beazley; Itzykson, Claude; Wolfart, Jürgen

1994-07-01

According to a theorem of Belyi, a smooth projective algebraic curve is defined over a number field if and only if there exists a non-constant element of its function field ramified only over 0, 1 and . The existence of such a Belyi function is equivalent to that of a representation of the curve as a possibly compactified quotient space of the Poincaré upper half plane by a subgroup of finite index in a Fuchsian triangle group. On the other hand, Fuchsian triangle groups arise in many contexts, such as in the theory of hypergeometric functions and certain triangular billiard problems, which would appear at first sight to have no relation to the Galois problems that motivated the above discovery of Belyi. In this note we review several results related to Belyi's theorem and we develop certain aspects giving examples. For preliminary accounts, see the preprint [Wo1], the conference proceedings article [BauItz] and the Comptes Rendus note [CoWo2].

77 FR 19835 - Grant of Individual Exemption Involving BlackRock, Inc. and Its Investment Advisory, Investment...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-04-02

... implicit U.S. Government guarantee as opposed to an explicit U.S. Government guarantee, (a) the BlackRock... 2510.3-101(i) which is accompanied by an implicit U.S. Government guarantee as opposed to an explicit U... or any member of the ECO Function in the performance of his or her duties; 6. The ECO is responsible...

The Effect of Response and Type of Posttest on Understanding of and Memory for Text.

ERIC Educational Resources Information Center

Raphael, Taffy E.; Wonnacott, Clydie A.

A study examined whether (1) the performance of students on text explicit (TE), text implicit (TI), and script implicit (SI) questions inserted in a text would vary as a function of the type of question received; (2) students responding in writing to the inserted questions would perform at a higher level on a subsequent criterion test than those…

Equivalent Stimuli Are More Strongly Related after Training with Delayed Matching than after Simultaneous Matching: A Study Using the Implicit Relational Assessment Procedure (IRAP)

ERIC Educational Resources Information Center

Bortoloti, Renato; de Rose, Julio C.

2012-01-01

Bortoloti and de Rose (2009) found evidence that the level of functional transfer is higher in equivalence classes generated by delayed matching to sample (DMTS) than in classes generated by simultaneous matching (SMTS). We attempted to replicate these findings with the Implicit Relational Assessment Procedure (IRAP). Two experimental groups…

APPROXIMATION OF SOLUTIONS OF THE EQUATION \\overline\\partial^jf=0, j\\geq1, IN DOMAINS WITH QUASICONFORMAL BOUNDARY

NASA Astrophysics Data System (ADS)

Andrievskiĭ, V. V.; Belyĭ, V. I.; Maĭmeskul, V. V.

1991-02-01

This article establishes direct and inverse theorems of approximation theory (of the same type as theorems of Dzyadyk) that describe the quantitative connection between the smoothness properties of solutions of the equation \\overline\\partial^jf=0, j\\geq1, and the rate of their approximation by "module" polynomials of the form \\displaystyle P_N(z)=\\sum_{n=0}^{j-1}\\sum_{m=0}^{N-n}a_{m,n}z^m\\overline{z}^n,\\qquad N\\geq j-1.In particular, a constructive characterization is obtained for generalized Hölder classes of such functions on domains with quasiconformal boundary.Bibliography: 19 titles.

A stability theorem for energy-balance climate models

NASA Technical Reports Server (NTRS)

Cahalan, R. F.; North, G. R.

1979-01-01

The paper treats the stability of steady-state solutions of some simple, latitude-dependent, energy-balance climate models. For north-south symmetric solutions of models with an ice-cap-type albedo feedback, and for the sum of horizontal transport and infrared radiation given by a linear operator, it is possible to prove a 'slope stability' theorem, i.e., if the local slope of the steady-state iceline latitude versus solar constant curve is positive (negative) the steady-state solution is stable (unstable). Certain rather weak restrictions on the albedo function and on the heat transport are required for the proof, and their physical basis is discussed.

An investigation of the forward scattering theorem

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.

1987-01-01

The calculation of an EM wave's extinction loss during propagation within an inhomogeneous medium, as in active and passive remote sensing modeling, can be undertaken either through the summation of the scattering and absorption losses or through the use of the forward scattering theorem. Attention is presently given to the similarities and differences of these two approaches as a function of dielectric properties of a spherical scatterer and the incident frequency. Scattering loss is obtainable by integrating the magnitude-squared of the scattered field over a spherical surface surrounding the scatterer; the scattered field and the field within the scatterer are computed according to Mie theory.

Generating Test Templates via Automated Theorem Proving

NASA Technical Reports Server (NTRS)

Kancherla, Mani Prasad

1997-01-01

Testing can be used during the software development process to maintain fidelity between evolving specifications, program designs, and code implementations. We use a form of specification-based testing that employs the use of an automated theorem prover to generate test templates. A similar approach was developed using a model checker on state-intensive systems. This method applies to systems with functional rather than state-based behaviors. This approach allows for the use of incomplete specifications to aid in generation of tests for potential failure cases. We illustrate the technique on the cannonical triangle testing problem and discuss its use on analysis of a spacecraft scheduling system.

Mathematical Features of the Calculus

ERIC Educational Resources Information Center

Sauerheber, Richard D.

2010-01-01

The fundamental theorems of the calculus describe the relationships between derivatives and integrals of functions. The value of any function at a particular location is the definite derivative of its integral and the definite integral of its derivative. Thus, any value is the magnitude of the slope of the tangent of its integral at that position,…

Naïve Bayes classification in R.

PubMed

Zhang, Zhongheng

2016-06-01

Naïve Bayes classification is a kind of simple probabilistic classification methods based on Bayes' theorem with the assumption of independence between features. The model is trained on training dataset to make predictions by predict() function. This article introduces two functions naiveBayes() and train() for the performance of Naïve Bayes classification.

Nonorthogonal orbital based N-body reduced density matrices and their applications to valence bond theory. I. Hamiltonian matrix elements between internally contracted excited valence bond wave functions

NASA Astrophysics Data System (ADS)

Chen, Zhenhua; Chen, Xun; Wu, Wei

2013-04-01

In this series, the n-body reduced density matrix (n-RDM) approach for nonorthogonal orbitals and their applications to ab initio valence bond (VB) methods are presented. As the first paper of this series, Hamiltonian matrix elements between internally contracted VB wave functions are explicitly provided by means of nonorthogonal orbital based RDM approach. To this end, a more generalized Wick's theorem, called enhanced Wick's theorem, is presented both in arithmetical and in graphical forms, by which the deduction of expressions for the matrix elements between internally contracted VB wave functions is dramatically simplified, and the matrix elements are finally expressed in terms of tensor contractions of electronic integrals and n-RDMs of the reference VB self-consistent field wave function. A string-based algorithm is developed for the purpose of evaluating n-RDMs in an efficient way. Using the techniques presented in this paper, one is able to develop new methods and efficient algorithms for nonorthogonal orbital based many-electron theory much easier than by use of the first quantized formulism.

Circularly-symmetric complex normal ratio distribution for scalar transmissibility functions. Part I: Fundamentals

NASA Astrophysics Data System (ADS)

Yan, Wang-Ji; Ren, Wei-Xin

2016-12-01

Recent advances in signal processing and structural dynamics have spurred the adoption of transmissibility functions in academia and industry alike. Due to the inherent randomness of measurement and variability of environmental conditions, uncertainty impacts its applications. This study is focused on statistical inference for raw scalar transmissibility functions modeled as complex ratio random variables. The goal is achieved through companion papers. This paper (Part I) is dedicated to dealing with a formal mathematical proof. New theorems on multivariate circularly-symmetric complex normal ratio distribution are proved on the basis of principle of probabilistic transformation of continuous random vectors. The closed-form distributional formulas for multivariate ratios of correlated circularly-symmetric complex normal random variables are analytically derived. Afterwards, several properties are deduced as corollaries and lemmas to the new theorems. Monte Carlo simulation (MCS) is utilized to verify the accuracy of some representative cases. This work lays the mathematical groundwork to find probabilistic models for raw scalar transmissibility functions, which are to be expounded in detail in Part II of this study.

Slowly changing potential problems in Quantum Mechanics: Adiabatic theorems, ergodic theorems, and scattering

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

Fishman, S., E-mail: fishman@physics.technion.ac.il; Soffer, A., E-mail: soffer@math.rutgers.edu

2016-07-15

We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.

Arbitrary nonlinearity is sufficient to represent all functions by neural networks - A theorem

NASA Technical Reports Server (NTRS)

Kreinovich, Vladik YA.

1991-01-01

It is proved that if we have neurons implementing arbitrary linear functions and a neuron implementing one (arbitrary but smooth) nonlinear function g(x), then for every continuous function f(x sub 1,..., x sub m) of arbitrarily many variables, and for arbitrary e above 0, we can construct a network that consists of g-neurons and linear neurons, and computes f with precision e.

Functional thermo-dynamics: a generalization of dynamic density functional theory to non-isothermal situations.

PubMed

Anero, Jesús G; Español, Pep; Tarazona, Pedro

2013-07-21

We present a generalization of Density Functional Theory (DFT) to non-equilibrium non-isothermal situations. By using the original approach set forth by Gibbs in his consideration of Macroscopic Thermodynamics (MT), we consider a Functional Thermo-Dynamics (FTD) description based on the density field and the energy density field. A crucial ingredient of the theory is an entropy functional, which is a concave functional. Therefore, there is a one to one connection between the density and energy fields with the conjugate thermodynamic fields. The connection between the three levels of description (MT, DFT, FTD) is clarified through a bridge theorem that relates the entropy of different levels of description and that constitutes a generalization of Mermin's theorem to arbitrary levels of description whose relevant variables are connected linearly. Although the FTD level of description does not provide any new information about averages and correlations at equilibrium, it is a crucial ingredient for the dynamics in non-equilibrium states. We obtain with the technique of projection operators the set of dynamic equations that describe the evolution of the density and energy density fields from an initial non-equilibrium state towards equilibrium. These equations generalize time dependent density functional theory to non-isothermal situations. We also present an explicit model for the entropy functional for hard spheres.

Shades of American Identity: Implicit Relations between Ethnic and National Identities

PubMed Central

Devos, Thierry; Mohamed, Hafsa

2015-01-01

The issue of ethnic diversity and national identity in an immigrant nation such as the USA is a recurrent topic of debate. We review and integrate research examining the extent to which the American identity is implicitly granted or denied to members of different ethnic groups. Consistently, European Americans are implicitly conceived of as being more American than African, Asian, Latino, and even Native Americans. This implicit American = White effect emerges when explicit knowledge or perceptions point in the opposite direction. The propensity to deny the American identity to members of ethnic minorities is particularly pronounced when targets (individuals or groups) are construed through the lenses of ethnic identities. Implicit ethnic–national associations fluctuate as a function of perceivers’ ethnic identity and political orientation, but also contextual or situational factors. The tendency to equate being American with being White accounts for the strength of national identification (among European Americans) and behavioral responses including hiring recommendations and voting intentions. The robust propensity to deny the American identity to ethnic minority groups reflects an exclusionary national identity. PMID:27011765

Time-of-day effects in implicit racial in-group preferences are likely selection effects, not circadian rhythms

PubMed Central

2016-01-01

Time-of-day effects in human psychological functioning have been known of since the 1800s. However, outside of research specifically focused on the quantification of circadian rhythms, their study has largely been neglected. Moves toward online data collection now mean that psychological investigations take place around the clock, which affords researchers the ability to easily study time-of-day effects. Recent analyses have shown, for instance, that implicit attitudes have time-of-day effects. The plausibility that these effects indicate circadian rhythms rather than selection effects is considered in the current study. There was little evidence that the time-of-day effects in implicit attitudes shifted appropriately with factors known to influence the time of circadian rhythms. Moreover, even variables that cannot logically show circadian rhythms demonstrated stronger time-of-day effects than did implicit attitudes. Taken together, these results suggest that time-of-day effects in implicit attitudes are more likely to represent processes of selection rather than circadian rhythms, but do not rule out the latter possibility. PMID:27114886

Time-of-day effects in implicit racial in-group preferences are likely selection effects, not circadian rhythms.

PubMed

Schofield, Timothy P

2016-01-01

Time-of-day effects in human psychological functioning have been known of since the 1800s. However, outside of research specifically focused on the quantification of circadian rhythms, their study has largely been neglected. Moves toward online data collection now mean that psychological investigations take place around the clock, which affords researchers the ability to easily study time-of-day effects. Recent analyses have shown, for instance, that implicit attitudes have time-of-day effects. The plausibility that these effects indicate circadian rhythms rather than selection effects is considered in the current study. There was little evidence that the time-of-day effects in implicit attitudes shifted appropriately with factors known to influence the time of circadian rhythms. Moreover, even variables that cannot logically show circadian rhythms demonstrated stronger time-of-day effects than did implicit attitudes. Taken together, these results suggest that time-of-day effects in implicit attitudes are more likely to represent processes of selection rather than circadian rhythms, but do not rule out the latter possibility.

Dispositional mindfulness is associated with reduced implicit learning.

PubMed

Stillman, Chelsea M; Feldman, Halley; Wambach, Caroline G; Howard, James H; Howard, Darlene V

2014-08-01

Behavioral and neuroimaging evidence suggest that mindfulness exerts its salutary effects by disengaging habitual processes supported by subcortical regions and increasing effortful control processes supported by the frontal lobes. Here we investigated whether individual differences in dispositional mindfulness relate to performance on implicit sequence learning tasks in which optimal learning may in fact be impeded by the engagement of effortful control processes. We report results from two studies where participants completed a widely used questionnaire assessing mindfulness and one of two implicit sequence learning tasks. Learning was quantified using two commonly used measures of sequence learning. In both studies we detected a negative relationship between mindfulness and sequence learning, and the relationship was consistent across both learning measures. Our results, the first to show a negative relationship between mindfulness and implicit sequence learning, suggest that the beneficial effects of mindfulness do not extend to all cognitive functions. Copyright © 2014 Elsevier Inc. All rights reserved.

Free-form geometric modeling by integrating parametric and implicit PDEs.

PubMed

Du, Haixia; Qin, Hong

2007-01-01

Parametric PDE techniques, which use partial differential equations (PDEs) defined over a 2D or 3D parametric domain to model graphical objects and processes, can unify geometric attributes and functional constraints of the models. PDEs can also model implicit shapes defined by level sets of scalar intensity fields. In this paper, we present an approach that integrates parametric and implicit trivariate PDEs to define geometric solid models containing both geometric information and intensity distribution subject to flexible boundary conditions. The integrated formulation of second-order or fourth-order elliptic PDEs permits designers to manipulate PDE objects of complex geometry and/or arbitrary topology through direct sculpting and free-form modeling. We developed a PDE-based geometric modeling system for shape design and manipulation of PDE objects. The integration of implicit PDEs with parametric geometry offers more general and arbitrary shape blending and free-form modeling for objects with intensity attributes than pure geometric models.

Dissociating word stem completion and cued recall as a function of divided attention at retrieval.

PubMed

Clarke, A J Benjamin; Butler, Laurie T

2008-10-01

The aim of this study was to investigate the widely held, but largely untested, view that implicit memory (repetition priming) reflects an automatic form of retrieval. Specifically, in Experiment 1 we explored whether a secondary task (syllable monitoring), performed during retrieval, would disrupt performance on explicit (cued recall) and implicit (stem completion) memory tasks equally. Surprisingly, despite substantial memory and secondary costs to cued recall when performed with a syllable-monitoring task, the same manipulation had no effect on stem completion priming or on secondary task performance. In Experiment 2 we demonstrated that even when using a particularly demanding version of the stem completion task that incurred secondary task costs, the corresponding disruption to implicit memory performance was minimal. Collectively, the results are consistent with the view that implicit memory retrieval requires little or no processing capacity and is not seemingly susceptible to the effects of dividing attention at retrieval.

Quality correction factors of composite IMRT beam deliveries: theoretical considerations.

PubMed

Bouchard, Hugo

2012-11-01

In the scope of intensity modulated radiation therapy (IMRT) dosimetry using ionization chambers, quality correction factors of plan-class-specific reference (PCSR) fields are theoretically investigated. The symmetry of the problem is studied to provide recommendable criteria for composite beam deliveries where correction factors are minimal and also to establish a theoretical limit for PCSR delivery k(Q) factors. The concept of virtual symmetric collapsed (VSC) beam, being associated to a given modulated composite delivery, is defined in the scope of this investigation. Under symmetrical measurement conditions, any composite delivery has the property of having a k(Q) factor identical to its associated VSC beam. Using this concept of VSC, a fundamental property of IMRT k(Q) factors is demonstrated in the form of a theorem. The sensitivity to the conditions required by the theorem is thoroughly examined. The theorem states that if a composite modulated beam delivery produces a uniform dose distribution in a volume V(cyl) which is symmetric with the cylindrical delivery and all beams fulfills two conditions in V(cyl): (1) the dose modulation function is unchanged along the beam axis, and (2) the dose gradient in the beam direction is constant for a given lateral position; then its associated VSC beam produces no lateral dose gradient in V(cyl), no matter what beam modulation or gantry angles are being used. The examination of the conditions required by the theorem lead to the following results. The effect of the depth-dose gradient not being perfectly constant with depth on the VSC beam lateral dose gradient is found negligible. The effect of the dose modulation function being degraded with depth on the VSC beam lateral dose gradient is found to be only related to scatter and beam hardening, as the theorem holds also for diverging beams. The use of the symmetry of the problem in the present paper leads to a valuable theorem showing that k(Q) factors of composite IMRT beam deliveries are close to unity under specific conditions. The theoretical limit k(Q(pcsr),Q(msr) ) (f(pcsr),f(msr) )=1 is determined based on the property of PCSR deliveries to provide a uniform dose in the target volume. The present approach explains recent experimental observations and proposes ideal conditions for IMRT reference dosimetry. The result of this study could potentially serve as a theoretical basis for reference dosimetry of composite IMRT beam deliveries or for routine IMRT quality assurance.

The Non-Signalling theorem in generalizations of Bell's theorem

NASA Astrophysics Data System (ADS)

Walleczek, J.; Grössing, G.

2014-04-01

Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational interpretation of the non-signalling theorem. We here argue that the non-signalling theorem must instead be viewed as an epistemic, operational theorem i.e. one that refers exclusively to what epistemic agents can, or rather cannot, do. That is, we emphasize that the non-signalling theorem is a theorem about the operational inability of epistemic agents to signal information. In other words, as a proper principle, the non-signalling theorem may only be employed as an epistemic, phenomenological, or operational principle. Critically, our argument emphasizes that the non-signalling principle must not be used as an ontic principle about physical reality as such, i.e. as a theorem about the nature of physical reality independently of epistemic agents e.g. human observers. One major reason in favor of our conclusion is that any definition of signalling or of non-signalling invariably requires a reference to epistemic agents, and what these agents can actually measure and report. Otherwise, the non-signalling theorem would equal a general "no-influence" theorem. In conclusion, under the assumption that the non-signalling theorem is epistemic (i.e. "epistemic non-signalling"), the search for deterministic approaches to quantum mechanics, including NHVTs and an emergent quantum mechanics, continues to be a viable research program towards disclosing the foundations of physical reality at its smallest dimensions.

Explicit and implicit anti-fat attitudes in children and their relationships with their body images.

PubMed

Solbes, Irene; Enesco, Ileana

2010-02-01

This study aimed to explore the prevalence of negative attitudes toward overweight peers among children using different explicit and implicit measures, and to analyze their relationships with some aspects of their body image. A total of 120 children aged 6-11 years were interviewed using a computer program that simulated a game containing several tasks. Specifically, we have applied multiple measures of explicit attitudes toward average-weight/overweight peers, several personal body attitudes questions and a child-oriented version of the Implicit Association Test. Our participants showed important prejudice and stereotypes against overweight children, both at the explicit and implicit levels. However, we found important differences in the intensity of prejudice and its developmental course as a function of the tasks and the type of measurement used to assess it. Children who grow up in Western societies idealize thinness from an early age and denigrate overweight, to which they associate explicitly and implicitly a series of negative traits that have nothing to do with the weight. As they grow older, they seem to reduce their levels of explicit prejudice, but not the intensity of implicit bias. More research is needed to study in depth prejudice and discrimination toward overweight children from a developmental point of view. Copyright 2010 S. Karger AG, Basel.

Implicit Particle Filter for Power System State Estimation with Large Scale Renewable Power Integration.

NASA Astrophysics Data System (ADS)

Uzunoglu, B.; Hussaini, Y.

2017-12-01

Implicit Particle Filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability by an implicit step . It optimizes a nonlinear cost function which can be inherited from legacy assimilation routines . Dynamic state estimation for almost real-time applications in power systems are becomingly increasingly more important with integration of variable wind and solar power generation. New advanced state estimation tools that will replace the old generation state estimation in addition to having a general framework of complexities should be able to address the legacy software and able to integrate the old software in a mathematical framework while allowing the power industry need for a cautious and evolutionary change in comparison to a complete revolutionary approach while addressing nonlinearity and non-normal behaviour. This work implements implicit particle filter as a state estimation tool for the estimation of the states of a power system and presents the first implicit particle filter application study on a power system state estimation. The implicit particle filter is introduced into power systems and the simulations are presented for a three-node benchmark power system . The performance of the filter on the presented problem is analyzed and the results are presented.

Excitatory stimulation of the right inferior parietal cortex lessens implicit religiousness/spirituality.

PubMed

Crescentini, Cristiano; Di Bucchianico, Marilena; Fabbro, Franco; Urgesi, Cosimo

2015-04-01

Although religiousness and spirituality (RS) are considered two fundamental constituents of human life, neuroscientific investigation has long avoided the study of their neurocognitive basis. Nevertheless, recent investigations with brain imaging and brain damaged patients, and more recently with brain stimulation methods, have documented important associations between RS beliefs and experiences and frontoparietal neural activity. In this study, we further investigated how individuals' implicit RS self-representations can be modulated by changes in right inferior parietal lobe (IPL) excitability, a key region associated to RS. To this end, we combined continuous theta burst stimulation (cTBS), intermittent TBS (iTBS), and sham TBS with RS-related, Implicit Association Test (IAT) and with a control self-esteem (SE) IAT in a group of fourteen healthy adult individuals. A specific decrease of implicit RS, as measured with the IAT effect, was induced by increasing IPL excitability with iTBS; conversely cTBS, which is supposedly inhibitory, left participants' implicit RS unchanged. The performance in the control SE-IAT was left unchanged by any TBS stimulation. These data showed the causative role of right IPL functional state in mediating plastic changes of implicit RS. Implications of these results are also discussed in the light of the variability of behavioral effects associated with TBS. Copyright © 2015 Elsevier Ltd. All rights reserved.

Consistency of the adiabatic theorem.

PubMed

Amin, M H S

2009-06-05

The adiabatic theorem provides the basis for the adiabatic model of quantum computation. Recently the conditions required for the adiabatic theorem to hold have become a subject of some controversy. Here we show that the reported violations of the adiabatic theorem all arise from resonant transitions between energy levels. In the absence of fast driven oscillations the traditional adiabatic theorem holds. Implications for adiabatic quantum computation are discussed.

Normal order and extended Wick theorem for a multiconfiguration reference wave function

NASA Astrophysics Data System (ADS)

Kutzelnigg, Werner; Mukherjee, Debashis

1997-07-01

A generalization of normal ordering and of Wick's theorem with respect to an arbitrary reference function Φ as some generalized "physical vacuum" is formulated in a different (but essentially equivalent) way than that suggested previously by one of the present authors. Guiding principles are that normal order operators with respect to any reference state must be expressible as linear combinations of those with respect to the genuine vacuum, that the vacuum expectation value of a normal order operator must vanish (with respect to the vacuum to which it is in normal order), and that the well-known formalism for a single Slater determinant as physical vacuum must be contained as a special case. The derivation is largely based on the concepts of "Quantum Chemistry in Fock space," which means that particle-number-conserving operators (excitation operators) play a central role. Nevertheless, the contraction rules in the frame of a generalized Wick theorem are derived, that hold for non-particle-number-conserving operators as well. The contraction rules are formulated and illustrated in terms of diagrams. The contractions involve the "residual n-particle density matrices" λ, which are the irreducible (non-factorizable) parts of the conventional n-particle density matrices γ, in the sense of a cumulant expansion for the density. A spinfree formulation is presented as well. The expression of the Hamiltonian in normal order with respect to a multiconfiguration reference function leads to a natural definition of a generalized Fock operator. MC-SCF-theory is easily worked out in this context. The paper concludes with a discussion of the excited configurations and the first-order interacting space, that underlies a perturbative coupled cluster type correction to the MCSCF function for an arbitrary reference function, and with general implications of the new formalism, that is related to "internally contracted multireference configuration interaction." The present generalization of normal ordering is not only valid for arbitrary reference functions, but also if the reference state is an ensemble state.

Optimal no-go theorem on hidden-variable predictions of effect expectations

NASA Astrophysics Data System (ADS)

Blass, Andreas; Gurevich, Yuri

2018-03-01

No-go theorems prove that, under reasonable assumptions, classical hidden-variable theories cannot reproduce the predictions of quantum mechanics. Traditional no-go theorems proved that hidden-variable theories cannot predict correctly the values of observables. Recent expectation no-go theorems prove that hidden-variable theories cannot predict the expectations of observables. We prove the strongest expectation-focused no-go theorem to date. It is optimal in the sense that the natural weakenings of the assumptions and the natural strengthenings of the conclusion make the theorem fail. The literature on expectation no-go theorems strongly suggests that the expectation-focused approach is more general than the value-focused one. We establish that the expectation approach is not more general.

The invariant of the stiffness filter function with the weight filter function of the power function form

NASA Astrophysics Data System (ADS)

Shang, Zhen; Sui, Yun-Kang

2012-12-01

Based on the independent, continuous and mapping (ICM) method and homogenization method, a research model is constructed to propose and deduce a theorem and corollary from the invariant between the weight filter function and the corresponding stiffness filter function of the form of power function. The efficiency in searching for optimum solution will be raised via the choice of rational filter functions, so the above mentioned results are very important to the further study of structural topology optimization.

On the divergence of triangular and eccentric spherical sums of double Fourier series

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

Karagulyan, G A

We construct a continuous function on the torus with almost everywhere divergent triangular sums of double Fourier series. We also prove an analogous theorem for eccentric spherical sums. Bibliography: 14 titles.

Decomposition Theory in the Teaching of Elementary Linear Algebra.

ERIC Educational Resources Information Center

London, R. R.; Rogosinski, H. P.

1990-01-01

Described is a decomposition theory from which the Cayley-Hamilton theorem, the diagonalizability of complex square matrices, and functional calculus can be developed. The theory and its applications are based on elementary polynomial algebra. (KR)

Geometry and combinatorics of Julia sets of real quadratic maps

NASA Astrophysics Data System (ADS)

Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N.

1984-10-01

For real λ a correspondence is made between the Julia set B λ for z→( z- λ)2, in the hyperbolic case, and the set of λ-chains λ±√(λ±√(λ±..., with the aid of Cremer's theorem. It is shown how a number of features of Bλ can be understood in terms of λ-chains. The structure of B λ is determined by certain equivalence classes of λ-chains, fixed by orders of visitation of certain real cycles; and the bifurcation history of a given cycle can be conveniently computed via the combinatorics of λ-chains. The functional equations obeyed by attractive cycles are investigated, and their relation to λ-chains is given. The first cascade of period-doubling bifurcations is described from the point of view of the associated Julia sets and λ-chains. Certain "Julia sets" associated with the Feigenbaum function and some theorems of Lanford are discussed.

Nonequilibrium thermodynamics of restricted Boltzmann machines.

PubMed

Salazar, Domingos S P

2017-08-01

In this work, we analyze the nonequilibrium thermodynamics of a class of neural networks known as restricted Boltzmann machines (RBMs) in the context of unsupervised learning. We show how the network is described as a discrete Markov process and how the detailed balance condition and the Maxwell-Boltzmann equilibrium distribution are sufficient conditions for a complete thermodynamics description, including nonequilibrium fluctuation theorems. Numerical simulations in a fully trained RBM are performed and the heat exchange fluctuation theorem is verified with excellent agreement to the theory. We observe how the contrastive divergence functional, mostly used in unsupervised learning of RBMs, is closely related to nonequilibrium thermodynamic quantities. We also use the framework to interpret the estimation of the partition function of RBMs with the annealed importance sampling method from a thermodynamics standpoint. Finally, we argue that unsupervised learning of RBMs is equivalent to a work protocol in a system driven by the laws of thermodynamics in the absence of labeled data.

The complete proof on the optimal ordering policy under cash discount and trade credit

NASA Astrophysics Data System (ADS)

Chung, Kun-Jen

2010-04-01

Huang ((2005), 'Buyer's Optimal Ordering Policy and Payment Policy under Supplier Credit', International Journal of Systems Science, 36, 801-807) investigates the buyer's optimal ordering policy and payment policy under supplier credit. His inventory model is correct and interesting. Basically, he uses an algebraic method to locate the optimal solution of the annual total relevant cost TRC(T) and ignores the role of the functional behaviour of TRC(T) in locating the optimal solution of it. However, as argued in this article, Huang needs to explore the functional behaviour of TRC(T) to justify his solution. So, from the viewpoint of logic, the proof about Theorem 1 in Huang has some shortcomings such that the validity of Theorem 1 in Huang is questionable. The main purpose of this article is to remove and correct those shortcomings in Huang and present the complete proofs for Huang.

A Liouville type theorem for Lane-Emden systems involving the fractional Laplacian

NASA Astrophysics Data System (ADS)

Quaas, Alexander; Xia, Aliang

2016-08-01

We establish a Liouville type theorem for the fractional Lane-Emden system: {(-Δ)αu=vqin  RN,(-Δ)αv=upin  RN, where α \\in (0,1) , N>2α and p, q are positive real numbers and in an appropriate new range. To prove our result we will use the local realization of fractional Laplacian, which can be constructed as a Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre (2007 Commun. PDE 32 1245-60). Our proof is based on a monotonicity argument for suitable transformed functions and the method of moving planes in a half infinite cylinder ({IR}× S+N , where S+N is the half unit sphere in {{{R}}N+1} ) based on maximum principles which are obtained by barrier functions and a coupling argument using a fractional Sobolev trace inequality.

Quantum properties of supersymmetric theories regularized by higher covariant derivatives

NASA Astrophysics Data System (ADS)

Stepanyantz, Konstantin

2018-02-01

We investigate quantum corrections in \\mathscr{N} = 1 non-Abelian supersymmetric gauge theories, regularized by higher covariant derivatives. In particular, by the help of the Slavnov-Taylor identities we prove that the vertices with two ghost legs and one leg of the quantum gauge superfield are finite in all orders. This non-renormalization theorem is confirmed by an explicit one-loop calculation. By the help of this theorem we rewrite the exact NSVZ β-function in the form of the relation between the β-function and the anomalous dimensions of the matter superfields, of the quantum gauge superfield, and of the Faddeev-Popov ghosts. Such a relation has simple qualitative interpretation and allows suggesting a prescription producing the NSVZ scheme in all loops for the theories regularized by higher derivatives. This prescription is verified by the explicit three-loop calculation for the terms quartic in the Yukawa couplings.

Using Pictures to Enhance Students' Understanding of Bayes' Theorem

ERIC Educational Resources Information Center

Trafimow, David

2011-01-01

Students often have difficulty understanding algebraic proofs of statistics theorems. However, it sometimes is possible to prove statistical theorems with pictures in which case students can gain understanding more easily. I provide examples for two versions of Bayes' theorem.

A hierarchical generalization of the acoustic reciprocity theorem involving higher-order derivatives and interaction quantities.

PubMed

Lin, Ju; Li, Jie; Li, Xiaolei; Wang, Ning

2016-10-01

An acoustic reciprocity theorem is generalized, for a smoothly varying perturbed medium, to a hierarchy of reciprocity theorems including higher-order derivatives of acoustic fields. The standard reciprocity theorem is the first member of the hierarchy. It is shown that the conservation of higher-order interaction quantities is related closely to higher-order derivative distributions of perturbed media. Then integral reciprocity theorems are obtained by applying Gauss's divergence theorem, which give explicit integral representations connecting higher-order interactions and higher-order derivative distributions of perturbed media. Some possible applications to an inverse problem are also discussed.

Discrete Time Rescaling Theorem: Determining Goodness of Fit for Discrete Time Statistical Models of Neural Spiking

PubMed Central

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-01-01

One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time rescaling theorem provides a goodness of fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model’s spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies upon assumptions of continuously defined time and instantaneous events. However spikes have finite width and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time rescaling theorem which analytically corrects for the effects of finite resolution. This allows us to define a rescaled time which is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting Generalized Linear Models (GLMs) to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false positive rate of the KS test and greatly increasing the reliability of model evaluation based upon the time rescaling theorem. PMID:20608868

Discrete time rescaling theorem: determining goodness of fit for discrete time statistical models of neural spiking.

PubMed

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-10-01

One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time-rescaling theorem provides a goodness-of-fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model's spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov-Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies on assumptions of continuously defined time and instantaneous events. However, spikes have finite width, and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time-rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time-rescaling theorem that analytically corrects for the effects of finite resolution. This allows us to define a rescaled time that is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting generalized linear models to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false-positive rate of the KS test and greatly increasing the reliability of model evaluation based on the time-rescaling theorem.

Subcortical BOLD responses during visual sexual stimulation vary as a function of implicit porn associations in women

PubMed Central

de Jong, Peter J.; Georgiadis, Janniko R.

2014-01-01

Lifetime experiences shape people’s attitudes toward sexual stimuli. Visual sexual stimulation (VSS), for instance, may be perceived as pleasurable by some, but as disgusting or ambiguous by others. VSS depicting explicit penile–vaginal penetration (PEN) is relevant in this respect, because the act of penetration is a core sexual activity. In this study, 20 women without sexual complaints participated. We used functional magnetic resonance imaging and a single-target implicit association task to investigate how brain responses to PEN were modulated by the initial associations in memory (PEN-‘hot’ vs PEN-disgust) with such hardcore pornographic stimuli. Many brain areas responded to PEN in the same way they responded to disgust stimuli, and PEN-induced brain activity was prone to modulation by subjective disgust ratings toward PEN stimuli. The relative implicit PEN-disgust (relative to PEN-‘hot’) associations exclusively modulated PEN-induced brain responses: comparatively negative (PEN-disgust) implicit associations with pornography predicted the strongest PEN-related responses in the basal forebrain (including nucleus accumbens and bed nucleus of stria terminalis), midbrain and amygdala. Since these areas are often implicated in visual sexual processing, the present findings should be taken as a warning: apparently their involvement may also indicate a negative or ambivalent attitude toward sexual stimuli. PMID:23051899

Subcortical BOLD responses during visual sexual stimulation vary as a function of implicit porn associations in women.

PubMed

Borg, Charmaine; de Jong, Peter J; Georgiadis, Janniko R

2014-02-01

Lifetime experiences shape people's attitudes toward sexual stimuli. Visual sexual stimulation (VSS), for instance, may be perceived as pleasurable by some, but as disgusting or ambiguous by others. VSS depicting explicit penile-vaginal penetration (PEN) is relevant in this respect, because the act of penetration is a core sexual activity. In this study, 20 women without sexual complaints participated. We used functional magnetic resonance imaging and a single-target implicit association task to investigate how brain responses to PEN were modulated by the initial associations in memory (PEN-'hot' vs PEN-disgust) with such hardcore pornographic stimuli. Many brain areas responded to PEN in the same way they responded to disgust stimuli, and PEN-induced brain activity was prone to modulation by subjective disgust ratings toward PEN stimuli. The relative implicit PEN-disgust (relative to PEN-'hot') associations exclusively modulated PEN-induced brain responses: comparatively negative (PEN-disgust) implicit associations with pornography predicted the strongest PEN-related responses in the basal forebrain (including nucleus accumbens and bed nucleus of stria terminalis), midbrain and amygdala. Since these areas are often implicated in visual sexual processing, the present findings should be taken as a warning: apparently their involvement may also indicate a negative or ambivalent attitude toward sexual stimuli.

Modulating Emotional Experience Using Electrical Stimulation of the Medial-Prefrontal Cortex: A Preliminary tDCS-fMRI Study.

PubMed

Abend, Rany; Sar-El, Roy; Gonen, Tal; Jalon, Itamar; Vaisvaser, Sharon; Bar-Haim, Yair; Hendler, Talma

2018-05-09

Implicit regulation of emotions involves medial-prefrontal cortex (mPFC) regions exerting regulatory control over limbic structures. Diminished regulation relates to aberrant mPFC functionality and psychopathology. Establishing means of modulating mPFC functionality could benefit research on emotion and its dysregulation. Here, we tested the capacity of transcranial direct current stimulation (tDCS) targeting mPFC to modulate subjective emotional states by facilitating implicit emotion regulation. Stimulation was applied concurrently with functional magnetic resonance imaging to validate its neurobehavioral effect. Sixteen participants were each scanned twice, counterbalancing active and sham tDCS application, while undergoing negative mood induction (clips featuring negative vs. neutral contents). Effects of stimulation on emotional experience were assessed using subjective and neural measures. Subjectively, active stimulation led to significant reduction in reported intensity of experienced emotions to negatively valenced (p = 0.005) clips but not to neutral clips (p > 0.99). Active stimulation further mitigated a rise in stress levels from pre- to post-induction (sham: p = 0.004; active: p = 0.15). Neurally, stimulation increased activation in mPFC regions associated with implicit emotion regulation (ventromedial-prefrontal cortex; subgenual anterior-cingulate cortex, sgACC), and in ventral striatum, a core limbic structure (all ps < 0.05). Stimulation also altered functional connectivity (assessed using whole-brain psycho-physiological interaction) between these regions, and with additional limbic regions. Stimulation-induced sgACC activation correlated with reported emotion intensity and depressive symptoms (rs > 0.64, ps < 0.018), suggesting individual differences in stimulation responsivity. Results of this study indicate the potential capacity of tDCS to facilitate brain activation in mPFC regions underlying implicit regulation of emotion and accordingly modulate subjective emotional experiences. © 2018 International Neuromodulation Society.

Working memory moderates the effect of the integrative process of implicit and explicit autonomous motivation on academic achievement.

PubMed

Gareau, Alexandre; Gaudreau, Patrick

2017-11-01

In previous research, autonomous motivation (AM) has been found to be associated with school achievement, but the relation has been largely heterogeneous across studies. AM has typically been assessed with explicit measures such as self-report questionnaires. Recent self-determination theory (SDT) research has suggested that converging implicit and explicit measures can be taken to characterize the integrative process in SDT. Drawing from dual-process theories, we contended that explicit AM is likely to promote school achievement when it is part of an integrated cognitive system that combines easily accessible mental representations (i.e., implicit AM) and efficient executive functioning. A sample of 272 university students completed a questionnaire and a lexical decision task to assess their explicit and implicit AM, respectively, and they also completed working memory capacity measures. Grades were obtained at the end of the semester to examine the short-term prospective effect of implicit and explicit AM, working memory, and their interaction. Results of moderation analyses have provided support for a synergistic interaction in which the association between explicit AM and academic achievement was positive and significant only for individuals with high level of implicit AM. Moreover, working memory was moderating the synergistic effect of explicit and implicit AM. Explicit AM was positively associated with academic achievement for students with average-to-high levels of working memory capacity, but only if their motivation operated synergistically with high implicit AM. The integrative process thus seems to hold better proprieties for achievement than the sole effect of explicit AM. Implications for SDT are outlined. © 2017 The British Psychological Society.

Role of Spontaneous Brain Activity in Explicit and Implicit Aspects of Cognitive Flexibility under Socially Conflicting Situations: A Resting-state fMRI Study using Fractional Amplitude of Low-frequency Fluctuations.

PubMed

Fujino, Junya; Tei, Shisei; Jankowski, Kathryn F; Kawada, Ryosaku; Murai, Toshiya; Takahashi, Hidehiko

2017-12-26

We are constantly exposed to socially conflicting situations in everyday life, and cognitive flexibility is essential for adaptively coping with such difficulties. Flexible goal choice and pursuit are not exclusively conscious, and therefore cognitive flexibility involves both explicit and implicit forms of processing. However, it is unclear how individual differences in explicit and implicit aspects of flexibility are associated with neural activity in a resting state. Here, we measured intrinsic fractional amplitude of low-frequency fluctuations (fALFF) by resting-state functional magnetic resonance imaging (RS-fMRI) as an indicator of regional brain spontaneous activity, together with explicit and implicit aspects of cognitive flexibility using the Cognitive Flexibility Scale (CFS) and Implicit Association Test (IAT). Consistent with the dual processing theory, there was a strong association between explicit aspects of flexibility (CFS score) and "rationalism" thinking style and between implicit aspects (IAT effect) and "experientialism." The level of explicit flexibility was also correlated with fALFF values in the left lateral prefrontal cortex, whereas the level of implicit flexibility was correlated with fALFF values in the right cerebellum. Furthermore, the fALFF values in both regions predicted individual preference for flexible decision-making strategy in a vignettes simulation task. These results add to our understanding of the neural mechanisms underlying flexible decision-making for solving social conflicts. More generally, our findings highlight the utility of RS-fMRI combined with both explicit and implicit psychometric measures for better understanding individual differences in social cognition. Copyright © 2017 The Author(s). Published by Elsevier Ltd.. All rights reserved.

Evidence for a neural dual-process account for adverse effects of cognitive control.

PubMed

Zink, Nicolas; Stock, Ann-Kathrin; Colzato, Lorenza; Beste, Christian

2018-06-09

Advantageous effects of cognitive control are well-known, but cognitive control may also have adverse effects, for example when it suppresses the implicit processing of stimulus-response (S-R) bindings that could benefit task performance. Yet, the neurophysiological and functional neuroanatomical structures associated with adverse effects of cognitive control are poorly understood. We used an extreme group approach to compare individuals who exhibit adverse effects of cognitive control to individuals who do not by combining event-related potentials (ERPs), source localization, time-frequency analysis and network analysis methods. While neurophysiological correlates of cognitive control (i.e. N2, N450, theta power and theta-mediated neuronal network efficiency) and task-set updating (P3) both reflect control demands and implicit information processing, differences in the degree of adverse cognitive control effects are associated with two independent neural mechanisms: Individuals, who show adverse behavioral effects of cognitive control, show reduced small-world properties and thus reduced efficiency in theta-modulated networks when they fail to effectively process implicit information. In contrast to this, individuals who do not display adverse control effects show enhanced task-set updating mechanism when effectively processing implicit information, which is reflected by the P3 ERP component and associated with the temporo-parietal junction (TPJ, BA 40) and medial frontal gyrus (MFG; BA 8). These findings suggest that implicit S-R contingencies, which benefit response selection without cognitive control, are always 'picked up', but may fail to be integrated with task representations to guide response selection. This provides evidence for a neurophysiological and functional neuroanatomical "dual-process" account of adverse cognitive control effects.

Implicit Coordination Strategies for Effective Team Communication.

PubMed

Butchibabu, Abhizna; Sparano-Huiban, Christopher; Sonenberg, Liz; Shah, Julie

2016-06-01

We investigated implicit communication strategies for anticipatory information sharing during team performance of tasks with varying degrees of complexity. We compared the strategies used by teams with the highest level of performance to those used by the lowest-performing teams to evaluate the frequency and methods of communications used as a function of task structure. High-performing teams share information by anticipating the needs of their teammates rather than explicitly requesting the exchange of information. As the complexity of a task increases to involve more interdependence among teammates, the impact of coordination on team performance also increases. This observation motivated us to conduct a study of anticipatory information sharing as a function of task complexity. We conducted an experiment in which 13 teams of four people performed collaborative search-and-deliver tasks with varying degrees of complexity in a simulation environment. We elaborated upon prior characterizations of communication as implicit versus explicit by dividing implicit communication into two subtypes: (a) deliberative/goal information and (b) reactive status updates. We then characterized relationships between task structure, implicit communication, and team performance. We found that the five teams with the fastest task completion times and lowest idle times exhibited higher rates of deliberative communication versus reactive communication during high-complexity tasks compared with the five teams with the slowest completion times and longest idle times (p = .039). Teams in which members proactively communicated information about their next goal to teammates exhibited improved team performance. The findings from our work can inform the design of communication strategies for team training to improve performance of complex tasks. © 2016, Human Factors and Ergonomics Society.

On the symmetry foundation of double soft theorems

NASA Astrophysics Data System (ADS)

Li, Zhi-Zhong; Lin, Hung-Hwa; Zhang, Shun-Qing

2017-12-01

Double-soft theorems, like its single-soft counterparts, arises from the underlying symmetry principles that constrain the interactions of massless particles. While single soft theorems can be derived in a non-perturbative fashion by employing current algebras, recent attempts of extending such an approach to known double soft theorems has been met with difficulties. In this work, we have traced the difficulty to two inequivalent expansion schemes, depending on whether the soft limit is taken asymmetrically or symmetrically, which we denote as type A and B respectively. The soft-behaviour for type A scheme can simply be derived from single soft theorems, and are thus non-perturbatively protected. For type B, the information of the four-point vertex is required to determine the corresponding soft theorems, and thus are in general not protected. This argument can be readily extended to general multi-soft theorems. We also ask whether unitarity can be emergent from locality together with the two kinds of soft theorems, which has not been fully investigated before.

An advanced probabilistic structural analysis method for implicit performance functions

NASA Technical Reports Server (NTRS)

Wu, Y.-T.; Millwater, H. R.; Cruse, T. A.

1989-01-01

In probabilistic structural analysis, the performance or response functions usually are implicitly defined and must be solved by numerical analysis methods such as finite element methods. In such cases, the most commonly used probabilistic analysis tool is the mean-based, second-moment method which provides only the first two statistical moments. This paper presents a generalized advanced mean value (AMV) method which is capable of establishing the distributions to provide additional information for reliability design. The method requires slightly more computations than the second-moment method but is highly efficient relative to the other alternative methods. In particular, the examples show that the AMV method can be used to solve problems involving non-monotonic functions that result in truncated distributions.

Possible roles for fronto-striatal circuits in reading disorder

PubMed Central

Hancock, Roeland; Richlan, Fabio; Hoeft, Fumiko

2016-01-01

Several studies have reported hyperactivation in frontal and striatal regions in individuals with reading disorder (RD) during reading-related tasks. Hyperactivation in these regions is typically interpreted as a form of neural compensation and related to articulatory processing. Fronto-striatal hyperactivation in RD can however, also arise from fundamental impairment in reading related processes, such as phonological processing and implicit sequence learning relevant to early language acquisition. We review current evidence for the compensation hypothesis in RD and apply large-scale reverse inference to investigate anatomical overlap between hyperactivation regions and neural systems for articulation, phonological processing, implicit sequence learning. We found anatomical convergence between hyperactivation regions and regions supporting articulation, consistent with the proposed compensatory role of these regions, and low convergence with phonological and implicit sequence learning regions. Although the application of large-scale reverse inference to decode function in a clinical population should be interpreted cautiously, our findings suggest future lines of research that may clarify the functional significance of hyperactivation in RD. PMID:27826071

Aspects of Higher-Spin Conformal Field Theories and Their Renormalization Group Flows

NASA Astrophysics Data System (ADS)

Diab, Kenan S.

In this thesis, we study conformal field theories (CFTs) with higher-spin symmetry and the renormalization group flows of some models with interactions that weakly break the higher-spin symmetry. When the higher-spin symmetry is exact, we will present CFT analogues of two classic results in quantum field theory: the Coleman-Mandula theorem, which is the subject of chapter 2, and the Weinberg-Witten theorem, which is the subject of chapter 3. Schematically, our Coleman-Mandula analogue states that a CFT that contains a symmetric conserved current of spin s > 2 in any dimension d > 3 is effectively free, and our Weinberg-Witten analogue states that the presence of certain short, higher-spin, "sufficiently asymmetric" representations of the conformal group is either inconsistent with conformal symmetry or leads to free theories in d = 4 dimensions. In both chapters, the basic strategy is to solve certain Ward identities in convenient kinematical limits and thereby show that the number of solutions is very limited. In the latter chapter, Hofman-Maldacena bounds, which constrain one-point functions of the stress tensor in general states, play a key role. Then, in chapter 4, we will focus on the particular examples of the O(N) and Gross-Neveu model in continuous dimensions. Using diagrammatic techniques, we explicitly calculate how the coefficients of the two-point function of a U(1) current and the two-point function of the stress tensor (CJ and CT, respectively) are renormalized in the 1/N and epsilon expansions. From the higher-spin perspective, these models are interesting since they are related via the AdS/CFT correspondence to Vasiliev gravity. In addition to checking and extending a number of previously-known results about CT and CJ in these theories, we find that in certain dimensions, CJ and CT are not monotonic along the renormalization group flow. Although it was already known that certain supersymmetric models do not satisfy a "CJ"- or " CT"-theorem, this shows that such a theorem is unlikely to hold even under more restrictive assumptions.

Chemical Equilibrium and Polynomial Equations: Beware of Roots.

ERIC Educational Resources Information Center

Smith, William R.; Missen, Ronald W.

1989-01-01

Describes two easily applied mathematical theorems, Budan's rule and Rolle's theorem, that in addition to Descartes's rule of signs and intermediate-value theorem, are useful in chemical equilibrium. Provides examples that illustrate the use of all four theorems. Discusses limitations of the polynomial equation representation of chemical…

Approaching Cauchy's Theorem

ERIC Educational Resources Information Center

Garcia, Stephan Ramon; Ross, William T.

2017-01-01

We hope to initiate a discussion about various methods for introducing Cauchy's Theorem. Although Cauchy's Theorem is the fundamental theorem upon which complex analysis is based, there is no "standard approach." The appropriate choice depends upon the prerequisites for the course and the level of rigor intended. Common methods include…

In search of the Hohenberg-Kohn theorem

NASA Astrophysics Data System (ADS)

Lammert, Paul E.

2018-04-01

The Hohenberg-Kohn theorem, a cornerstone of electronic density functional theory, concerns uniqueness of external potentials yielding given ground densities of an N -body system. The problem is rigorously explored in a universe of three-dimensional Kato-class potentials, with emphasis on trade-offs between conditions on the density and conditions on the potential sufficient to ensure uniqueness. Sufficient conditions range from none on potentials coupled with everywhere strict positivity of the density to none on the density coupled with something a little weaker than local 3 N /2 -power integrability of the potential on a connected full-measure set. A second theme is localizability, that is, the possibility of uniqueness over subsets of R3 under less stringent conditions.

Theorem Proving in Intel Hardware Design

NASA Technical Reports Server (NTRS)

O'Leary, John

2009-01-01

For the past decade, a framework combining model checking (symbolic trajectory evaluation) and higher-order logic theorem proving has been in production use at Intel. Our tools and methodology have been used to formally verify execution cluster functionality (including floating-point operations) for a number of Intel products, including the Pentium(Registered TradeMark)4 and Core(TradeMark)i7 processors. Hardware verification in 2009 is much more challenging than it was in 1999 - today s CPU chip designs contain many processor cores and significant firmware content. This talk will attempt to distill the lessons learned over the past ten years, discuss how they apply to today s problems, outline some future directions.

Mathematical and physical meaning of the Bell inequalities

NASA Astrophysics Data System (ADS)

Santos, Emilio

2016-09-01

It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values \\{0,1\\}. A hidden variables model may be defined as a mapping between a set of quantum projection operators and a set of random variables. The model is noncontextual if there is a joint probability distribution. The Bell inequalities are necessary conditions for its existence. The inequalities are most relevant when measurements are performed at space-like separation, thus showing a conflict between quantum mechanics and local realism (Bell's theorem). The relations of the Bell inequalities with contextuality, the Kochen-Specker theorem, and quantum entanglement are briefly discussed.

Early Vector Calculus: A Path through Multivariable Calculus

ERIC Educational Resources Information Center

Robertson, Robert L.

2013-01-01

The divergence theorem, Stokes' theorem, and Green's theorem appear near the end of calculus texts. These are important results, but many instructors struggle to reach them. We describe a pathway through a standard calculus text that allows instructors to emphasize these theorems. (Contains 2 figures.)

Pick's Theorem: What a Lemon!

ERIC Educational Resources Information Center

Russell, Alan R.

2004-01-01

Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.

Implicit structured sequence learning: an fMRI study of the structural mere-exposure effect

PubMed Central

Folia, Vasiliki; Petersson, Karl Magnus

2014-01-01

In this event-related fMRI study we investigated the effect of 5 days of implicit acquisition on preference classification by means of an artificial grammar learning (AGL) paradigm based on the structural mere-exposure effect and preference classification using a simple right-linear unification grammar. This allowed us to investigate implicit AGL in a proper learning design by including baseline measurements prior to grammar exposure. After 5 days of implicit acquisition, the fMRI results showed activations in a network of brain regions including the inferior frontal (centered on BA 44/45) and the medial prefrontal regions (centered on BA 8/32). Importantly, and central to this study, the inclusion of a naive preference fMRI baseline measurement allowed us to conclude that these fMRI findings were the intrinsic outcomes of the learning process itself and not a reflection of a preexisting functionality recruited during classification, independent of acquisition. Support for the implicit nature of the knowledge utilized during preference classification on day 5 come from the fact that the basal ganglia, associated with implicit procedural learning, were activated during classification, while the medial temporal lobe system, associated with explicit declarative memory, was consistently deactivated. Thus, preference classification in combination with structural mere-exposure can be used to investigate structural sequence processing (syntax) in unsupervised AGL paradigms with proper learning designs. PMID:24550865

Implicit structured sequence learning: an fMRI study of the structural mere-exposure effect.

PubMed

Folia, Vasiliki; Petersson, Karl Magnus

2014-01-01

In this event-related fMRI study we investigated the effect of 5 days of implicit acquisition on preference classification by means of an artificial grammar learning (AGL) paradigm based on the structural mere-exposure effect and preference classification using a simple right-linear unification grammar. This allowed us to investigate implicit AGL in a proper learning design by including baseline measurements prior to grammar exposure. After 5 days of implicit acquisition, the fMRI results showed activations in a network of brain regions including the inferior frontal (centered on BA 44/45) and the medial prefrontal regions (centered on BA 8/32). Importantly, and central to this study, the inclusion of a naive preference fMRI baseline measurement allowed us to conclude that these fMRI findings were the intrinsic outcomes of the learning process itself and not a reflection of a preexisting functionality recruited during classification, independent of acquisition. Support for the implicit nature of the knowledge utilized during preference classification on day 5 come from the fact that the basal ganglia, associated with implicit procedural learning, were activated during classification, while the medial temporal lobe system, associated with explicit declarative memory, was consistently deactivated. Thus, preference classification in combination with structural mere-exposure can be used to investigate structural sequence processing (syntax) in unsupervised AGL paradigms with proper learning designs.

Gender Differences in Liking and Wanting Sex: Examining the Role of Motivational Context and Implicit Versus Explicit Processing.

PubMed

Dewitte, Marieke

2015-08-01

The present study investigated the specificity of sexual appraisal processes by making a distinction between implicit and explicit appraisals and between the affective (liking) and motivational (wanting) valence of sexual stimuli. These appraisals are assumed to diverge between men and women, depending on the context in which the sexual stimulus is encountered. Using an Implicit Association Test, explicit ratings, and film clips to prime a sexual, romantic or neutral motivational context, we investigated whether liking and wanting of sexual stimuli differed at the implicit and explicit level, differed between men and women, and were differentially sensitive to context manipulations. Results showed that, at the implicit level, women wanted more sex after being primed with romantic mood whereas men showed the least wanting of sex in the romantic condition. At the explicit level, men reported greater liking and wanting of sex than women, independently of context. We also found that women's (self-reported) sexual behavior was best predicted by the incentive salience of sexual stimuli whereas men's sexual behavior was more closely related to the hedonic qualities of sexual stimuli. Results were discussed in relation to an emotion-motivational account of sexual functioning.

Dyslexics’ faster decay of implicit memory for sounds and words is manifested in their shorter neural adaptation

PubMed Central

Jaffe-Dax, Sagi; Frenkel, Or; Ahissar, Merav

2017-01-01

Dyslexia is a prevalent reading disability whose underlying mechanisms are still disputed. We studied the neural mechanisms underlying dyslexia using a simple frequency-discrimination task. Though participants were asked to compare the two tones in each trial, implicit memory of previous trials affected their responses. We hypothesized that implicit memory decays faster among dyslexics. We tested this by increasing the temporal intervals between consecutive trials, and by measuring the behavioral impact and ERP responses from the auditory cortex. Dyslexics showed a faster decay of implicit memory effects on both measures, with similar time constants. Finally, faster decay of implicit memory also characterized the impact of sound regularities in benefitting dyslexics' oral reading rate. Their benefit decreased faster as a function of the time interval from the previous reading of the same non-word. We propose that dyslexics’ shorter neural adaptation paradoxically accounts for their longer reading times, since it reduces their temporal window of integration of past stimuli, resulting in noisier and less reliable predictions for both simple and complex stimuli. Less reliable predictions limit their acquisition of reading expertise. DOI: http://dx.doi.org/10.7554/eLife.20557.001 PMID:28115055

The role of the temporoparietal junction in implicit and explicit sense of agency.

PubMed

Hughes, Gethin

2018-05-01

The experience of being in control of one's actions and thier outcomes is called the sense of agency. This is a fundamental feature of our human experience, and may underpin important social functions such as morality and responsibility. Sense of agency can be measured explicitly, by asking people to report their experience, or implicitly by recording the perceived time interval between actions and outcomes (intentional binding). The current studies used transcranial direct current stimulation to assess the role of left and right temporoparietal junction in both implicit and explicit sense of agency. Participants were informed that they could control the volume output of the computer with one of two buttons. Participants experienced reduced sense of agency when the outcome was inconsistent with their action. However, binding did not differ between congruent and incongruent action-outcomes. The modulation of explicit agency ratings by action-outcome congruency was significantly reduced by right TPJ stimulation (experiment 1) but not left TPJ stimulation (experiment 2). Implicit agency was not affected in either stimulation condition. These findings are discussed in terms of the possible neural mechanisms of implicit and explicit sense of agency. Copyright © 2018 Elsevier Ltd. All rights reserved.

Functional Bregman Divergence and Bayesian Estimation of Distributions (Preprint)

DTIC Science & Technology

2008-01-01

shows that if the set of possible minimizers A includes EPF [F ], then g∗ = EPF [F ] minimizes the expectation of any Bregman divergence. Note the theorem...probability distribution PF defined over the set M. Let A be a set of functions that includes EPF [F ] if it exists. Suppose the function g∗ minimizes...the expected Bregman divergence between the random function F and any function g ∈ A such that g∗ = arg inf g∈A EPF [dφ(F, g)]. Then, if g∗ exists

How to (properly) strengthen Bell's theorem using counterfactuals

NASA Astrophysics Data System (ADS)

Bigaj, Tomasz

Bell's theorem in its standard version demonstrates that the joint assumptions of the hidden-variable hypothesis and the principle of local causation lead to a conflict with quantum-mechanical predictions. In his latest counterfactual strengthening of Bell's theorem, Stapp attempts to prove that the locality assumption itself contradicts the quantum-mechanical predictions in the Hardy case. His method relies on constructing a complex, non-truth functional formula which consists of statements about measurements and outcomes in some region R, and whose truth value depends on the selection of a measurement setting in a space-like separated location L. Stapp argues that this fact shows that the information about the measurement selection made in L has to be present in R. I give detailed reasons why this conclusion can and should be resisted. Next I correct and formalize an informal argument by Shimony and Stein showing that the locality condition coupled with Einstein's criterion of reality is inconsistent with quantum-mechanical predictions. I discuss the possibility of avoiding the inconsistency by rejecting Einstein's criterion rather than the locality assumption.

Quantum mechanics problems in observer's mathematics

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

Khots, Boris; Khots, Dmitriy; iMath Consulting LLC, Omaha, Nebraska

2012-11-06

This work considers the ontology, guiding equation, Schrodinger's equation, relation to the Born Rule, the conditional wave function of a subsystem in a setting of arithmetic, algebra and topology provided by Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. Certain results and communications pertaining to solutions of these problems are provided. In particular, we prove the following theorems: Theorem I (Two-slit interference). Let {Psi}{sub 1} be a wave from slit 1, {Psi}{sub 2} - from slit 2, andmore » {Psi} = {Psi}{sub 1}+{Psi}{sub 2}. Then the probability of {Psi} being a wave equals to 0.5. Theorem II (k-bodies solution). For W{sub n} from m-observer point of view with m>log{sub 10}((2 Multiplication-Sign 10{sup 2n}-1){sup 2k}+1), the probability of standard expression of Hamiltonian variation is less than 1 and depends on n,m,k.« less

Analogues of Chernoff's theorem and the Lie-Trotter theorem

NASA Astrophysics Data System (ADS)

Neklyudov, Alexander Yu

2009-10-01

This paper is concerned with the abstract Cauchy problem \\dot x=\\mathrm{A}x, x(0)=x_0\\in\\mathscr{D}(\\mathrm{A}), where \\mathrm{A} is a densely defined linear operator on a Banach space \\mathbf X. It is proved that a solution x(\\,\\cdot\\,) of this problem can be represented as the weak limit \\lim_{n\\to\\infty}\\{\\mathrm F(t/n)^nx_0\\}, where the function \\mathrm F\\colon \\lbrack 0,\\infty)\\mapsto\\mathscr L(\\mathrm X) satisfies the equality \\mathrm F'(0)y=\\mathrm{A}y, y\\in\\mathscr{D}(\\mathrm{A}), for a natural class of operators. As distinct from Chernoff's theorem, the existence of a global solution to the Cauchy problem is not assumed. Based on this result, necessary and sufficient conditions are found for the linear operator \\mathrm{C} to be closable and for its closure to be the generator of a C_0-semigroup. Also, we obtain new criteria for the sum of two generators of C_0-semigroups to be the generator of a C_0-semigroup and for the Lie-Trotter formula to hold. Bibliography: 13 titles.

Prediction of HR/BP response to the spontaneous breathing trial by fluctuation dissipation theory

NASA Astrophysics Data System (ADS)

Chen, Man

2014-03-01

We applied the non-equilibrium fluctuation dissipation theorem to predict how critically-ill patients respond to treatment, based on both heart rate data and blood pressure data collected by standard hospital monitoring devices. The non-equilibrium fluctuation dissipation theorem relates the response of a system to a perturbation to the fluctuations in the stationary state of the system. It is shown that the response of patients to a standard procedure performed on patients, the spontaneous breathing trial (SBT), can be predicted by the non-equilibrium fluctuation dissipation approach. We classify patients into different groups according to the patients' characteristics. For each patient group, we extend the fluctuation dissipation theorem to predict interactions between blood pressure and beat-to-beat dynamics of heart rate in response to a perturbation (SBT), We also extract the form of the perturbation function directly from the physiological data, which may help to reduce the prediction error. We note this method is not limited to the analysis of the heart rate dynamics, but also can be applied to analyze the response of other physiological signals to other clinical interventions.

Implications of the Corotation Theorem on the MRI in Axial Symmetry

NASA Astrophysics Data System (ADS)

Montani, G.; Cianfrani, F.; Pugliese, D.

2016-08-01

We analyze the linear stability of an axially symmetric ideal plasma disk, embedded in a magnetic field and endowed with a differential rotation. This study is performed by adopting the magnetic flux function as the fundamental dynamical variable, in order to outline the role played by the corotation theorem on the linear mode structure. Using some specific assumptions (e.g., plasma incompressibility and propagation of the perturbations along the background magnetic field), we select the Alfvénic nature of the magnetorotational instability, and, in the geometric optics limit, we determine the dispersion relation describing the linear spectrum. We show how the implementation of the corotation theorem (valid for the background configuration) on the linear dynamics produces the cancellation of the vertical derivative of the disk angular velocity (we check such a feature also in the standard vector formalism to facilitate comparison with previous literature, in both the axisymmetric and three-dimensional cases). As a result, we clarify that the unstable modes have, for a stratified disk, the same morphology, proper of a thin-disk profile, and the z-dependence has a simple parametric role.

Lp-stability (1 less than or equal to p less than or equal to infinity) of multivariable nonlinear time-varying feedback systems that are open-loop unstable. [noting unstable convolution subsystem forward control and time varying nonlinear feedback

NASA Technical Reports Server (NTRS)

Callier, F. M.; Desoer, C. A.

1973-01-01

A class of multivariable, nonlinear time-varying feedback systems with an unstable convolution subsystem as feedforward and a time-varying nonlinear gain as feedback was considered. The impulse response of the convolution subsystem is the sum of a finite number of increasing exponentials multiplied by nonnegative powers of the time t, a term that is absolutely integrable and an infinite series of delayed impulses. The main result is a theorem. It essentially states that if the unstable convolution subsystem can be stabilized by a constant feedback gain F and if incremental gain of the difference between the nonlinear gain function and F is sufficiently small, then the nonlinear system is L(p)-stable for any p between one and infinity. Furthermore, the solutions of the nonlinear system depend continuously on the inputs in any L(p)-norm. The fixed point theorem is crucial in deriving the above theorem.

Flexible explicit but rigid implicit learning in a visuomotor adaptation task

PubMed Central

Bond, Krista M.

2015-01-01

There is mounting evidence for the idea that performance in a visuomotor rotation task can be supported by both implicit and explicit forms of learning. The implicit component of learning has been well characterized in previous experiments and is thought to arise from the adaptation of an internal model driven by sensorimotor prediction errors. However, the role of explicit learning is less clear, and previous investigations aimed at characterizing the explicit component have relied on indirect measures such as dual-task manipulations, posttests, and descriptive computational models. To address this problem, we developed a new method for directly assaying explicit learning by having participants verbally report their intended aiming direction on each trial. While our previous research employing this method has demonstrated the possibility of measuring explicit learning over the course of training, it was only tested over a limited scope of manipulations common to visuomotor rotation tasks. In the present study, we sought to better characterize explicit and implicit learning over a wider range of task conditions. We tested how explicit and implicit learning change as a function of the specific visual landmarks used to probe explicit learning, the number of training targets, and the size of the rotation. We found that explicit learning was remarkably flexible, responding appropriately to task demands. In contrast, implicit learning was strikingly rigid, with each task condition producing a similar degree of implicit learning. These results suggest that explicit learning is a fundamental component of motor learning and has been overlooked or conflated in previous visuomotor tasks. PMID:25855690

Experimental Test of the Differential Fluctuation Theorem and a Generalized Jarzynski Equality for Arbitrary Initial States

NASA Astrophysics Data System (ADS)

Hoang, Thai M.; Pan, Rui; Ahn, Jonghoon; Bang, Jaehoon; Quan, H. T.; Li, Tongcang

2018-02-01

Nonequilibrium processes of small systems such as molecular machines are ubiquitous in biology, chemistry, and physics but are often challenging to comprehend. In the past two decades, several exact thermodynamic relations of nonequilibrium processes, collectively known as fluctuation theorems, have been discovered and provided critical insights. These fluctuation theorems are generalizations of the second law and can be unified by a differential fluctuation theorem. Here we perform the first experimental test of the differential fluctuation theorem using an optically levitated nanosphere in both underdamped and overdamped regimes and in both spatial and velocity spaces. We also test several theorems that can be obtained from it directly, including a generalized Jarzynski equality that is valid for arbitrary initial states, and the Hummer-Szabo relation. Our study experimentally verifies these fundamental theorems and initiates the experimental study of stochastic energetics with the instantaneous velocity measurement.

Generalized virial theorem for massless electrons in graphene and other Dirac materials

NASA Astrophysics Data System (ADS)

Sokolik, A. A.; Zabolotskiy, A. D.; Lozovik, Yu. E.

2016-05-01

The virial theorem for a system of interacting electrons in a crystal, which is described within the framework of the tight-binding model, is derived. We show that, in the particular case of interacting massless electrons in graphene and other Dirac materials, the conventional virial theorem is violated. Starting from the tight-binding model, we derive the generalized virial theorem for Dirac electron systems, which contains an additional term associated with a momentum cutoff at the bottom of the energy band. Additionally, we derive the generalized virial theorem within the Dirac model using the minimization of the variational energy. The obtained theorem is illustrated by many-body calculations of the ground-state energy of an electron gas in graphene carried out in Hartree-Fock and self-consistent random-phase approximations. Experimental verification of the theorem in the case of graphene is discussed.

A note on generalized Weyl's theorem

NASA Astrophysics Data System (ADS)

Zguitti, H.

2006-04-01

We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.

Functional determinants, index theorems, and exact quantum black hole entropy

NASA Astrophysics Data System (ADS)

Murthy, Sameer; Reys, Valentin

2015-12-01

The exact quantum entropy of BPS black holes can be evaluated using localization in supergravity. An important ingredient in this program, that has been lacking so far, is the one-loop effect arising from the quadratic fluctuations of the exact deformation (the QV operator). We compute the fluctuation determinant for vector multiplets and hyper multiplets around Q-invariant off-shell configurations in four-dimensional N=2 supergravity with AdS 2 × S 2 boundary conditions, using the Atiyah-Bott fixed-point index theorem and a subsequent zeta function regularization. Our results extend the large-charge on-shell entropy computations in the literature to a regime of finite charges. Based on our results, we present an exact formula for the quantum entropy of BPS black holes in N=2 supergravity. We explain cancellations concerning 1/8 -BPS black holes in N=8 supergravity that were observed in arXiv:1111.1161. We also make comments about the interpretation of a logarithmic term in the topological string partition function in the low energy supergravity theory.

Means and the Mean Value Theorem

ERIC Educational Resources Information Center

Merikoski, Jorma K.; Halmetoja, Markku; Tossavainen, Timo

2009-01-01

Let I be a real interval. We call a continuous function [mu] : I x I [right arrow] [Bold R] a proper mean if it is symmetric, reflexive, homogeneous, monotonic and internal. Let f : I [right arrow] [Bold R} be a differentiable and strictly convex or strictly concave function. If a, b [image omitted] I with a [not equal to] b, then there exists a…

Approximate solution for the electronic density profile at the surface of jellium

NASA Astrophysics Data System (ADS)

Schmickler, Wolfgang; Henderson, Douglas

1984-09-01

A simple family of trial functions for the electronic density at the surface of jellium, which accounts for Friedel oscillations and incorporates the Budd-Vannimenus theorem, is proposed. The free parameters are determined by energy minimization. Model calculations give good results for the work function and for the induced surface charge in the presence of an external field.

Two Functions of Language

ERIC Educational Resources Information Center

Feldman, Carol Fleisher

1977-01-01

Author advocates the view that meaning is necessarily dependent upon the communicative function of language and examines the objections, particularly those of Noam Chomsky, to this view. Argues that while Chomsky disagrees with the idea that communication is the essential function of language, he implicitly agrees that it has a function.…

Does Conceptual Understanding of Limit Partially Lead Students to Misconceptions?

NASA Astrophysics Data System (ADS)

Mulyono, B.; Hapizah

2017-09-01

This article talks about the result of preliminary research of my dissertation, which will investigate student’s retention of conceptual understanding. In my preliminary research, I surveyed 73 students of mathematics education program by giving some questions to test their retention of conceptual understanding of limits. Based on the results of analyzing of students’ answers I conclude that most of the students have problems with their retention of conceptual understanding and they also have misconception of limits. The first misconception I identified is that students always used the substitution method to determine a limit of a function at a point, but they did not check whether the function is continue or not at the point. It means that they only use the substitution theorem partially, because they do not consider that the substitution theorem \\mathop{{lim}}\\limits\\text{x\\to \\text{c}}f(x)=f(c) works only if f(x) is defined at χ = c. The other misconception identified is that some students always think there must be available of variables χ in a function to determine the limit of the function. I conjecture that conceptual understanding of limit partially leads students to misconceptions.

Discovering the Theorem of Pythagoras

NASA Technical Reports Server (NTRS)

Lattanzio, Robert (Editor)

1988-01-01

In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.

Bertrand's theorem and virial theorem in fractional classical mechanics

NASA Astrophysics Data System (ADS)

Yu, Rui-Yan; Wang, Towe

2017-09-01

Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.

Guided Discovery of the Nine-Point Circle Theorem and Its Proof

ERIC Educational Resources Information Center

Buchbinder, Orly

2018-01-01

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

Quality correction factors of composite IMRT beam deliveries: Theoretical considerations

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

Bouchard, Hugo

2012-11-15

Purpose: In the scope of intensity modulated radiation therapy (IMRT) dosimetry using ionization chambers, quality correction factors of plan-class-specific reference (PCSR) fields are theoretically investigated. The symmetry of the problem is studied to provide recommendable criteria for composite beam deliveries where correction factors are minimal and also to establish a theoretical limit for PCSR delivery k{sub Q} factors. Methods: The concept of virtual symmetric collapsed (VSC) beam, being associated to a given modulated composite delivery, is defined in the scope of this investigation. Under symmetrical measurement conditions, any composite delivery has the property of having a k{sub Q} factor identicalmore » to its associated VSC beam. Using this concept of VSC, a fundamental property of IMRT k{sub Q} factors is demonstrated in the form of a theorem. The sensitivity to the conditions required by the theorem is thoroughly examined. Results: The theorem states that if a composite modulated beam delivery produces a uniform dose distribution in a volume V{sub cyl} which is symmetric with the cylindrical delivery and all beams fulfills two conditions in V{sub cyl}: (1) the dose modulation function is unchanged along the beam axis, and (2) the dose gradient in the beam direction is constant for a given lateral position; then its associated VSC beam produces no lateral dose gradient in V{sub cyl}, no matter what beam modulation or gantry angles are being used. The examination of the conditions required by the theorem lead to the following results. The effect of the depth-dose gradient not being perfectly constant with depth on the VSC beam lateral dose gradient is found negligible. The effect of the dose modulation function being degraded with depth on the VSC beam lateral dose gradient is found to be only related to scatter and beam hardening, as the theorem holds also for diverging beams. Conclusions: The use of the symmetry of the problem in the present paper leads to a valuable theorem showing that k{sub Q} factors of composite IMRT beam deliveries are close to unity under specific conditions. The theoretical limit k{sub Q{sub p{sub c{sub s{sub r,Q{sub m{sub s{sub r}{sup f{sub p}{sub c}{sub s}{sub r},f{sub m}{sub s}{sub r}}}}}}}}}=1 is determined based on the property of PCSR deliveries to provide a uniform dose in the target volume. The present approach explains recent experimental observations and proposes ideal conditions for IMRT reference dosimetry. The result of this study could potentially serve as a theoretical basis for reference dosimetry of composite IMRT beam deliveries or for routine IMRT quality assurance.« less

Neurocognitive performance in unmedicated patients with hoarding disorder.

PubMed

Sumner, Jennifer M; Noack, Carolyn G; Filoteo, J Vincent; Maddox, W Todd; Saxena, Sanjaya

2016-02-01

Hoarding disorder (HD) is an often incapacitating psychiatric illness associated with a wide range of neurocognitive abnormalities. Some prior neuropsychological studies have found executive dysfunction in HD, but no clear pattern has emerged. One potential reason for discrepant results in previous studies might be the inclusion of patients on psychotropic and other medications that can affect neurocognitive performance. Therefore, we examined neurocognitive functioning in medication-free HD patients. We also added a novel investigation of implicit learning, which has been found to be abnormal in obsessive-compulsive disorder (OCD) and related disorders. Twenty-six participants meeting the Diagnostic and Statistical Manual of Mental Disorders (5th ed.; DSM-5; American Psychiatric Association, 2013) diagnostic criteria for HD and 23 normal controls were administered a battery of neuropsychological tests and symptom rating scales. All participants were free of psychotropic medications for at least 6 weeks prior to the study. HD participants showed no significant differences from normal controls on measures of verbal memory, attention, or executive functioning, including response inhibition, planning, organization, and decision making. However, HD participants demonstrated a trend toward less implicit learning and greater use of explicit learning strategies during perceptual categorization compared to normal controls. HD participants who used an implicit strategy performed significantly worse than controls who used an implicit strategy. Hoarding symptom severity was not associated with neurocognitive performance. HD patients may have a tendency to use explicit rather than implicit learning strategies for perceptual categorization but perform as well as normal controls on many other neurocognitive measures. Future studies should assess unmedicated participants and examine test strategies, not just outcomes. PsycINFO Database Record (c) 2016 APA, all rights reserved.

A Numerical Model for Predicting Shoreline Changes.

DTIC Science & Technology

1980-07-01

minimal shorelines for finite - difference scheme of time lAt (B) . . . 27 11 Transport function Q(ao) = cos ao sin za o for selected values of z . 28 12...generate the preceding examples was based on the use of implicit finite differences . Such schemes, whether implicit or ex- plicit (or both), are...10(A) shows an initially straight shoreline. In any finite - difference scheme, after one time increment At, the shoreline is bounded below by the solid

A Historical Gem from Vito Volterra.

ERIC Educational Resources Information Center

Dunham, William

1990-01-01

Presented is the theorem proposed by Volterra based on the idea that there is no function continuous at each rational point and discontinuous at each irrational point. Discussed are the two conclusions that were drawn by Volterra based on his solution to this problem. (KR)

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

NASA Technical Reports Server (NTRS)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

Do all pure entangled states violate Bell's inequalities for correlation functions?

PubMed

Zukowski, Marek; Brukner, Caslav; Laskowski, Wiesław; Wieśniak, Marcin

2002-05-27

Any pure entangled state of two particles violates a Bell inequality for two-particle correlation functions (Gisin's theorem). We show that there exist pure entangled N>2 qubit states that do not violate any Bell inequality for N particle correlation functions for experiments involving two dichotomic observables per local measuring station. We also find that Mermin-Ardehali-Belinskii-Klyshko inequalities may not always be optimal for refutation of local realistic description.

Algebraic Functions of H-Functions with Specific Dependency Structure.

DTIC Science & Technology

1984-05-01

a study of its characteristic function. Such analysis is reproduced in books by Springer (17), Anderson (23), Feller (34,35), Mood and Graybill (52...following linearity property for expectations of jointly distributed random variables is derived. r 1 Theorem 1.1: If X and Y are real random variables...appear in American Journal of Mathematical and Management Science. 13. Mathai, A.M., and R.K. Saxena, "On linear combinations of stochastic variables

Extended optical theorem in isotropic solids and its application to the elastic radiation force

NASA Astrophysics Data System (ADS)

Leão-Neto, J. P.; Lopes, J. H.; Silva, G. T.

2017-04-01

In this article, we derive the extended optical theorem for the elastic-wave scattering by a spherical inclusion (with and without absorption) in a solid matrix. This theorem expresses the extinction cross-section, i.e., the time-averaged power extracted from the incoming beam per its intensity, regarding the partial-wave expansion coefficients of the incident and scattered waves. We also establish the connection between the optical theorem and the elastic radiation force by a plane wave in a linear and isotropic solid. We obtain the absorption, scattering, and extinction efficiencies (the corresponding power per characteristic incident intensity per sphere cross-section area) for a plane wave and a spherically focused beam. We discuss to which extent the radiation force theory for plane waves can be used to the focused beam case. Considering an iron sphere embedded in an aluminum matrix, we numerically compute the scattering and elastic radiation force efficiencies. The radiation force on a stainless steel sphere embedded in a tissue-like medium (soft solid) is also computed. In this case, resonances are observed in the force as a function of the sphere size parameter (the wavenumber times the sphere radius). Remarkably, the relative difference between our findings and previous lossless liquid models is about 100% in the long-wavelength limit. Regarding some applications, the obtained results have a direct impact on ultrasound-based elastography techniques and ultrasonic nondestructive testing, as well as implantable devices activated by ultrasound.

On the Feynman-Hellmann theorem in quantum field theory and the calculation of matrix elements

DOE PAGES

Bouchard, Chris; Chang, Chia Cheng; Kurth, Thorsten; ...

2017-07-12

In this paper, the Feynman-Hellmann theorem can be derived from the long Euclidean-time limit of correlation functions determined with functional derivatives of the partition function. Using this insight, we fully develop an improved method for computing matrix elements of external currents utilizing only two-point correlation functions. Our method applies to matrix elements of any external bilinear current, including nonzero momentum transfer, flavor-changing, and two or more current insertion matrix elements. The ability to identify and control all the systematic uncertainties in the analysis of the correlation functions stems from the unique time dependence of the ground-state matrix elements and the fact that all excited states and contact terms are Euclidean-time dependent. We demonstrate the utility of our method with a calculation of the nucleon axial charge using gradient-flowed domain-wall valence quarks on themore » $$N_f=2+1+1$$ MILC highly improved staggered quark ensemble with lattice spacing and pion mass of approximately 0.15 fm and 310 MeV respectively. We show full control over excited-state systematics with the new method and obtain a value of $$g_A = 1.213(26)$$ with a quark-mass-dependent renormalization coefficient.« less

Heat flow in chains driven by thermal noise

NASA Astrophysics Data System (ADS)

Fogedby, Hans C.; Imparato, Alberto

2012-04-01

We consider the large deviation function for a classical harmonic chain composed of N particles driven at the end points by heat reservoirs, first derived in the quantum regime by Saito and Dhar (2007 Phys. Rev. Lett. 99 180601) and in the classical regime by Saito and Dhar (2011 Phys. Rev. E 83 041121) and Kundu et al (2011 J. Stat. Mech. P03007). Within a Langevin description we perform this calculation on the basis of a standard path integral calculation in Fourier space. The cumulant generating function yielding the large deviation function is given in terms of a transmission Green's function and is consistent with the fluctuation theorem. We find a simple expression for the tails of the heat distribution, which turns out to decay exponentially. We, moreover, consider an extension of a single-particle model suggested by Derrida and Brunet (2005 Einstein Aujourd'hui (Les Ulis: EDP Sciences)) and discuss the two-particle case. We also discuss the limit for large N and present a closed expression for the cumulant generating function. Finally, we present a derivation of the fluctuation theorem on the basis of a Fokker-Planck description. This result is not restricted to the harmonic case but is valid for a general interaction potential between the particles.

Knowing who's boss: implicit perceptions of status from the nonverbal expression of pride.

PubMed

Shariff, Azim F; Tracy, Jessica L

2009-10-01

Evolutionary theory suggests that the universal recognition of nonverbal expressions of emotions functions to enhance fitness. Specifically, emotion expressions may send survival-relevant messages to other social group members, who have the capacity to automatically interpret these signals. In the present research, we used 3 different implicit association methodologies to test whether the nonverbal expression of pride sends a functional, automatically perceived signal about a social group member's increased social status. Results suggest that the pride expression strongly signals high status, and this association cannot be accounted for by positive valence or artifacts of the expression such as expanded size due to outstretched arms. These findings suggest that the pride expression may function to uniquely communicate the high status of those who show it. Discussion focuses on the implications of these findings for social functions of emotion expressions and the automatic communication of status.

Free-energy functional of the Debye-Hückel model of simple fluids

NASA Astrophysics Data System (ADS)

Piron, R.; Blenski, T.

2016-12-01

The Debye-Hückel approximation to the free energy of a simple fluid is written as a functional of the pair correlation function. This functional can be seen as the Debye-Hückel equivalent to the functional derived in the hypernetted chain framework by Morita and Hiroike, as well as by Lado. It allows one to obtain the Debye-Hückel integral equation through a minimization with respect to the pair correlation function, leads to the correct form of the internal energy, and fulfills the virial theorem.

Direct and converse theorems in problems of approximation by vectors of finite degree

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

Radzievski, G V

1998-04-30

Let A be a linear operator in a complex Banach space X with domain D(A) and a non-empty resolvent set. An element g element of D{sub {infinity}}(A):= intersection{sub j=0,1,...}D(A{sup j}) is called a vector of degree at most {zeta}(>0) with respect to A if ||A{sup j}g||{sub X}{<=}c(g){zeta}{sup j}, j=0,1,.... The set of vectors of degree at most {zeta} is denoted by G{sub {zeta}}(A). The quantity E{sub {zeta}}(f,A){sub X}=inf{sub gelement} {sub of{sub G}{sub {zeta}}}{sub (A)}||f-g||{sub X} is introduced and estimated in terms of the K-functional K({zeta}{sup -r},f;X,D(A{sup r}))=inf{sub gelementof} {sub D(A{sup r})}(||f-g||{sub X}+{zeta}{sup -r}||A{sup r}f||{sub X}) (the direct theorem). An estimatemore » of this K-functional in terms of E{sub {zeta}}(f,A){sub X} and ||f||{sub x} is established (the converse theorem). Using the estimates obtained, necessary and sufficient conditions for the following properties are found in terms of E{sub {zeta}}(f,A){sub X}: 1) f element of D{sub {infinity}}(A); 2) the series e{sup zA}f:={sigma}{sub r=0}{sup {infinity}}(z{sup r}A{sup r}f)/(r{exclamation_point}) converges in some disc; 3) the series e{sup zA}f converges in the entire complex plane. The growth order and the type of the entire function e{sup zA}f are calculated in terms of E{sub {zeta}}(f,A){sub X}.« less

Tracking Temporal Hazard in the Human Electroencephalogram Using a Forward Encoding Model

PubMed Central

2018-01-01

Abstract Human observers automatically extract temporal contingencies from the environment and predict the onset of future events. Temporal predictions are modeled by the hazard function, which describes the instantaneous probability for an event to occur given it has not occurred yet. Here, we tackle the question of whether and how the human brain tracks continuous temporal hazard on a moment-to-moment basis, and how flexibly it adjusts to strictly implicit variations in the hazard function. We applied an encoding-model approach to human electroencephalographic data recorded during a pitch-discrimination task, in which we implicitly manipulated temporal predictability of the target tones by varying the interval between cue and target tone (i.e. the foreperiod). Critically, temporal predictability either was driven solely by the passage of time (resulting in a monotonic hazard function) or was modulated to increase at intermediate foreperiods (resulting in a modulated hazard function with a peak at the intermediate foreperiod). Forward-encoding models trained to predict the recorded EEG signal from different temporal hazard functions were able to distinguish between experimental conditions, showing that implicit variations of temporal hazard bear tractable signatures in the human electroencephalogram. Notably, this tracking signal was reconstructed best from the supplementary motor area, underlining this area’s link to cognitive processing of time. Our results underline the relevance of temporal hazard to cognitive processing and show that the predictive accuracy of the encoding-model approach can be utilized to track abstract time-resolved stimuli. PMID:29740594

Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials

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

Olesov, A V

2014-10-31

New inequalities are established for analytic functions satisfying Meiman's majorization conditions. Estimates for values of and differential inequalities involving rational trigonometric functions with an integer majorant on an interval of length less than the period and with prescribed poles which are symmetrically positioned relative to the real axis, as well as differential inequalities for trigonometric polynomials in some classes, are given as applications. These results improve several theorems due to Meiman, Genchev, Smirnov and Rusak. Bibliography: 27 titles.

The explicit form of the rate function for semi-Markov processes and its contractions

NASA Astrophysics Data System (ADS)

Sughiyama, Yuki; Kobayashi, Testuya J.

2018-03-01

We derive the explicit form of the rate function for semi-Markov processes. Here, the ‘random time change trick’ plays an essential role. Also, by exploiting the contraction principle of large deviation theory to the explicit form, we show that the fluctuation theorem (Gallavotti-Cohen symmetry) holds for semi-Markov cases. Furthermore, we elucidate that our rate function is an extension of the level 2.5 rate function for Markov processes to semi-Markov cases.

Excitonic magnet in external field: Complex order parameter and spin currents

NASA Astrophysics Data System (ADS)

Geffroy, D.; Hariki, A.; Kuneš, J.

2018-04-01

We investigate spin-triplet exciton condensation in the two-orbital Hubbard model close to half-filling by means of dynamical mean-field theory. Employing an impurity solver that handles complex off-diagonal hybridization functions, we study the behavior of excitonic condensate in stoichiometric and doped systems subject to external magnetic field. We find a general tendency of the triplet order parameter to lie perpendicular with the applied field and identify exceptions from this rule. For solutions exhibiting k -odd spin textures, we discuss the Bloch theorem, which, in the absence of spin-orbit coupling, forbids the appearance of spontaneous net spin current. We demonstrate that the Bloch theorem is not obeyed by the dynamical mean-field theory.

Brownian motion of graphene.

PubMed

Maragó, Onofrio M; Bonaccorso, Francesco; Saija, Rosalba; Privitera, Giulia; Gucciardi, Pietro G; Iatì, Maria Antonia; Calogero, Giuseppe; Jones, Philip H; Borghese, Ferdinando; Denti, Paolo; Nicolosi, Valeria; Ferrari, Andrea C

2010-12-28

Brownian motion is a manifestation of the fluctuation-dissipation theorem of statistical mechanics. It regulates systems in physics, biology, chemistry, and finance. We use graphene as prototype material to unravel the consequences of the fluctuation-dissipation theorem in two dimensions, by studying the Brownian motion of optically trapped graphene flakes. These orient orthogonal to the light polarization, due to the optical constants anisotropy. We explain the flake dynamics in the optical trap and measure force and torque constants from the correlation functions of the tracking signals, as well as comparing experiments with a full electromagnetic theory of optical trapping. The understanding of optical trapping of two-dimensional nanostructures gained through our Brownian motion analysis paves the way to light-controlled manipulation and all-optical sorting of biological membranes and anisotropic macromolecules.

A Numerical, Literal, and Converged Perturbation Algorithm

NASA Astrophysics Data System (ADS)

Wiesel, William E.

2017-09-01

The KAM theorem and von Ziepel's method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generating function does not contain momentum dependence. The KAM iteration is extended to allow for frequency and angle changes, and in the process apparently can be successfully applied to degenerate systems normally ruled out by the classical KAM theorem. Convergence is observed to be geometric, not exponential, but it does proceed smoothly to machine precision. The algorithm produces a converged perturbation solution by numerical methods, while still retaining literal variable dependence, at least in the vicinity of a given trajectory.

The Poincaré-Hopf Theorem for line fields revisited

NASA Astrophysics Data System (ADS)

Crowley, Diarmuid; Grant, Mark

2017-07-01

A Poincaré-Hopf Theorem for line fields with point singularities on orientable surfaces can be found in Hopf's 1956 Lecture Notes on Differential Geometry. In 1955 Markus presented such a theorem in all dimensions, but Markus' statement only holds in even dimensions 2 k ≥ 4. In 1984 Jänich presented a Poincaré-Hopf theorem for line fields with more complicated singularities and focussed on the complexities arising in the generalized setting. In this expository note we review the Poincaré-Hopf Theorem for line fields with point singularities, presenting a careful proof which is valid in all dimensions.

Common fixed point theorems for maps under a contractive condition of integral type

NASA Astrophysics Data System (ADS)

Djoudi, A.; Merghadi, F.

2008-05-01

Two common fixed point theorems for mapping of complete metric space under a general contractive inequality of integral type and satisfying minimal commutativity conditions are proved. These results extend and improve several previous results, particularly Theorem 4 of Rhoades [B.E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 63 (2003) 4007-4013] and Theorem 4 of Sessa [S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.) 32 (46) (1982) 149-153].

Statistical Mechanics and Applications in Condensed Matter

NASA Astrophysics Data System (ADS)

Di Castro, Carlo; Raimondi, Roberto

2015-08-01

Preface; 1. Thermodynamics: a brief overview; 2. Kinetics; 3. From Boltzmann to Gibbs; 4. More ensembles; 5. The thermodynamic limit and its thermodynamic stability; 6. Density matrix and quantum statistical mechanics; 7. The quantum gases; 8. Mean-field theories and critical phenomena; 9. Second quantization and Hartree-Fock approximation; 10. Linear response and fluctuation-dissipation theorem in quantum systems: equilibrium and small deviations; 11. Brownian motion and transport in disordered systems; 12. Fermi liquids; 13. The Landau theory of the second order phase transitions; 14. The Landau-Wilson model for critical phenomena; 15. Superfluidity and superconductivity; 16. The scaling theory; 17. The renormalization group approach; 18. Thermal Green functions; 19. The microscopic foundations of Fermi liquids; 20. The Luttinger liquid; 21. Quantum interference effects in disordered electron systems; Appendix A. The central limit theorem; Appendix B. Some useful properties of the Euler Gamma function; Appendix C. Proof of the second theorem of Yang and Lee; Appendix D. The most probable distribution for the quantum gases; Appendix E. Fermi-Dirac and Bose-Einstein integrals; Appendix F. The Fermi gas in a uniform magnetic field: Landau diamagnetism; Appendix G. Ising and gas-lattice models; Appendix H. Sum over discrete Matsubara frequencies; Appendix I. Hydrodynamics of the two-fluid model of superfluidity; Appendix J. The Cooper problem in the theory of superconductivity; Appendix K. Superconductive fluctuations phenomena; Appendix L. Diagrammatic aspects of the exact solution of the Tomonaga Luttinger model; Appendix M. Details on the theory of the disordered Fermi liquid; References; Author index; Index.

Implicit and explicit processing of emotional facial expressions in Parkinson's disease.

PubMed

Wagenbreth, Caroline; Wattenberg, Lena; Heinze, Hans-Jochen; Zaehle, Tino

2016-04-15

Besides motor problems, Parkinson's disease (PD) is associated with detrimental emotional and cognitive functioning. Deficient explicit emotional processing has been observed, whilst patients also show impaired Theory of Mind (ToM) abilities. However, it is unclear whether this PD patients' ToM deficit is based on an inability to infer otherś emotional states or whether it is due to explicit emotional processing deficits. We investigated implicit and explicit emotional processing in PD with an affective priming paradigm in which we used pictures of human eyes for emotional primes and a lexical decision task (LDT) with emotional connoted words for target stimuli. Sixteen PD patients and sixteen matched healthy controls performed a LTD combined with an emotional priming paradigm providing emotional information through the facial eye region to assess implicit emotional processing. Second, participants explicitly evaluated the emotional status of eyes and words used in the implicit task. Compared to controls implicit emotional processing abilities were generally preserved in PD with, however, considerable alterations for happiness and disgust processing. Furthermore, we observed a general impairment of patients for explicit evaluation of emotional stimuli, which was augmented for the rating of facial expressions. This is the first study reporting results for affective priming with facial eye expressions in PD patients. Our findings indicate largely preserved implicit emotional processing, with a specific altered processing of disgust and happiness. Explicit emotional processing was considerably impaired for semantic and especially for facial stimulus material. Poor ToM abilities in PD patients might be based on deficient explicit emotional processing, with preserved ability to implicitly infer other people's feelings. Copyright © 2016 Elsevier B.V. All rights reserved.

Can a continuum solvent model reproduce the free energy landscape of a -hairpin folding in water?

NASA Astrophysics Data System (ADS)

Zhou, Ruhong; Berne, Bruce J.

2002-10-01

The folding free energy landscape of the C-terminal -hairpin of protein G is explored using the surface-generalized Born (SGB) implicit solvent model, and the results are compared with the landscape from an earlier study with explicit solvent model. The OPLSAA force field is used for the -hairpin in both implicit and explicit solvent simulations, and the conformational space sampling is carried out with a highly parallel replica-exchange method. Surprisingly, we find from exhaustive conformation space sampling that the free energy landscape from the implicit solvent model is quite different from that of the explicit solvent model. In the implicit solvent model some nonnative states are heavily overweighted, and more importantly, the lowest free energy state is no longer the native -strand structure. An overly strong salt-bridge effect between charged residues (E42, D46, D47, E56, and K50) is found to be responsible for this behavior in the implicit solvent model. Despite this, we find that the OPLSAA/SGB energies of all the nonnative structures are higher than that of the native structure; thus the OPLSAA/SGB energy is still a good scoring function for structure prediction for this -hairpin. Furthermore, the -hairpin population at 282 K is found to be less than 40% from the implicit solvent model, which is much smaller than the 72% from the explicit solvent model and 80% from experiment. On the other hand, both implicit and explicit solvent simulations with the OPLSAA force field exhibit no meaningful helical content during the folding process, which is in contrast to some very recent studies using other force fields.

Can a continuum solvent model reproduce the free energy landscape of a β-hairpin folding in water?

PubMed Central

Zhou, Ruhong; Berne, Bruce J.

2002-01-01

The folding free energy landscape of the C-terminal β-hairpin of protein G is explored using the surface-generalized Born (SGB) implicit solvent model, and the results are compared with the landscape from an earlier study with explicit solvent model. The OPLSAA force field is used for the β-hairpin in both implicit and explicit solvent simulations, and the conformational space sampling is carried out with a highly parallel replica-exchange method. Surprisingly, we find from exhaustive conformation space sampling that the free energy landscape from the implicit solvent model is quite different from that of the explicit solvent model. In the implicit solvent model some nonnative states are heavily overweighted, and more importantly, the lowest free energy state is no longer the native β-strand structure. An overly strong salt-bridge effect between charged residues (E42, D46, D47, E56, and K50) is found to be responsible for this behavior in the implicit solvent model. Despite this, we find that the OPLSAA/SGB energies of all the nonnative structures are higher than that of the native structure; thus the OPLSAA/SGB energy is still a good scoring function for structure prediction for this β-hairpin. Furthermore, the β-hairpin population at 282 K is found to be less than 40% from the implicit solvent model, which is much smaller than the 72% from the explicit solvent model and ≈80% from experiment. On the other hand, both implicit and explicit solvent simulations with the OPLSAA force field exhibit no meaningful helical content during the folding process, which is in contrast to some very recent studies using other force fields. PMID:12242327

Can a continuum solvent model reproduce the free energy landscape of a beta -hairpin folding in water?

PubMed

Zhou, Ruhong; Berne, Bruce J

2002-10-01

The folding free energy landscape of the C-terminal beta-hairpin of protein G is explored using the surface-generalized Born (SGB) implicit solvent model, and the results are compared with the landscape from an earlier study with explicit solvent model. The OPLSAA force field is used for the beta-hairpin in both implicit and explicit solvent simulations, and the conformational space sampling is carried out with a highly parallel replica-exchange method. Surprisingly, we find from exhaustive conformation space sampling that the free energy landscape from the implicit solvent model is quite different from that of the explicit solvent model. In the implicit solvent model some nonnative states are heavily overweighted, and more importantly, the lowest free energy state is no longer the native beta-strand structure. An overly strong salt-bridge effect between charged residues (E42, D46, D47, E56, and K50) is found to be responsible for this behavior in the implicit solvent model. Despite this, we find that the OPLSAA/SGB energies of all the nonnative structures are higher than that of the native structure; thus the OPLSAA/SGB energy is still a good scoring function for structure prediction for this beta-hairpin. Furthermore, the beta-hairpin population at 282 K is found to be less than 40% from the implicit solvent model, which is much smaller than the 72% from the explicit solvent model and approximately equal 80% from experiment. On the other hand, both implicit and explicit solvent simulations with the OPLSAA force field exhibit no meaningful helical content during the folding process, which is in contrast to some very recent studies using other force fields.

Both memory and attention systems contribute to visual search for targets cued by implicitly learned context

PubMed Central

Giesbrecht, Barry; Sy, Jocelyn L.; Guerin, Scott A.

2012-01-01

Environmental context learned without awareness can facilitate visual processing of goal-relevant information. According to one view, the benefit of implicitly learned context relies on the neural systems involved in spatial attention and hippocampus-mediated memory. While this view has received empirical support, it contradicts traditional models of hippocampal function. The purpose of the present work was to clarify the influence of spatial context on visual search performance and on brain structures involved memory and attention. Event-related functional magnetic resonance imaging revealed that activity in the hippocampus as well as in visual and parietal cortex was modulated by learned visual context even though participants’ subjective reports and performance on a post-experiment recognition task indicated no explicit knowledge of the learned context. Moreover, the magnitude of the initial selective hippocampus response predicted the magnitude of the behavioral benefit due to context observed at the end of the experiment. The results suggest that implicit contextual learning is mediated by attention and memory and that these systems interact to support search of our environment. PMID:23099047

On the solubility of certain classes of non-linear integral equations in p-adic string theory

NASA Astrophysics Data System (ADS)

Khachatryan, Kh. A.

2018-04-01

We study classes of non-linear integral equations that have immediate application to p-adic mathematical physics and to cosmology. We prove existence and uniqueness theorems for non-trivial solutions in the space of bounded functions.

Infinity: The Twilight Zone of Mathematics.

ERIC Educational Resources Information Center

Love, William P.

1989-01-01

The theorems and proofs presented are designed to enhance student understanding of the theory of infinity as developed by Cantor and others. Three transfinite numbers are defined to express the cardinality of infinite algebraic sets, infinite sets of geometric points and infinite sets of functions. (DC)

Black-hole solutions with scalar hair in Einstein-scalar-Gauss-Bonnet theories

NASA Astrophysics Data System (ADS)

Antoniou, G.; Bakopoulos, A.; Kanti, P.

2018-04-01

In the context of the Einstein-scalar-Gauss-Bonnet theory, with a general coupling function between the scalar field and the quadratic Gauss-Bonnet term, we investigate the existence of regular black-hole solutions with scalar hair. Based on a previous theoretical analysis, which studied the evasion of the old and novel no-hair theorems, we consider a variety of forms for the coupling function (exponential, even and odd polynomial, inverse polynomial, and logarithmic) that, in conjunction with the profile of the scalar field, satisfy a basic constraint. Our numerical analysis then always leads to families of regular, asymptotically flat black-hole solutions with nontrivial scalar hair. The solution for the scalar field and the profile of the corresponding energy-momentum tensor, depending on the value of the coupling constant, may exhibit a nonmonotonic behavior, an unusual feature that highlights the limitations of the existing no-hair theorems. We also determine and study in detail the scalar charge, horizon area, and entropy of our solutions.

Essentially Entropic Lattice Boltzmann Model

NASA Astrophysics Data System (ADS)

Atif, Mohammad; Kolluru, Praveen Kumar; Thantanapally, Chakradhar; Ansumali, Santosh

2017-12-01

The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality. This inequality is solved by creating a new framework for construction of Padé approximants via quadrature on appropriate convex function. This exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step. Since our formulation is devoid of complex mathematical library functions, the computational cost is drastically reduced. To illustrate this, we have simulated a model setup of flow over the NACA-0012 airfoil at a Reynolds number of 2.88 ×106.

On the probability of violations of Fourier's law for heat flow in small systems observed for short times

NASA Astrophysics Data System (ADS)

Evans, Denis J.; Searles, Debra J.; Williams, Stephen R.

2010-01-01

We study the statistical mechanics of thermal conduction in a classical many-body system that is in contact with two thermal reservoirs maintained at different temperatures. The ratio of the probabilities, that when observed for a finite time, the time averaged heat flux flows in and against the direction required by Fourier's Law for heat flow, is derived from first principles. This result is obtained using the transient fluctuation theorem. We show that the argument of that theorem, namely, the dissipation function is, close to equilibrium, equal to a microscopic expression for the entropy production. We also prove that if transient time correlation functions of smooth zero mean variables decay to zero at long times, the system will relax to a unique nonequilibrium steady state, and for this state, the thermal conductivity must be positive. Our expressions are tested using nonequilibrium molecular dynamics simulations of heat flow between thermostated walls.

A simple low-computation-intensity model for approximating the distribution function of a sum of non-identical lognormals for financial applications

NASA Astrophysics Data System (ADS)

Messica, A.

2016-10-01

The probability distribution function of a weighted sum of non-identical lognormal random variables is required in various fields of science and engineering and specifically in finance for portfolio management as well as exotic options valuation. Unfortunately, it has no known closed form and therefore has to be approximated. Most of the approximations presented to date are complex as well as complicated for implementation. This paper presents a simple, and easy to implement, approximation method via modified moments matching and a polynomial asymptotic series expansion correction for a central limit theorem of a finite sum. The method results in an intuitively-appealing and computation-efficient approximation for a finite sum of lognormals of at least ten summands and naturally improves as the number of summands increases. The accuracy of the method is tested against the results of Monte Carlo simulationsand also compared against the standard central limit theorem andthe commonly practiced Markowitz' portfolio equations.

A Converse of the Mean Value Theorem Made Easy

ERIC Educational Resources Information Center

Mortici, Cristinel

2011-01-01

The aim of this article is to discuss some results about the converse mean value theorem stated by Tong and Braza [J. Tong and P. Braza, "A converse of the mean value theorem", Amer. Math. Monthly 104(10), (1997), pp. 939-942] and Almeida [R. Almeida, "An elementary proof of a converse mean-value theorem", Internat. J. Math. Ed. Sci. Tech. 39(8)…

Recurrence theorems: A unified account

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

Wallace, David, E-mail: david.wallace@balliol.ox.ac.uk

I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way, I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.

A variational theorem for creep with applications to plates and columns

NASA Technical Reports Server (NTRS)

Sanders, J Lyell, Jr; Mccomb, Harvey G , Jr; Schlechte, Floyd R

1958-01-01

A variational theorem is presented for a body undergoing creep. Solutions to problems of the creep behavior of plates, columns, beams, and shells can be obtained by means of the direct methods of the calculus of variations in conjunction with the stated theorem. The application of the theorem is illustrated for plates and columns by the solution of two sample problems.

Correcting Duporcq's theorem☆

PubMed Central

Nawratil, Georg

2014-01-01

In 1898, Ernest Duporcq stated a famous theorem about rigid-body motions with spherical trajectories, without giving a rigorous proof. Today, this theorem is again of interest, as it is strongly connected with the topic of self-motions of planar Stewart–Gough platforms. We discuss Duporcq's theorem from this point of view and demonstrate that it is not correct. Moreover, we also present a revised version of this theorem. PMID:25540467

Math Majors' Visual Proofs in a Dynamic Environment: The Case of Limit of a Function and the ?-d Approach

ERIC Educational Resources Information Center

Caglayan, Günhan

2015-01-01

Despite few limitations, GeoGebra as a dynamic geometry software stood as a powerful instrument in helping university math majors understand, explore, and gain experiences in visualizing the limits of functions and the ?-d formalism. During the process of visualizing a theorem, the order mattered in the sequence of constituents. Students made use…

A conservative implicit finite difference algorithm for the unsteady transonic full potential equation

NASA Technical Reports Server (NTRS)

Steger, J. L.; Caradonna, F. X.

1980-01-01

An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm.

The mere exposure effect and recognition depend on the way you look!

PubMed

Willems, Sylvie; Dedonder, Jonathan; Van der Linden, Martial

2010-01-01

In line with Whittlesea and Price (2001), we investigated whether the memory effect measured with an implicit memory paradigm (mere exposure effect) and an explicit recognition task depended on perceptual processing strategies, regardless of whether the task required intentional retrieval. We found that manipulation intended to prompt functional implicit-explicit dissociation no longer had a differential effect when we induced similar perceptual strategies in both tasks. Indeed, the results showed that prompting a nonanalytic strategy ensured performance above chance on both tasks. Conversely, inducing an analytic strategy drastically decreased both explicit and implicit performance. Furthermore, we noted that the nonanalytic strategy involved less extensive gaze scanning than the analytic strategy and that memory effects under this processing strategy were largely independent of gaze movement.

Implicit Solvation Parameters Derived from Explicit Water Forces in Large-Scale Molecular Dynamics Simulations

PubMed Central

2012-01-01

Implicit solvation is a mean force approach to model solvent forces acting on a solute molecule. It is frequently used in molecular simulations to reduce the computational cost of solvent treatment. In the first instance, the free energy of solvation and the associated solvent–solute forces can be approximated by a function of the solvent-accessible surface area (SASA) of the solute and differentiated by an atom–specific solvation parameter σiSASA. A procedure for the determination of values for the σiSASA parameters through matching of explicit and implicit solvation forces is proposed. Using the results of Molecular Dynamics simulations of 188 topologically diverse protein structures in water and in implicit solvent, values for the σiSASA parameters for atom types i of the standard amino acids in the GROMOS force field have been determined. A simplified representation based on groups of atom types σgSASA was obtained via partitioning of the atom–type σiSASA distributions by dynamic programming. Three groups of atom types with well separated parameter ranges were obtained, and their performance in implicit versus explicit simulations was assessed. The solvent forces are available at http://mathbio.nimr.mrc.ac.uk/wiki/Solvent_Forces. PMID:23180979

Differential patterns of implicit emotional processing in Alzheimer's disease and healthy aging.

PubMed

García-Rodríguez, Beatriz; Fusari, Anna; Rodríguez, Beatriz; Hernández, José Martín Zurdo; Ellgring, Heiner

2009-01-01

Implicit memory for emotional facial expressions (EFEs) was investigated in young adults, healthy old adults, and mild Alzheimer's disease (AD) patients. Implicit memory is revealed by the effect of experience on performance by studying previously encoded versus novel stimuli, a phenomenon referred to as perceptual priming. The aim was to assess the changes in the patterns of priming as a function of aging and dementia. Participants identified EFEs taken from the Facial Action Coding System and the stimuli used represented the emotions of happiness, sadness, surprise, fear, anger, and disgust. In the study phase, participants rated the pleasantness of 36 faces using a Likert-type scale. Subsequently, the response to the 36 previously studied and 36 novel EFEs was tested when they were randomly presented in a cued naming task. The results showed that implicit memory for EFEs is preserved in AD and aging, and no specific age-related effects on implicit memory for EFEs were observed. However, different priming patterns were evident in AD patients that may reflect pathological brain damage and the effect of stimulus complexity. These findings provide evidence of how progressive neuropathological changes in the temporal and frontal areas may affect emotional processing in more advanced stages of the disease.

Voronovskaja's theorem revisited

NASA Astrophysics Data System (ADS)

Tachev, Gancho T.

2008-07-01

We represent a new quantitative variant of Voronovskaja's theorem for Bernstein operator. This estimate improves the recent quantitative versions of Voronovskaja's theorem for certain Bernstein-type operators, obtained by H. Gonska, P. Pitul and I. Rasa in 2006.

Riemannian and Lorentzian flow-cut theorems

NASA Astrophysics Data System (ADS)

Headrick, Matthew; Hubeny, Veronika E.

2018-05-01

We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.

Random Walks on Cartesian Products of Certain Nonamenable Groups and Integer Lattices

NASA Astrophysics Data System (ADS)

Vishnepolsky, Rachel

A random walk on a discrete group satisfies a local limit theorem with power law exponent \\alpha if the return probabilities follow the asymptotic law. P{ return to starting point after n steps } ˜ Crhonn-alpha.. A group has a universal local limit theorem if all random walks on the group with finitely supported step distributions obey a local limit theorem with the same power law exponent. Given two groups that obey universal local limit theorems, it is not known whether their cartesian product also has a universal local limit theorem. We settle the question affirmatively in one case, by considering a random walk on the cartesian product of a nonamenable group whose Cayley graph is a tree, and the integer lattice. As corollaries, we derive large deviations estimates and a central limit theorem.

An Introduction to Kristof's Theorem for Solving Least-Square Optimization Problems Without Calculus.

PubMed

Waller, Niels

2018-01-01

Kristof's Theorem (Kristof, 1970 ) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof's Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof's ( 1964 , 1970 ) writings. In this article, I describe the underlying logic of Kristof's Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof. I then show how Kristof's Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 ) code to perform the calculations described in the text.

On Nonlinear Functionals of Random Spherical Eigenfunctions

NASA Astrophysics Data System (ADS)

Marinucci, Domenico; Wigman, Igor

2014-05-01

We prove central limit theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combines asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and total variation bounds for Gaussian subordinated fields. We discuss applications to geometric functionals like the defect and invariant statistics, e.g., polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.

Understanding squeezing of quantum states with the Wigner function

NASA Technical Reports Server (NTRS)

Royer, Antoine

1994-01-01

The Wigner function is argued to be the only natural phase space function evolving classically under quadratic Hamiltonians with time-dependent bilinear part. This is used to understand graphically how certain quadratic time-dependent Hamiltonians induce squeezing of quantum states. The Wigner representation is also used to generalize Ehrenfest's theorem to the quantum uncertainties. This makes it possible to deduce features of the quantum evolution, such as squeezing, from the classical evolution, whatever the Hamiltonian.

Brain Regions Influencing Implicit Violent Attitudes: A Lesion-Mapping Study.

PubMed

Cristofori, Irene; Zhong, Wanting; Mandoske, Valerie; Chau, Aileen; Krueger, Frank; Strenziok, Maren; Grafman, Jordan

2016-03-02

Increased aggression is common after traumatic brain injuries and may persist after cognitive recovery. Maladaptive aggression and violence are associated with dysfunction in the prefrontal and temporal cortex, but such dysfunctional behaviors are typically measured by explicit scales and history. However, it is well known that answers on explicit scales on sensitive topics--such as aggressive thoughts and behaviors--may not reveal true tendencies. Here, we investigated the neural basis of implicit attitudes toward aggression in humans using a modified version of the Implicit Association Task (IAT) with a unique sample of 112 Vietnam War veterans who suffered penetrating brain injury and 33 healthy controls who also served in combat in Vietnam but had no history of brain injury. We hypothesized that dorsolateral prefrontal cortex (dlPFC) lesions, due to the crucial role of the dlPFC in response inhibition, could influence performance on the IAT. In addition, we investigated the causal contribution of specific brain areas to implicit attitudes toward violence. We found a more positive implicit attitude toward aggression among individuals with lesions to the dlPFC and inferior posterior temporal cortex (ipTC). Furthermore, executive functions were critically involved in regulating implicit attitudes toward violence and aggression. Our findings complement existing evidence on the neural basis of explicit aggression centered on the ventromedial prefrontal cortex. These findings highlight that dlPFC and ipTC play a causal role in modulating implicit attitudes about violence and are crucially involved in the pathogenesis of aggressive behavior. Maladaptive aggression and violence can lead to interpersonal conflict and criminal behavior. Surprisingly little is known about implicit attitudes toward violence and aggression. Here, we used a range of techniques, including voxel-based lesion-symptom mapping, to examine the causal role of brain structures underpinning implicit attitudes toward aggression in a unique sample of combat veterans with traumatic brain injury. We found that damage to the dorsolateral prefrontal cortex (dlPFC) led to a more positive implicit attitude toward violence that under most normal situations would be considered inappropriate. These results suggest that treatments aimed at increasing cognitive control using cognitive behavioral therapies dependent on the intact dlPFC could treat aggressive and violent behavior. Copyright © 2016 the authors 0270-6474/16/362757-12$15.00/0.

Double soft graviton theorems and Bondi-Metzner-Sachs symmetries

NASA Astrophysics Data System (ADS)

Anupam, A. H.; Kundu, Arpan; Ray, Krishnendu

2018-05-01

It is now well understood that Ward identities associated with the (extended) BMS algebra are equivalent to single soft graviton theorems. In this work, we show that if we consider nested Ward identities constructed out of two BMS charges, a class of double soft factorization theorems can be recovered. By making connections with earlier works in the literature, we argue that at the subleading order, these double soft graviton theorems are the so-called consecutive double soft graviton theorems. We also show how these nested Ward identities can be understood as Ward identities associated with BMS symmetries in scattering states defined around (non-Fock) vacua parametrized by supertranslations or superrotations.

A fermionic de Finetti theorem

NASA Astrophysics Data System (ADS)

Krumnow, Christian; Zimborás, Zoltán; Eisert, Jens

2017-12-01

Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing one to bound the error made by mean-field approaches. Such theorems link the symmetry of a quantum state under the exchange of subsystems to negligible quantum correlations and are well understood and established in the context of distinguishable particles. In this work, we derive a de Finetti theorem for finite sized Majorana fermionic systems. It is shown, much reflecting the spirit of other quantum de Finetti theorems, that a state which is invariant under certain permutations of modes loses most of its anti-symmetric character and is locally well described by a mode separable state. We discuss the structure of the resulting mode separable states and establish in specific instances a quantitative link to the quality of the Hartree-Fock approximation of quantum systems. We hint at a link to generalized Pauli principles for one-body reduced density operators. Finally, building upon the obtained de Finetti theorem, we generalize and extend the applicability of Hudson's fermionic central limit theorem.

Mathematics from Still and Moving Images

ERIC Educational Resources Information Center

Pierce, Robyn; Stacey, Kaye; Ball, Lynda

2005-01-01

Digital photos and digital movies offer an excellent way of bringing real world situations into the mathematics classroom. The technologies surveyed here are feasible for everyday classroom use and inexpensive. Examples are drawn from the teaching of Cartesian coordinates, linear functions, ratio and Pythagoras' theorem using still images, and…

Estimation of the neural drive to the muscle from surface electromyograms

NASA Astrophysics Data System (ADS)

Hofmann, David

Muscle force is highly correlated with the standard deviation of the surface electromyogram (sEMG) produced by the active muscle. Correctly estimating this quantity of non-stationary sEMG and understanding its relation to neural drive and muscle force is of paramount importance. The single constituents of the sEMG are called motor unit action potentials whose biphasic amplitude can interfere (named amplitude cancellation), potentially affecting the standard deviation (Keenan etal. 2005). However, when certain conditions are met the Campbell-Hardy theorem suggests that amplitude cancellation does not affect the standard deviation. By simulation of the sEMG, we verify the applicability of this theorem to myoelectric signals and investigate deviations from its conditions to obtain a more realistic setting. We find no difference in estimated standard deviation with and without interference, standing in stark contrast to previous results (Keenan etal. 2008, Farina etal. 2010). Furthermore, since the theorem provides us with the functional relationship between standard deviation and neural drive we conclude that complex methods based on high density electrode arrays and blind source separation might not bear substantial advantages for neural drive estimation (Farina and Holobar 2016). Funded by NIH Grant Number 1 R01 EB022872 and NSF Grant Number 1208126.

Visual Theorems.

ERIC Educational Resources Information Center

Davis, Philip J.

1993-01-01

Argues for a mathematics education that interprets the word "theorem" in a sense that is wide enough to include the visual aspects of mathematical intuition and reasoning. Defines the term "visual theorems" and illustrates the concept using the Marigold of Theodorus. (Author/MDH)

Note on the theorems of Bjerknes and Crocco

NASA Technical Reports Server (NTRS)

Theodorsen, Theodore

1946-01-01

The theorems of Bjerknes and Crocco are of great interest in the theory of flow around airfoils at Mach numbers near and above unity. A brief note shows how both theorems are developed by short vector transformations.

Analysis of non locality proofs in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe

2012-02-01

Two kinds of non-locality theorems in Quantum Mechanics are taken into account: the theorems based on the criterion of reality and the quite different theorem proposed by Stapp. In the present work the analyses of the theorem due to Greenberger, Horne, Shimony and Zeilinger, based on the criterion of reality, and of Stapp's argument are shown. The results of these analyses show that the alleged violations of locality cannot be considered definitive.

PYGMALION: A Creative Programming Environment

DTIC Science & Technology

1975-06-01

iiiiiimimmmimm wm^m^mmm’ wi-i ,»■»’■’.■- v* 26 Examples of Purely Iconic Reasoning 1-H Pythagoras ’ original proof of the Pythagorean Theorem ... Theorem Proving Machine񓟋. His program employed properties of the representation to guide the proof of theorems . His simple heruristic "Reject...one theorem the square of the hypotenuse. "Every proposition is presented as a self-contained fact relying on its own intrinsic evidence. Instead

A Maximal Element Theorem in FWC-Spaces and Its Applications

PubMed Central

Hu, Qingwen; Miao, Yulin

2014-01-01

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature. PMID:24782672

Affective decision-making moderates the effects of automatic associations on alcohol use among drug offenders.

PubMed

Cappelli, Christopher; Ames, Susan; Shono, Yusuke; Dust, Mark; Stacy, Alan

2017-09-01

This study used a dual-process model of cognition in order to investigate the possible influence of automatic and deliberative processes on lifetime alcohol use in a sample of drug offenders. The objective was to determine if automatic/implicit associations in memory can exert an influence over an individual's alcohol use and if decision-making ability could potentially modify the influence of these associations. 168 participants completed a battery of cognitive tests measuring implicit alcohol associations in memory (verb generation) as well as their affective decision-making ability (Iowa Gambling Task). Structural equation modeling procedures were used to test the relationship between implicit associations, decision-making, and lifetime alcohol use. Results revealed that among participants with lower levels of decision-making, implicit alcohol associations more strongly predicted higher lifetime alcohol use. These findings provide further support for the interaction between a specific decision function and its influence over automatic processes in regulating alcohol use behavior in a risky population. Understanding the interaction between automatic associations and decision processes may aid in developing more effective intervention components.

Tailoring the Variational Implicit Solvent Method for New Challenges: Biomolecular Recognition and Assembly

PubMed Central

Ricci, Clarisse Gravina; Li, Bo; Cheng, Li-Tien; Dzubiella, Joachim; McCammon, J. Andrew

2018-01-01

Predicting solvation free energies and describing the complex water behavior that plays an important role in essentially all biological processes is a major challenge from the computational standpoint. While an atomistic, explicit description of the solvent can turn out to be too expensive in large biomolecular systems, most implicit solvent methods fail to capture “dewetting” effects and heterogeneous hydration by relying on a pre-established (i.e., guessed) solvation interface. Here we focus on the Variational Implicit Solvent Method, an implicit solvent method that adds water “plasticity” back to the picture by formulating the solvation free energy as a functional of all possible solvation interfaces. We survey VISM's applications to the problem of molecular recognition and report some of the most recent efforts to tailor VISM for more challenging scenarios, with the ultimate goal of including thermal fluctuations into the framework. The advances reported herein pave the way to make VISM a uniquely successful approach to characterize complex solvation properties in the recognition and binding of large-scale biomolecular complexes. PMID:29484300

Inattentional blindness for ignored words: comparison of explicit and implicit memory tasks.

PubMed

Butler, Beverly C; Klein, Raymond

2009-09-01

Inattentional blindness is described as the failure to perceive a supra-threshold stimulus when attention is directed away from that stimulus. Based on performance on an explicit recognition memory test and concurrent functional imaging data Rees, Russell, Frith, and Driver [Rees, G., Russell, C., Frith, C. D., & Driver, J. (1999). Inattentional blindness versus inattentional amnesia for fixated but ignored words. Science, 286, 2504-2507] reported inattentional blindness for word stimuli that were fixated but ignored. The present study examined both explicit and implicit memory for fixated but ignored words using a selective-attention task in which overlapping picture/word stimuli were presented at fixation. No explicit awareness of the unattended words was apparent on a recognition memory test. Analysis of an implicit memory task, however, indicated that unattended words were perceived at a perceptual level. Thus, the selective-attention task did not result in perfect filtering as suggested by Rees et al. While there was no evidence of conscious perception, subjects were not blind to the implicit perceptual properties of fixated but ignored words.

IMPLICIT DUAL CONTROL BASED ON PARTICLE FILTERING AND FORWARD DYNAMIC PROGRAMMING.

PubMed

Bayard, David S; Schumitzky, Alan

2010-03-01

This paper develops a sampling-based approach to implicit dual control. Implicit dual control methods synthesize stochastic control policies by systematically approximating the stochastic dynamic programming equations of Bellman, in contrast to explicit dual control methods that artificially induce probing into the control law by modifying the cost function to include a term that rewards learning. The proposed implicit dual control approach is novel in that it combines a particle filter with a policy-iteration method for forward dynamic programming. The integration of the two methods provides a complete sampling-based approach to the problem. Implementation of the approach is simplified by making use of a specific architecture denoted as an H-block. Practical suggestions are given for reducing computational loads within the H-block for real-time applications. As an example, the method is applied to the control of a stochastic pendulum model having unknown mass, length, initial position and velocity, and unknown sign of its dc gain. Simulation results indicate that active controllers based on the described method can systematically improve closed-loop performance with respect to other more common stochastic control approaches.

Making the Implicit Explicit: Towards an Assurance Case for DO-178C

NASA Technical Reports Server (NTRS)

Holloway, C. Michael

2013-01-01

For about two decades, compliance with Software Considerations in Airborne Systems and Equipment Certification (DO-178B) has been the primary means for receiving regulatory approval for using software on commercial airplanes. A new edition of the standard, DO-178C, was published in December 2011, and regulatory bodies have started the process towards recognizing this edition. The stated purpose of DO-178C remains unchanged from its predecessor: providing guidance “for the production of software for airborne systems and equipment that performs its intended function with a level of confidence in safety that complies with airworthiness requirements.” Within the text of the guidance, little or no rationale is given for how a particular objective or collection of objectives contributes to achieving this purpose. Thus the assurance case for the document is implicit. This paper discusses a current effort to make the implicit explicit. In particular, the paper describes the current status of the research seeking to identify the specific arguments contained in, or implied by, the DO-178C guidance that implicitly justify the assumption that the document meets its stated purpose.

Blue and red shifted temperature dependence of implicit phonon shifts in graphene

NASA Astrophysics Data System (ADS)

Mann, Sarita; Jindal, V. K.

2017-07-01

We have calculated the implicit shift for various modes of frequency in a pure graphene sheet. Thermal expansion and Grüneisen parameter which are required for implicit shift calculation have already been studied and reported. For this calculation, phonon frequencies are obtained using force constants derived from dynamical matrix calculated using VASP code where the density functional perturbation theory (DFPT) is used in interface with phonopy software. The implicit phonon shift shows an unusual behavior as compared to the bulk materials. The frequency shift is large negative (red shift) for ZA and ZO modes and the value of negative shift increases with increase in temperature. On the other hand, blue shift arises for all other longitudinal and transverse modes with a similar trend of increase with increase in temperature. The q dependence of phonon shifts has also been studied. Such simultaneous red and blue shifts in transverse or out plane modes and surface modes, respectively leads to speculation of surface softening in out of plane direction in preference to surface melting.

Generalized Bloch theorem and topological characterization

NASA Astrophysics Data System (ADS)

Dobardžić, E.; Dimitrijević, M.; Milovanović, M. V.

2015-03-01

The Bloch theorem enables reduction of the eigenvalue problem of the single-particle Hamiltonian that commutes with the translational group. Based on a group theory analysis we present a generalization of the Bloch theorem that incorporates all additional symmetries of a crystal. The generalized Bloch theorem constrains the form of the Hamiltonian which becomes manifestly invariant under additional symmetries. In the case of isotropic interactions the generalized Bloch theorem gives a unique Hamiltonian. This Hamiltonian coincides with the Hamiltonian in the periodic gauge. In the case of anisotropic interactions the generalized Bloch theorem allows a family of Hamiltonians. Due to the continuity argument we expect that even in this case the Hamiltonian in the periodic gauge defines observables, such as Berry curvature, in the inverse space. For both cases we present examples and demonstrate that the average of the Berry curvatures of all possible Hamiltonians in the Bloch gauge is the Berry curvature in the periodic gauge.

On Monotone Embedding in Information Geometry (Open Access)

DTIC Science & Technology

2015-06-25

the non-parametric ( infinite - dimensional ) setting, as well [4,6], with the α-connection structure cast in a more general way. Theorem 1 of [4] gives... the weighting function for taking the expectation of random variables in calculating the Riemannian metric (G = 1 reduces to F - geometry , with the ...is a trivial rewriting of the convex function f used by [2]. This paper will start in Section 1

On an application of conformal maps to inequalities for rational functions

NASA Astrophysics Data System (ADS)

Dubinin, V. N.

2002-04-01

Using classical properties of conformal maps, we get new exact inequalities for rational functions with prescribed poles. In particular, we prove a new Bernstein-type inequality, an inequality for Blaschke products and a theorem that generalizes the Turan inequality for polynomials. The estimates obtained strengthen some familiar inequalities of Videnskii and Rusak. They are also related to recent results of Borwein, Erdelyi, Li, Mohapatra, Rodriguez, Aziz and others.

Revisiting Ramakrishnan's approach to relatively. [Velocity addition theorem uniqueness

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

Nandi, K.K.; Shankara, T.S.

The conditions under which the velocity addition theorem (VAT) is formulated by Ramakrishnan gave rise to doubts about the uniqueness of the theorem. These conditions are rediscussed with reference to their algebraic and experimental implications. 9 references.

General Theorems about Homogeneous Ellipsoidal Inclusions

ERIC Educational Resources Information Center

Korringa, J.; And Others

1978-01-01

Mathematical theorems about the properties of ellipsoids are developed. Included are Poisson's theorem concerning the magnetization of a homogeneous body of ellipsoidal shape, the polarization of a dielectric, the transport of heat or electricity through an ellipsoid, and other problems. (BB)

A no-hair theorem for black holes in f(R) gravity

NASA Astrophysics Data System (ADS)

Cañate, Pedro

2018-01-01

In this work we present a no-hair theorem which discards the existence of four-dimensional asymptotically flat, static and spherically symmetric or stationary axisymmetric, non-trivial black holes in the frame of f(R) gravity under metric formalism. Here we show that our no-hair theorem also can discard asymptotic de Sitter stationary and axisymmetric non-trivial black holes. The novelty is that this no-hair theorem is built without resorting to known mapping between f(R) gravity and scalar–tensor theory. Thus, an advantage will be that our no-hair theorem applies as well to metric f(R) models that cannot be mapped to scalar–tensor theory.

Algebraic independence results for reciprocal sums of Fibonacci and Lucas numbers

NASA Astrophysics Data System (ADS)

Stein, Martin

2011-09-01

Let Fn and Ln denote the Fibonacci and Lucas numbers, respectively. D. Duverney, Ke. Nishioka, Ku. Nishioka and I. Shiokawa proved that the values of the Fibonacci zeta function ζF(2s) = Σn = 1∞Fn-2s are transcendental for any s∈N using Nesterenko's theorem on Ramanujan functions P(q), Q(q), and R(q). They obtained similar results for the Lucas zeta function ζL(2s) = Σn = 1∞Ln-2s and some related series. Later, C. Elsner, S. Shimomura and I. Shiokawa found conditions for the algebraic independence of these series. In my PhD thesis I generalized their approach and treated the following problem: We investigate all subsets of { ∑ n = 1∞1/Fn2s1, ∑ n = 1∞(-1)n+1/Fn2s2, ∑ n = 1∞1/Ln2s3, ∑ n = 1∞(-1)n+1/Ln2s4:s1,s2,s3,s4∈N} and decide on their algebraic independence over Q. Actually this is a special case of a more general theorem for reciprocal sums of binary recurrent sequences.

Extension theorems for homogenization on lattice structures

NASA Technical Reports Server (NTRS)

Miller, Robert E.

1992-01-01

When applying homogenization techniques to problems involving lattice structures, it is necessary to extend certain functions defined on a perforated domain to a simply connected domain. This paper provides general extension operators which preserve bounds on derivatives of order l. Only the special case of honeycomb structures is considered.

Lanchester-Type Models of Warfare. Volume II

DTIC Science & Technology

1980-10-01

the so-called PERRON - FROBENIUS theorem50 for nonnegative matrices that one can guarantee that (without any further assumptions about A and B) there...always exists a vector of nonnegative values such that, for example, (7.18.6) holds. Before we state the PERRON - FROBENIUS theorem for nonnegative...a proof of this important theorem). THEOREM .5.-1.1 ( PERRON [121] and FROBENIUS [60]): Let C z 0 be an n x n matrix. Then, 1. C has a nonnegative real

A remark on the energy conditions for Hawking's area theorem

NASA Astrophysics Data System (ADS)

Lesourd, Martin

2018-06-01

Hawking's area theorem is a fundamental result in black hole theory that is universally associated with the null energy condition. That this condition can be weakened is illustrated by the formulation of a strengthened version of the theorem based on an energy condition that allows for violations of the null energy condition. With the semi-classical context in mind, some brief remarks pertaining to the suitability of the area theorem and its energy condition are made.

Gibbs-Curie-Wulff Theorem in Organic Materials: A Case Study on the Relationship between Surface Energy and Crystal Growth.

PubMed

Li, Rongjin; Zhang, Xiaotao; Dong, Huanli; Li, Qikai; Shuai, Zhigang; Hu, Wenping

2016-02-24

The equilibrium crystal shape and shape evolution of organic crystals are found to follow the Gibbs-Curie-Wulff theorem. Organic crystals are grown by the physical vapor transport technique and exhibit exactly the same shape as predicted by the Gibbs-Curie-Wulff theorem under optimal conditions. This accordance provides concrete proof for the theorem. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Explicit and implicit reinforcement learning across the psychosis spectrum.

PubMed

Barch, Deanna M; Carter, Cameron S; Gold, James M; Johnson, Sheri L; Kring, Ann M; MacDonald, Angus W; Pizzagalli, Diego A; Ragland, J Daniel; Silverstein, Steven M; Strauss, Milton E

2017-07-01

Motivational and hedonic impairments are core features of a variety of types of psychopathology. An important aspect of motivational function is reinforcement learning (RL), including implicit (i.e., outside of conscious awareness) and explicit (i.e., including explicit representations about potential reward associations) learning, as well as both positive reinforcement (learning about actions that lead to reward) and punishment (learning to avoid actions that lead to loss). Here we present data from paradigms designed to assess both positive and negative components of both implicit and explicit RL, examine performance on each of these tasks among individuals with schizophrenia, schizoaffective disorder, and bipolar disorder with psychosis, and examine their relative relationships to specific symptom domains transdiagnostically. None of the diagnostic groups differed significantly from controls on the implicit RL tasks in either bias toward a rewarded response or bias away from a punished response. However, on the explicit RL task, both the individuals with schizophrenia and schizoaffective disorder performed significantly worse than controls, but the individuals with bipolar did not. Worse performance on the explicit RL task, but not the implicit RL task, was related to worse motivation and pleasure symptoms across all diagnostic categories. Performance on explicit RL, but not implicit RL, was related to working memory, which accounted for some of the diagnostic group differences. However, working memory did not account for the relationship of explicit RL to motivation and pleasure symptoms. These findings suggest transdiagnostic relationships across the spectrum of psychotic disorders between motivation and pleasure impairments and explicit RL. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

The transmission of attitudes towards food: twofold specificity of similarities with parents and friends.

PubMed

Guidetti, Margherita; Conner, Mark; Prestwich, Andrew; Cavazza, Nicoletta

2012-05-01

The present study explored whether similarity of students' food attitudes with those of their parents and friends varies as a function of both the food and type of measurement. We expected greater resemblance with parents for attitudes towards fruit and for implicit attitudes and greater resemblance with friends for attitudes towards snacks and for explicit attitudes. We compared the resemblance in implicit and explicit attitudes towards fruit and preference for sweet over savoury snacks between target-parent and target-friend pairings. The parental-peer mutual influence effect was separated from cultural effect by comparing real and random dyads. Target participants were 85 students who recruited one parent and one best friend each. All participants completed online two Implicit Association Tests and rated their liking for fruit and sweet/savoury snacks. Our target participants' attitudes towards fruit were predicted by those of their parents rather than friends, with this relationship being detected through implicit but not explicit measures. Conversely, target participants' preference for sweet over savoury snacks was predicted with those of their friends but not parents, with this relationship being detected through explicit but not implicit measures. Young adults' resemblance to parents and friends, in terms of food attitudes, seems specific both to the food type and to the attitude measure, suggesting that parents' influence concerns healthy food and is exerted at an implicit attitude level; whereas friends' influence concerns junk food and is exerted at an explicit attitude level. The theoretical and practical implications are discussed. ©2011 The British Psychological Society.

A critical role of the human hippocampus in an electrophysiological measure of implicit memory

PubMed Central

Addante, Richard James

2015-01-01

The hippocampus has traditionally been thought to be critical for conscious explicit memory but not necessary for unconscious implicit memory processing. In a recent study of a group of mild amnesia patients with evidence of MTL damage limited to the hippocampus, subjects were tested on a direct test of item recognition confidence while electroencephalogram (EEG) was acquired, and revealed intact measures of explicit memory from 400–600ms (mid-frontal old-new effect, FN400). The current investigation re-analyzed this data to study event-related potentials (ERPs) of implicit memory, using a recently developed procedure that eliminated declarative memory differences. Prior ERP findings from this technique were first replicated in two independent matched control groups, which exhibited reliable implicit memory effects in posterior scalp regions from 400–600 msec, which were topographically dissociated from the explicit memory effects of familiarity. However, patients were found to be dramatically impaired in implicit memory effects relative to control subjects, as quantified by a reliable condition × group interaction. Several control analysis were conducted to consider alternative factors that could account for the results, including outliers, sample size, age, or contamination by explicit memory, and each of these factors were systematically ruled out. Results suggest that the hippocampus plays a fundamental role in aspects of memory processing that is beyond conscious awareness. The current findings therefore indicate that both memory systems of implicit and explicit memory may rely upon the same neural structures – but function in different physiological ways. PMID:25562828

Markov and semi-Markov processes as a failure rate

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

Grabski, Franciszek

2016-06-08

In this paper the reliability function is defined by the stochastic failure rate process with a non negative and right continuous trajectories. Equations for the conditional reliability functions of an object, under assumption that the failure rate is a semi-Markov process with an at most countable state space are derived. A proper theorem is presented. The linear systems of equations for the appropriate Laplace transforms allow to find the reliability functions for the alternating, the Poisson and the Furry-Yule failure rate processes.

Hartree-Fock theory of the inhomogeneous electron gas at a jellium metal surface: Rigorous upper bounds to the surface energy and accurate work functions

NASA Astrophysics Data System (ADS)

Sahni, V.; Ma, C. Q.

1980-12-01

The inhomogeneous electron gas at a jellium metal surface is studied in the Hartree-Fock approximation by Kohn-Sham density functional theory. Rigorous upper bounds to the surface energy are derived by application of the Rayleigh-Ritz variational principle for the energy, the surface kinetic, electrostatic, and nonlocal exchange energy functionals being determined exactly for the accurate linear-potential model electronic wave functions. The densities obtained by the energy minimization constraint are then employed to determine work-function results via the variationally accurate "displaced-profile change-in-self-consistent-field" expression. The theoretical basis of this non-self-consistent procedure and its demonstrated accuracy for the fully correlated system (as treated within the local-density approximation for exchange and correlation) leads us to conclude these results for the surface energies and work functions to be essentially exact. Work-function values are also determined by the Koopmans'-theorem expression, both for these densities as well as for those obtained by satisfaction of the constraint set on the electrostatic potential by the Budd-Vannimenus theorem. The use of the Hartree-Fock results in the accurate estimation of correlation-effect contributions to these surface properties of the nonuniform electron gas is also indicated. In addition, the original work and approximations made by Bardeen in this attempt at a solution of the Hartree-Fock problem are briefly reviewed in order to contrast with the present work.

Squared eigenvalue condition numbers and eigenvector correlations from the single ring theorem

NASA Astrophysics Data System (ADS)

Belinschi, Serban; Nowak, Maciej A.; Speicher, Roland; Tarnowski, Wojciech

2017-03-01

We extend the so-called ‘single ring theorem’ (Feinberg and Zee 1997 Nucl. Phys. B 504 579), also known as the Haagerup-Larsen theorem (Haagerup and Larsen 2000 J. Funct. Anal. 176 331). We do this by showing that in the limit when the size of the matrix goes to infinity a particular correlator between left and right eigenvectors of the relevant non-hermitian matrix X, being the spectral density weighted by the squared eigenvalue condition number, is given by a simple formula involving only the radial spectral cumulative distribution function of X. We show that this object allows the calculation of the conditional expectation of the squared eigenvalue condition number. We give examples and provide a cross-check of the analytic prediction by the large scale numerics.

Verbal implicit sequence learning in persons who stutter and persons with Parkinson's disease.

PubMed

Smits-Bandstra, Sarah; Gracco, Vincent

2013-01-01

The authors investigated the integrity of implicit learning systems in 14 persons with Parkinson's disease (PPD), 14 persons who stutter (PWS), and 14 control participants. In a 120-min session participants completed a verbal serial reaction time task, naming aloud 4 syllables in response to 4 visual stimuli. Unbeknownst to participants, the syllables formed a repeating 8-item sequence. PWS and PPD demonstrated slower reaction times for early but not late learning trials relative to controls reflecting delays but not deficiencies in general learning. PPD also demonstrated less accuracy in general learning relative to controls. All groups demonstrated similar limited explicit sequence knowledge. Both PWS and PPD demonstrated significantly less implicit sequence learning relative to controls, suggesting that stuttering may be associated with compromised functional integrity of the cortico-striato-thalamo-cortical loop.

A Vorticity-preserving Hydrodynamical Scheme for Modeling Accretion Disk Flows

NASA Astrophysics Data System (ADS)

Seligman, Darryl; Laughlin, Gregory

2017-10-01

Vortices, turbulence, and unsteady nonlaminar flows are likely both prominent and dynamically important features of astrophysical disks. Such strongly nonlinear phenomena are often difficult, however, to simulate accurately, and are generally amenable to analytic treatment only in idealized form. In this paper, we explore the evolution of compressible two-dimensional flows using an implicit dual-time hydrodynamical scheme that strictly conserves vorticity (if applied to simulate inviscid flows for which Kelvin’s Circulation Theorem is applicable). The algorithm is based on the work of Lerat et al., who proposed it in the context of terrestrial applications such as the blade-vortex interactions generated by helicopter rotors. We present several tests of Lerat et al.'s vorticity-preserving approach, which we have implemented to second-order accuracy, providing side-by-side comparisons with other algorithms that are frequently used in protostellar disk simulations. The comparison codes include one based on explicit, second-order van Leer advection, one based on spectral methods, and another that implements a higher-order Godunov solver. Our results suggest that the Lerat et al. algorithm will be useful for simulations of astrophysical environments in which vortices play a dynamical role, and where strong shocks are not expected.

Rectification of General Relativity, Experimental Verifications, and Errors of the Wheeler School

NASA Astrophysics Data System (ADS)

Lo, C. Y.

2013-09-01

General relativity is not yet consistent. Pauli has misinterpreted Einstein's 1916 equivalence principle that can derive a valid field equation. The Wheeler School has distorted Einstein's 1916 principle to be his 1911 assumption of equivalence, and created new errors. Moreover, errors on dynamic solutions have allowed the implicit assumption of a unique coupling sign that violates the principle of causality. This leads to the space-time singularity theorems of Hawking and Penrose who "refute" applications for microscopic phenomena, and obstruct efforts to obtain a valid equation for the dynamic case. These errors also explain the mistakes in the press release of the 1993 Nobel Committee, who was unaware of the non-existence of dynamic solutions. To illustrate the damages to education, the MIT Open Course Phys. 8.033 is chosen. Rectification of errors confirms that E = mc2 is only conditionally valid, and leads to the discovery of the charge-mass interaction that is experimentally confirmed and subsequently the unification of gravitation and electromagnetism. The charge-mass interaction together with the unification predicts the weight reduction (instead of increment) of charged capacitors and heated metals, and helps to explain NASA's Pioneer anomaly and potentially other anomalies as well.

Functional Magnetic Resonance Imaging Clinical Trial of a Dual-Processing Treatment Protocol for Substance-Dependent Adults

ERIC Educational Resources Information Center

Matto, Holly C.; Hadjiyane, Maria C.; Kost, Michelle; Marshall, Jennifer; Wiley, Joseph; Strolin-Goltzman, Jessica; Khatiwada, Manish; VanMeter, John W.

2014-01-01

Objectives: Empirical evidence suggests substance dependence creates stress system dysregulation which, in turn, may limit the efficacy of verbal-based treatment interventions, as the recovering brain may not be functionally capable of executive level processing. Treatment models that target implicit functioning are necessary. Methods: An RCT was…

Recurrence of random walks with long-range steps generated by fractional Laplacian matrices on regular networks and simple cubic lattices

NASA Astrophysics Data System (ADS)

Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.

2017-12-01

We analyze a Markovian random walk strategy on undirected regular networks involving power matrix functions of the type L\\frac{α{2}} where L indicates a ‘simple’ Laplacian matrix. We refer to such walks as ‘fractional random walks’ with admissible interval 0<α ≤slant 2 . We deduce probability-generating functions (network Green’s functions) for the fractional random walk. From these analytical results we establish a generalization of Polya’s recurrence theorem for fractional random walks on d-dimensional infinite lattices: The fractional random walk is transient for dimensions d > α (recurrent for d≤slantα ) of the lattice. As a consequence, for 0<α< 1 the fractional random walk is transient for all lattice dimensions d=1, 2, .. and in the range 1≤slantα < 2 for dimensions d≥slant 2 . Finally, for α=2 , Polya’s classical recurrence theorem is recovered, namely the walk is transient only for lattice dimensions d≥slant 3 . The generalization of Polya’s recurrence theorem remains valid for the class of random walks with Lévy flight asymptotics for long-range steps. We also analyze the mean first passage probabilities, mean residence times, mean first passage times and global mean first passage times (Kemeny constant) for the fractional random walk. For an infinite 1D lattice (infinite ring) we obtain for the transient regime 0<α<1 closed form expressions for the fractional lattice Green’s function matrix containing the escape and ever passage probabilities. The ever passage probabilities (fractional lattice Green’s functions) in the transient regime fulfil Riesz potential power law decay asymptotic behavior for nodes far from the departure node. The non-locality of the fractional random walk is generated by the non-diagonality of the fractional Laplacian matrix with Lévy-type heavy tailed inverse power law decay for the probability of long-range moves. This non-local and asymptotic behavior of the fractional random walk introduces small-world properties with the emergence of Lévy flights on large (infinite) lattices.

A Membrane Model from Implicit Elasticity Theory

PubMed Central

Freed, A. D.; Liao, J.; Einstein, D. R.

2014-01-01

A Fungean solid is derived for membranous materials as a body defined by isotropic response functions whose mathematical structure is that of a Hookean solid where the elastic constants are replaced by functions of state derived from an implicit, thermodynamic, internal-energy function. The theory utilizes Biot’s (1939) definitions for stress and strain that, in 1-dimension, are the stress/strain measures adopted by Fung (1967) when he postulated what is now known as Fung’s law. Our Fungean membrane model is parameterized against a biaxial data set acquired from a porcine pleural membrane subjected to three, sequential, proportional, planar extensions. These data support an isotropic/deviatoric split in the stress and strain-rate hypothesized by our theory. These data also demonstrate that the material response is highly non-linear but, otherwise, mechanically isotropic. These data are described reasonably well by our otherwise simple, four-parameter, material model. PMID:24282079

The Holographic Electron Density Theorem, de-quantization, re-quantization, and nuclear charge space extrapolations of the Universal Molecule Model

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2017-11-01

Two strongly related theorems on non-degenerate ground state electron densities serve as the basis of "Molecular Informatics". The Hohenberg-Kohn theorem is a statement on global molecular information, ensuring that the complete electron density contains the complete molecular information. However, the Holographic Electron Density Theorem states more: the local information present in each and every positive volume density fragment is already complete: the information in the fragment is equivalent to the complete molecular information. In other words, the complete molecular information provided by the Hohenberg-Kohn Theorem is already provided, in full, by any positive volume, otherwise arbitrarily small electron density fragment. In this contribution some of the consequences of the Holographic Electron Density Theorem are discussed within the framework of the "Nuclear Charge Space" and the Universal Molecule Model. In the Nuclear Charge Space" the nuclear charges are regarded as continuous variables, and in the more general Universal Molecule Model some other quantized parameteres are also allowed to become "de-quantized and then re-quantized, leading to interrelations among real molecules through abstract molecules. Here the specific role of the Holographic Electron Density Theorem is discussed within the above context.

Generalized Dandelin’s Theorem

NASA Astrophysics Data System (ADS)

Kheyfets, A. L.

2017-11-01

The paper gives a geometric proof of the theorem which states that in case of the plane section of a second-order surface of rotation (quadrics of rotation, QR), such conics as an ellipse, a hyperbola or a parabola (types of conic sections) are formed. The theorem supplements the well-known Dandelin’s theorem which gives the geometric proof only for a circular cone and applies the proof to all QR, namely an ellipsoid, a hyperboloid, a paraboloid and a cylinder. That’s why the considered theorem is known as the generalized Dandelin’s theorem (GDT). The GDT proof is based on a relatively unknown generalized directrix definition (GDD) of conics. The work outlines the GDD proof for all types of conics as their necessary and sufficient condition. Based on the GDD, the author proves the GDT for all QR in case of a random position of the cutting plane. The graphical stereometric structures necessary for the proof are given. The implementation of the structures by 3d computer methods is considered. The article shows the examples of the builds made in the AutoCAD package. The theorem is intended for the training course of theoretical training of elite student groups of architectural and construction specialties.

The B-field soft theorem and its unification with the graviton and dilaton

NASA Astrophysics Data System (ADS)

Di Vecchia, Paolo; Marotta, Raffaele; Mojaza, Matin

2017-10-01

In theories of Einstein gravity coupled with a dilaton and a two-form, a soft theorem for the two-form, known as the Kalb-Ramond B-field, has so far been missing. In this work we fill the gap, and in turn formulate a unified soft theorem valid for gravitons, dilatons and B-fields in any tree-level scattering amplitude involving the three massless states. The new soft theorem is fixed by means of on-shell gauge invariance and enters at the subleading order of the graviton's soft theorem. In contrast to the subsubleading soft behavior of gravitons and dilatons, we show that the soft behavior of B-fields at this order cannot be fully fixed by gauge invariance. Nevertheless, we show that it is possible to establish a gauge invariant decomposition of the amplitudes to any order in the soft expansion. We check explicitly the new soft theorem in the bosonic string and in Type II superstring theories, and furthermore demonstrate that, at the next order in the soft expansion, totally gauge invariant terms appear in both string theories which cannot be factorized into a soft theorem.