Confabulation Theory

Confabulation Theory [Hecht-Nielsen R. Confabulation theory. Springer-Verlag; 2007] is the first comprehensive theory of human and animal cognition. Here, we briefly describe Confabulation Theory and discuss experimental results that suggest the theory is correct. Simply put, Confabulation Theory proposes that thinking is like moving. In humans, the theory postulates that there are roughly 4000 thalamocortical modules, the “muscles of thought”. Each module performs an internal competition (confabulation) between its symbols, influenced by inputs delivered via learned axonal associations with symbols in other modules. In each module, this competition is controlled, as in an individual muscle, by a single graded (i.e., analog) thought control signal. The final result of this confabulation process is a single active symbol, the expression of which also results in launching of action commands that trigger and control subsequent movements and/or thought processes. Modules are manipulated in groups under coordinated, event-contingent control, in a similar manner to our 700 muscles. Confabulation Theory hypothesizes that the control of thinking is a direct evolutionary outgrowth of the control of movement. Establishing a complete understanding of Confabulation Theory will require launching and sustaining a massive new phalanx of confabulation neuroscience research.     

Potential energy curves for theB 2 Σ andX 2 Σ states of scandium monoxide

For theB ² Σ andX ² Σ states of scandium monoxide, the potential energy curves are constructed by the Rydberg-Klein-Rees and the Morse methods. Morse model is shown to be adequate for the (B→X) band system of ScO. The r_e values are found to be 1.717 Å and 1.665 Å for theB andX states respectively.     

On effectiveness of Morse and Lippincott potential functions forA andX states of MgH

Molecular properties like potential curve,r-centroids, dissociation energy for theA ²II-X ² Σ band system of MgH are studied using Morse and Lippincott functions. Calculations for potential curve and dissociation energy indicate that the Lippincott function is not very appropriate forA andX states of MgH.r-centroids calculated using graphical as well as numerical methods agree well with each other. A smooth relationship between wavelength andr-centroid is obtained. Based on the dissertation submitted to the South Gujarat University by GKP in partial fulfilment of M. Phil. degree, 1976.     

Franck-Condon Factors and r-Centroids for the (B [sbnd] X) and (C [sbnd] X) Bands of the 107Ag 109Ag Molecule

Arrays of Franck-Condon factors q(v′, v″) and r-centroids r(v′, v″) were computed using Morse potentials for C¹Π [sbnd] X¹Σ⁺ _g and B O⁺ _u [sbnd] X¹Σ⁺ _g bands of the ¹⁰⁷Ag ¹⁰⁹Ag molecule.     

Quantum mechanical calculation of rotational constants and Franck-Condon factors of diatomic molecules

In this paper, the question of reliability of the Morse potential as a potential curve for a diatomic molecule is investigated on the basis of calculating the rotational constant. It is shown that the Morse potential describes well potential curves of X¹Σ _q ⁺ and B¹Π_u electronic states of a Na₂ molecule. Calculations of Franck-Condon factors for X¹Σ _q ⁺ ? B¹Π_u band of a Na₂ molecule using wave functions of the Morse potential confirm the known correlation between the values of Franck-Condon factors and rotational constants of combined electronic states.     

Calculation of the Spectroscopic Constants and Strength of the Electron Transition <Emphasis Type="Italic">A</Emphasis>0<Superscript>+</Superscript>-<Emphasis Type="Italic">X</Emphasis><Superscript>1</Superscript>Σ<Superscript>+</Superscript> of the AgAu Molecule

The vibrational, rotational, and centrifugal constants for the electronic states A and X ¹Σ⁺ of the AgAu molecule have been calculated. The calculation is based on the Morse potential functions that were used to approximate the real potential curves of the ground and excited states of AgAu. Using the experimental data on the lifetime of the vibrational levels of the excited electronic state, the strength of the A-X transition was calculated.__________Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 2, pp. 176–180, March–April, 2005     

Study of correlation effects on stability of many-body complexes in III–V nitride quantum dots

The aim of this work is to analyze theoretically the correlation energies, for neutral, positive and negative excitons and bi-excitons in the III–V nitride In_xGa_1−xN/GaN quantum dot; where x=17.5% denotes the indium concentration. So, we propose a model consistent with experimental observations that is small In_xGa_1−xN truncated pyramids with circular base lying on wetting layer, both buried into GaN matrix. The correlation energies of many-body complexes X, X⁻, X⁺ and XX are investigated as a function of the quantum dot radius r_c and the intrinsic electric field.     

Duality Theorems in Ergodic Transport

We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class of problems is the following: suppose ?? is the shift acting on Bernoulli space X={1,2,??,d}^?, and, consider a fixed continuous cost function c:X×X???. Denote by ?? the set of all Borel probabilities ?? on X×X, such that, both its x and y marginals are ??-invariant probabilities. We are interested in the optimal plan ?? which minimizes ??c? d?? among the probabilities in ??. We show, among other things, the analogous Kantorovich Duality Theorem. We also analyze uniqueness of the optimal plan under generic assumptions on c. We investigate the existence of a dual pair of Lipschitz functions which realizes the present dual Kantorovich problem under the assumption that the cost is Lipschitz continuous. For continuous costs c the corresponding results in the Classical Transport Theory and in Ergodic Transport Theory can be, eventually, different. We also consider the problem of approximating the optimal plan ?? by convex combinations of plans such that the support projects in periodic orbits.     

Electronic spectrum of the BaO molecule

The emission spectrum of the BaO molecule corresponding to B → X transitions has been studied experimentally using a d.c. arc with barium electrodes in an oxygen atmosphere. No Q branches were observed. This result implies a Σ¹ → Σ¹ transition for the system. In addition, the data on the singlet system, A′¹Π → X¹Σ, have been reviewed to establish valid molecular constants for the states involved and Frank-Condon factors and r-centroids corresponding to wavefunctions for a Morse potential have been calculated using these constants.     

Laser spectroscopy of LaF: Determination of the separation of the singlet and triplet state manifolds

Tunable dye lasers have been used to excite several known transitions in LaF. Resolved fluorescence spectra obtained after excitation of B¹Π-X¹Σ⁺ and C¹Π-X¹Σ⁺ bands showed transitions to both X¹Σ⁺ and a³Δ states. Analysis of the spectra shows that the state is 1432 cm⁻¹ above X¹Σ⁺, is at 1808 cm⁻¹, and there is an Ω = 2 state (probably ¹Δ) at 5478 cm⁻¹. A new 0⁺-X¹Σ⁺ (v = 0) band has been observed in the vicinity of the B¹Π-X¹Σ⁺ 1-0 band. High resolution excitation spectra of both bands have been obtained, term energies and rotational constants calculated, and the Λ-doubling in B¹Π, v = 1 has been studied. The principal constants (in cm⁻¹) obtained from the analyses wereThe assignments of the low lying states are discussed in terms of their electron configurations and are shown to be in accord with predictions of Ligand Field Theory.     

Multifractal Spectrum of an Experimental (Video Feedback) Farey Tree

A camera films a screen to which it is connected. It films its own image, feeding back the image to the screen. The camera can turn around an optical axis. A pattern of p light spots on the screen and q turns (feedback loops) of the camera appears, where p and q follow the hierarchy of a Farey tree. The Farey tree induces a measure distribution μ on the unit segment, different from the hyperbolic one μ ^H induced by the Farey-Brocot interpolation. In this paper the multifractal spectrum of μ is studied and compared with that of μ ^H ; the study of the latter spectrum is refined. The spectra are studied in this paper by means of different tools from Number Theory. The results of this study are interpreted in terms of p and q, empirically obtained in the video feedback experiment.     

decays in Chiral Perturbation Theory

We study the decays K→ππ in one-loop two-flavour Chiral Perturbation Theory. We provide arguments why the calculation of the coefficient of the pionic chiral logarithm ℓ_M=M²logM² is unique and then perform the calculation. As a check we perform the reduction of the known three-flavour result. Our result can be used to perform the extrapolation to the physical pion mass of direct lattice QCD calculations of K→ππ at fixed m_s or . The underlying arguments are expected to be valid for heavier particles and other processes as well.     

Short-Range Characterization of the MeAr (Me=Zn, Cd) Ground-State Potentials from Fluorescence Spectra

First-time observed D1(¹Π)_v′=10→X0⁺(¹Σ) fluorescence in ZnAr, and A0⁺(³Π)_v′=4→X0⁺ and D1(¹Π)_v′=7,8→X0⁺ fluorescence in CdAr van der Waals (vdW) molecules were produced in a continuous supersonic molecular beam crossed with a pulsed dye-laser beam, following excitation of single vibronic levels. The dispersed fluorescence spectra displayed characteristic Condon internal diffraction (CID) patterns consisting of bound-free, reflection type, continuous spectra, and, in certain cases, bound-bound discrete features. An analysis of the A0⁺→X0⁺ and D1→X0⁺ bound-bound spectra indicates that Morse functions are adequate representations of the X0⁺ potential energy (PE) curves below their dissociation limits. In simulation of the A0⁺→X0⁺ and D1→X0⁺ bound-free spectra, the Morse, Lennard-Jones L-J(n−6), and Maitland-Smith M-S(n₀,n₁) functions were tested, and the respective M-S(11.3, 9.0) and M-S(10.6, 7.0) potentials were found to be good representations for the repulsive walls of the X0⁺ PE curves of ZnAr and CdAr, respectively, over the short range, R=2.45-4.38 Å (ZnAr) and R=2.85-4.31 Å (CdAr), of internuclear separations.     

Long range relationship between Morse and Lennard–Jones potential energy functions

Arising from the use of the Morse function–which is well-known for its applicability for describing bonded interaction energy–in van der Waals systems, an attempt is made herein to express parameters of the Lennard–Jones potential function in terms of the Morse function to enable normalized comparison. In a departure from previous work where the parameter relationships enforce equal curvature at the minimum well-depth, the present approach replaces this rule with equal area above the curves for 1?≤?(r/R)?≤?∞. Results show good approximations of the Morse function to the Lennard–Jones curve and vice versa. Comparison with the previous relation for short range interaction shows that the present relations offer superior agreement with the Lennard–Jones function over a longer range. The conversion relations provide a cost-effective, less time-consuming and reasonably reliable method for obtaining Morse parameters from those of the Lennard–Jones function and vice versa.     

Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential

We investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, ρ(r) = ρ ₀, the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, ρ(r) = ρ ₀ r ², we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and ℓ quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of ρ ₀, in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.     

Hydration of nitriles: an examination in terms of No Barrier Theory

Nitriles pose an interesting problem to the explanatory powers of organic chemistry because, despite the favorable overall thermodynamics of hydrolysis to the corresponding amides, the reactions are inherently slow. The rate determining step is hydration of the nitrile to give the imidic acid, which quickly tautomerizes to the amide. In terms of Marcus Theory, the intrinsic barriers for acid and base‐catalyzed hydration are higher for nitriles than for amides, which are themselves slow reactions. It is remarkable that hydration of a nitrile, for which the free energy change is close to zero except for polyhaloacetonitriles, is much slower than hydration of an amide, which is energetically unfavorable. This can be explained by No Barrier Theory in terms of the high energetic cost of the geometrical distortions in “one thing at a time” corner species. There are no experimental equilibrium constants for this initial hydration step, so we have determined them computationally. The free energy change for the initial hydration is small; it is the fast and energetically downhill second step, tautomerization to the amide, which makes the overall hydrolysis of nitrile to amide thermodynamically favorable. Very few of the pK_a values needed in the acid and base‐catalyzed mechanisms are known, so we used linear free energy relations and treat the parent pK_a values as adjustable parameters. This procedure leads to pK_a values in accord with expectation based on such data as are available and permits calculation of rate constants in satisfactory agreement with experiment. Copyright © 2013 John Wiley & Sons, Ltd.     

Ab Initio Calculation of Hyperfine Interaction Parameters: Recent Evolutions, Recent Examples

For some years already, ab initio calculations based on Density Functional Theory (DFT) belong to the toolbox of the field of hyperfine interaction studies. In this paper, the standard ab initio approach is schematically sketched. New features, methods and possibilities that broke through during the past few years are listed, and their relation to the standard approach is explained. All this is illustrated by some highlights of recent ab initio work done by the Nuclear Condensed Matter Group at the K.U.Leuven.     

On Quantization of Complex Symplectic Manifolds

Let X be a complex symplectic manifold. By showing that any Lagrangian subvariety has a unique lift to a contactification, we associate to X a triangulated category of regular holonomic microdifferential modules. If X is compact, this is a Calabi-Yau category of complex dimension dim X + 1. We further show that regular holonomic microdifferential modules can be realized as modules over a quantization algebroid canonically associated to X.     

The dynamics of a one-dimensional disordered morse attice: Cooling caused by adiabatic stretching

The dynamics of a disordered one-dimensional lattice of a finite length consisting of N particles interacting according to the Morse potential was studied. Disordering was caused by random interaction potential values between neighboring particles. The dynamics of adiabatic stretching of the Morse lattice was considered in detail. An equation relating temperature to the geometric mean normal vibration frequency, that is, $ T \propto \sqrt[N]{{\omega ^1 \omega ^2 \ldots \omega ^N }} The dynamics of a disordered one-dimensional lattice of a finite length consisting of N particles interacting according to the Morse potential was studied. Disordering was caused by random interaction potential values between neighboring particles. The dynamics of adiabatic stretching of the Morse lattice was considered in detail. An equation relating temperature to the geometric mean normal vibration frequency, that is, , was obtained in the quasi-harmonic limit. At low temperatures and certain deformation values, strong interaction between modes was observed which resulted in intense energy exchange between them. The reason for this was pair resonances of the nω ⁱ = ω ^j type. In addition, there were triple resonances ω ⁱ + ω ^j = ω ^k . Close agreement between analytic results and numerical simulation was obtained. At low specific energy € values, the dynamics of the Morse lattice closely resembled the dynamics of the Fermi-Pasta-Ulam lattice. Original Russian Text ? V.N. Likhachev, T.Yu. Astakhova, G.A. Vinogradov, 2009, published in Khimicheskaya Fizika, 2009, Vol. 28, No. 1, pp. 71–82.