Canonical Space Research Articles

Influence of thermostats on the calculations of heat capacities from Born‐Oppenheimer molecular dynamics simulations

AbstractThe temperature dependency of the vibrational molecular heat capacity of the copper dimer is calculated from classical Born‐Oppenheimer molecular dynamics (BOMD) simulations employing four different thermostats. The resulting heat capacity curves are compared with their the polyatomic ideal gas counterparts. It is shown that the Nosé‐Hoover chain thermostat yields realistic temperature profiles and reliable heat capacities. This result is also supported by the corresponding canonical phase space distribution. This work demonstrates that canonical BOMD simulations with the Nosé‐Hoover chain thermostat are well suited to obtain reliable thermodynamic properties for small finite systems. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Second order minimax estimation of the mean

In this study we consider the problem of the improvement of the sample mean in the second order minimax estimation sense for a mean belonging to an unrestricted mean parameter space R + . We solve this problem for the class of natural exponential families (NEF's) whose variance functions (VF's) are regular at zero and at infinity. Such a class of VF's (or NEF's) is huge and contains (among others): Polynomial VF's (e.g., quadratic VF's in the Morris class, cubic VF's in the Letac&Mora class and VF's in the Hinde–Demétrio class); VF's belonging to the Tweedie class with power VF's, VF's belonging to the Babel class and many others. Moreover, we show that if the canonical parameter space of the corresponding NEF is R (which is obviously the case if the support of the NEF is bounded), then the sample mean as an estimator of the mean cannot be further improved. This work presents an original constructive methodology and provides with constructive tools enabling to obtain explicit forms of the second order minimax estimators as well as the forms of the related weight functions. Our work establishes a substantial generalization of the results obtained so far in the literature. Illustrations of the resulting methods are provided and a simulation-based analysis is presented for the negative binomial case.

Léon Rosenfeld's pioneering steps toward a quantum theory of gravity

In an article published in 1930 Léon Rosenfeld invented a general Hamiltonian formalism that purported to realize general coordinate, local Lorentz, and U(1) symmetries as canonical phase space transformations. He applied the formalism to a q-number version of tetrad gravity in interaction with both the electromagnetic field and a spinorial Dirac electron matter field. His procedure predated by almost two decades the algorithms of Dirac and Bergmann, and with regard to internal (non-spacetime) symmetries is fully equivalent to them. Dirac was in fact already in 1932 familiar with Rosenfelds work, although as far as I can tell he never acknowledged in print his perhaps unconscious debt to Rosenfeld. I will review the general formalism, comparing and contrasting with the work of Dirac, Bergmann and his associates. Although Rosenfeld formulated a correct prescription for constructing the vanishing Hamiltonian generator of time evolution, he evidently did not succeed in carrying out the construction. Nor did he have the correct phase space generators of diffeomorphism-induced symmetry variations. He did not take into account that some of the Lagrangian symmetries are not projectable under the Legendre transformation to phase space.

PATH INTEGRAL QUANTIZATION OF SUPERSTRING

Motivated by the Hamilton–Jacobi approach of constrained systems, we analyze the classical structure of a four-dimensional superstring. The equations of motion for a singular system are obtained as total differential equations in many variables. The path integral quantization based on Hamilton–Jacobi approach is applied to quantize the system, and the integration is taken over the canonical phase space coordinates.

Contractibility of the maximal ideal space of algebras of measures in a half-space

Let H (n) be the canonical half space in R n , that is, H (n) = {(t1,...,tn) ∈ R n {0} | ∀j, (tj 6 0 and t1 = t2 = � � � = tj 1 = 0) ⇒ tj > 0} ∪ {0}. Let M(H (n) ) denote the Banach algebra of all complex Borel measures with support contained in H (n) , with the usual addition and scalar multiplication, and with convolution ∗, and the norm being the total variation of µ. It is shown that the maximal ideal space X(M(H (n) )) of M(H (n) ), equipped with the Gelfand topology, is contractible as a topological space. In particular, it follows that M(H (n) ) is a projective free ring. In fact, for all subalgebras R of M(H (n) ) that satisfy a certain mild condition, it is shown that the maximal ideal space X(R) of R is contractible. Several examples of such subalgebras are also given.

TheE(2)particle

Recently it has been advocated [A. G. Cohen and S. L. Glashow, Phys. Rev. Lett. 97, 021601 (2006)] that for describing nature within the minimal symmetry requirement, certain subgroups of the Lorentz group may play a fundamental role. One such group is $E(2)$ which induces a Lie algebraic noncommutative spacetime [M. M. Sheikh-Jabbari and A. Tureanu, Phys. Rev. Lett. 101, 261601 (2008); arXiv:0811.3670] where translation invariance is not fully maintained. We have constructed a consistent structure of noncommutative phase space for this system, and furthermore we have studied an appropriate point particle action on it. Interestingly, the Einstein dispersion relation ${p}^{2}={m}^{2}$ remains intact. The model is constructed by exploiting a dual canonical phase space following the scheme developed by us earlier [S. Ghosh and P. Pal, Phys. Rev. D 75, 105021 (2007)].

Using the Canonical Design Space to Obtain c-optimal Designs for the Quadratic Logistic Model

c-optimal designs for estimating the model parameters of the quadratic logistic regression model are considered. The designs are constructed via the canonical design space. It is shown that the number of design points varies between 1 and 4 depending on the parameter being estimated. Furthermore, formulae for finding the design points along with the corresponding design weights are derived.

Euler–Lagrange equation from nonlocal-in-time kinetic energy of nonconservative system

This Letter focuses on studying generalized Euler–Lagrange equation and Hamiltonian framework from nonlocal-in-time kinetic energy of nonconservative system. According to Suykens' approach, we extend his results and formulate some work related to the nonconservative system. With the Lagrangian and nonconservative force in nonlocal-in-time form, we obtain the higher order generalized Euler–Lagrange equation which leads to an extension of Newton's second law of motion. The Hamiltonian is studied in relation to the Lagrangian in the canonical phase space. Finally, the particle with nonconservative force case is studied and compared with quantum mechanical results. The extended equation gives a possible approach for understanding the connection between classical and quantum mechanics.

Feasibility of computer-aided identification of foraminiferal tests

Over the past two decades, several investigators have worked on computerized systems to accelerate the identification of foraminiferal tests (forams). Leading examples have focused on fully-automatic identification using neural networks and supervised learning. This paper introduces an alternative semi-automatic or computer-aided approach. Such an approach reduces the workload associated with foram identification without the challenges of training set collection and fully-automatic recognition. The proposed method begins by photographing a collection of specimens sprinkled on a microscopy slide. Segmented images are then mapped into a canonical space where position, rotation, and scale are normalized. Specimens are clustered based on image similarity in the canonical space. A specialist then identifies the clusters by inspecting representative templates. Experimental results show that the identification effort can be reduced by 35%, yet the accuracy remains comparable to when every specimen is individually identified. Further reduction of effort was prevented by the significant variability of illumination direction in the canonical images. These results encourage further work on a computer-aided approach to foram identification.

Affine Diffusion Processes: Theory and Applications

We revisit affine diffusion processes on general and on the canonical state space in particular. A detailed study of theoretic and applied aspects of this class of Markov processes is given. In particular, we derive admissibility conditions and provide a full proof of existence and uniqueness through stochastic invariance of the canonical state space. Existence of exponential moments and the full range of validity of the affine transform formula are established. This is applied to the pricing of bond and stock options, which is illustrated for the Vasicek Cox-Ingersoll-Ross and Heston Models.

Quantization of symplectic vector spaces over finite fields

In this paper, we construct a quantization functor, associating a complex vector space $\cal{H}(V)$ to a finite-dimensional symplectic vector space V over a finite field of odd characteristic. As a result, we obtain a canonical model for the Weil representation of the symplectic group Sp$(V )$. The main new technical result is a proof of a stronger form of the Stone–von Neumann property for the Heisenberg group $H(V )$. Our result answers, for the case of the Heisenberg group, a question of Kazhdan about the possible existence of a canonical vector space attached to a coadjoint orbit of a general unipotent group over finite field.

Phase-space-region operators and the Wigner function: Geometric constructions and tomography

Quasiprobability measures on a canonical phase space give rise through the action of Weyl's quantization map to operator-valued measures and, in particular, to region operators. Spectral properties, transformations, and general construction methods of such operators are investigated. Geometric trace-increasing maps of density operators are introduced for the construction of region operators associated with one-dimensional domains, as well as with two-dimensional shapes (segments, canonical polygons, lattices, etc.). Operational methods are developed that implement such maps in terms of unitary operations by introducing extensions of the original quantum system with ancillary spaces (qubits). Tomographic methods of reconstruction of the Wigner function based on the radon transform technique are derived by the construction methods for region operators. A Hamiltonian realization of the region operator associated with the radon transform is provided, together with physical interpretations.

Θ-TWISTED GRAVITY

We describe a theory of gravitation on canonical noncommutative space–times. The construction is based on θ-twisted general coordinate transformations and local Lorentz invariance.

Characterizing Cell-Decomposable Metrics

To a finite metric space $(X,d)$ one can associate the so called tight-span $T(d)$ of $d$, that is, a canonical metric space $(T(d),d_\infty)$ into which $(X,d)$ isometrically embeds and which may be thought of as the abstract convex hull of $(X,d)$. Amongst other applications, the tight-span of a finite metric space has been used to decompose and classify finite metrics, to solve instances of the server and multicommodity flow problems, and to perform evolutionary analyses of molecular data. To better understand the structure of $(T(d),d_\infty)$ the concept of a cell-decomposable metric was recently introduced, a metric whose associated tight-span can be decomposed into simpler tight-spans. Here we show that cell-decomposable metrics and totally split-decomposable metrics — a class of metrics commonly applied within phylogenetic analysis — are one and the same thing, and also provide some additional characterizations of such metrics.

Robust Noise Suppression Algorithm with the Kalman Filter Theory for White and Colored Disturbance

We propose a noise suppression algorithm with the Kalman filter theory. The algorithm aims to achieve robust noise suppression for the additive white and colored disturbance from the canonical state space models with (i) a state equation composed of the speech signal and (ii) an observation equation composed of the speech signal and additive noise. The remarkable features of the proposed algorithm are (1) applied to adaptive white and colored noises where the additive colored noise uses babble noise, (2) realization of high performance noise suppression without sacrificing high quality of the speech signal despite simple noise suppression using only the Kalman filter algorithm, while many conventional methods based on the Kalman filter theory usually perform the noise suppression using the parameter estimation algorithm of AR (auto-regressive) system and the Kalman filter algorithm. We show the effectiveness of the proposed method, which utilizes the Kalman filter theory for the proposed canonical state space model with the colored driving source, using numerical results and subjective evaluation results.

A Hull and White Formula for a General Stochastic Volatility Jump‐Diffusion Model with Applications to the Study of the Short‐Time Behavior of the Implied Volatility

We obtain a Hull and White type formula for a general jump‐diffusion stochastic volatility model, where the involved stochastic volatility process is correlated not only with the Brownian motion driving the asset price but also with the asset price jumps. Towards this end, we establish an anticipative Itô′s formula, using Malliavin calculus techniques for Lévy processes on the canonical space. As an application, we show that the dependence of the volatility process on the asset price jumps has no effect on the short‐time behavior of the at‐the‐money implied volatility skew.

Two Families of Self-adjoint Indecomposable Operators in an Orthomodular Space

Orthomodular spaces are the counterpart of Hilbert spaces for fields other than ℝ or ℂ. Both share numerous properties, foremost among them is the validity of the Projection theorem. Nevertheless in the study of bounded linear operators which started in [3], there appeared striking differences with the classical theory. In fact, in this paper we shall construct, on the canonical non-archimedean orthomodular space E of [5], two infinite families of self-adjoint bounded linear operators having no invariant closed subspaces other than the trivial ones. Spectrums of such operators contain exactly one point which, therefore, is not an eigenvalue. We also study relations between the subalgebras of bounded linear operators of E, which are the commutant of each of these operators, and the algebra 𝒜 studied in [3].

Schur-class multipliers on the Arveson space: De Branges–Rovnyak reproducing kernel spaces and commutative transfer-function realizations

An interesting and recently much studied generalization of the classical Schur class is the class of contractive operator-valued multipliers S ( λ ) for the reproducing kernel Hilbert space H ( k d ) on the unit ball B d ⊂ C d , where k d is the positive kernel k d ( λ , ζ ) = 1 / ( 1 − 〈 λ , ζ 〉 ) on B d . The reproducing kernel space H ( K S ) associated with the positive kernel K S ( λ , ζ ) = ( I − S ( λ ) S ( ζ ) ∗ ) ⋅ k d ( λ , ζ ) is a natural multivariable generalization of the classical de Branges–Rovnyak canonical model space. A special feature appearing in the multivariable case is that the space H ( K S ) in general may not be invariant under the adjoints M λ j ∗ of the multiplication operators M λ j : f ( λ ) ↦ λ j f ( λ ) on H ( k d ) . We show that invariance of H ( K S ) under M λ j ∗ for each j = 1 , … , d is equivalent to the existence of a realization for S ( λ ) of the form S ( λ ) = D + C ( I − λ 1 A 1 − ⋯ − λ d A d ) −1 ( λ 1 B 1 + ⋯ + λ d B d ) such that connecting operator U = [ A 1 B 1 ⋮ ⋮ A d B d C D ] has adjoint U ∗ which is isometric on a certain natural subspace ( U is “weakly coisometric”) and has the additional property that the state operators A 1 , … , A d pairwise commute; in this case one can take the state space to be the functional-model space H ( K S ) and the state operators A 1 , … , A d to be given by A j = M λ j ∗ | H ( K S ) (a de Branges–Rovnyak functional-model realization). We show that this special situation always occurs for the case of inner functions S (where the associated multiplication operator M S is a partial isometry), and that inner multipliers are characterized by the existence of such a realization such that the state operators A 1 , … , A d satisfy an additional stability property.

Least-square conformal brain mapping with spring energy

The human brain cortex is a highly convoluted sheet. Mapping of the cortical surface into a canonical coordinate space is an important tool for the study of the structure and function of the brain. Here, we present a technique based on least-square conformal mapping with spring energy for the mapping of the cortical surface. This method aims to reduce the metric and area distortion while maintaining the conformal map and computation efficiency. We demonstrate through numerical results that this method effectively controls metric and area distortion, and is computational efficient. This technique is particularly useful for fast visualization of the brain cortex.

Intercomparison of regional flood frequency estimation methods at ungauged sites for a Mexican case study

This paper presents an adaptation of some regional estimation approaches to tropical climates and a comparison of their performance on the basis of their application to data from the Balsas, Lerma and Pánuco River Basins located in Mexico. Four approaches are used in this study for the delineation of homogeneous regions: The first one is the hierarchical cluster analysis approach which leads to fixed hydrologic regions. The second one is the canonical correlation analysis (CCA) which allows the determination of hydrologic neighborhoods that are specific to the site of interest. The third one is a revised version of the canonical correlation analysis approach that is free of parameter optimization and which can be automated easily. Finally, the fourth one is the technique of canonical kriging which consists in interpolating hydrological variables over the canonical physiographical space. The methods based on the canonical correlation analysis approach provide also the basis for identifying the explanatory variables to be used during the step of regional estimation. Regional estimation is carried out based on a multiple regression approach. A data set of 29 stations from several Mexican River Basins in and around the Balsas region is used to show the advantages and weaknesses of each method and to demonstrate their usefulness in the context of regional flood quantile estimation. This study allows also to test the robustness of these methods through their application to a real world case study with a relatively limited number of stations. While all methods performed quite adequately, results indicate clearly the advantages of the neighborhood type of approach and the superiority of the canonical correlation analysis based methods. Results demonstrate that CCA-based methods lead to best performances overall. While hierarchical clustering seems generally to lead to less biased quantile estimates, the lowest root mean square error values are almost consistently obtained for the CCA-based methods. Results seem also to point out that all methods are quite sensitive to the quality and quantity of data available. The method of canonical kriging does not seem to be more sensitive to the database quality than the other two CCA-based methods.