Theoretic Expressions Research Articles

Identification and Lossy Reconstruction in Noisy Databases

A high-dimensional database system is studied where the noisy versions of the underlying feature vectors are observed in both the enrollment and query phases. The noisy observations are compressed before being stored in the database, and the user wishes to both identify the correct entry corresponding to the noisy query vector and reconstruct the original feature vector within a desired distortion level. A fundamental capacity-storage-distortion tradeoff is identified for this system in the form of single-letter information theoretic expressions. The relation of this problem to the classical Wyner-Ziv rate-distortion problem is shown, where the noisy query vector acts as the correlated side information available only in the lossy reconstruction of the feature vector.

Frequency estimation of undersampled sinusoidal signal based on chinese remainder theorem

Frequency estimation based on the reconstruction algorithm of the Chinese remainder theorem(CRT) is one of the frontier focuses in the fields of signal processing, electromagnetism, and optics etc. Howerver, the existing studies can only realize a rough frequency estimation of complex exponential signals. Hence this paper generalizes the CRT-based frequency reconstruction from a rough frequency estimation of complex exponential signals to the accurate frequency estimation of sinusoidal signals. The procedure of the proposed estimation scheme is as follows: (1) Detect zero crossing point on the original high-frequency sinusoidal waveform so as to determine the ideal phase information; (2) implement fast Fourier transform(FFT) to each path's undersampled signal, and then use Candan estimator to correct the frequencies at the peak FFT spectral bins so that the frequency biases can be extracted to realize phase correction; (3) use the proposed classification method based on phase features to screen the corrected remainders; (4)substitute the filtered frequency remainders into the closed-form robust Chinese remainder theorem to obtain the high-accuracy frequency estimation of the original signal. Additionally, this paper also deduces the theoretic expressions of the frequency estimation variance, which is also verified through numerical simulation. And the experimental results also reflect that the proposed scheme possesses high precision and high robustness to noise.

The Transient Process Analyse of the Circuit with a Resistance-Capacitance Branch

In this paper the auther made deep research on the principle and the transient process of resistance-capacitance over voltage protection circuit in different working condition during the electric locomotive running, and based on the analysis of the Circuit Transient Process, obtained the theoretic expressions of the voltage and the current of the resistance and the expression of the energy absorbed by the resistance during the working process. The research offers theoretical basis for design and improvement of the resistance-capacitance protection circuit.

Downlink performance of distributed antenna systems in multicell environment

In this study, the authors investigate the downlink performance of distributed antenna systems (DAS) in multicell environment with blanket transmission. In most existing works, the interference plus noise is treated as Gaussian random variable with fixed variance by the central limit theorem. However, doing this will ignore the effect of the short-term fading on interference that is called as restrictive condition. To avoid the restrictive condition, the authors consider the variance of interference plus noise as a random variable with changeable variance that is influenced by the short-term fading when propagation pathloss and transmit power are given. From the perspective of information theoretic, the closed-form and approximate analytical expressions of downlink achievable throughput, outage probability and average bit error rate in the cellular system are derived for no-shadowing and shadowing scenarios, respectively. Extensive simulation results validate the theoretical analysis and demonstrate that the system performances can be significantly improved for cell-edge users. Moreover, the proposed analytical method can obtain more accurate system performances.

Graph-Theoretic Analysis and Synthesis of Relative Sensing Networks

This work provides a general framework for the analysis and synthesis of a class of relative sensing networks (RSNs) in the context of its <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. We consider RSNs with homogeneous and heterogeneous agent dynamics. In both cases, explicit graph theoretic expressions and bounds for the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance are derived. The <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> performance turns out to be a function of the number of edges in the graph, whereas the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance is structure dependent and related to the spectral radius of the graph Laplacian. The analysis results are then used to develop synthesis methods for RSNs. An optimal topology is designed using the Kruskal's Algorithm for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> performance, and a semi-definite program for the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance of uncertain RSNs.

Effective oscillator strengths and transition energies for the hydrogen molecular ion

The variation-perturbation method using finite basis sets is applied to the hydrogen molecular ion H+ 2. Sets of ‘pseudostates’ consisting of N pairs of effective oscillator strengths and transition energies are determined and tabulations with N = 6, for both parallel and perpendicular electric dipole transitions, are presented over a range of internuclear distances. Various oscillator strength sums, including those involving the logarithms of the transition energies, and Rayleigh-Schrodinger perturbation theoretic expressions are evaluated. In particular, the isotropic and anisotropic components of the dipole-dipole dispersion energy between H+ 2 and each of a number of atoms, H2, and N2 are determined using published pseudostates.

Meson mass splittings in the nonrelativistic model.

Mass splittings between isodoublet meson pairs and between $0^{-}$ and $1^{-}$ mesons of the same valence quark content are computed in a detailed nonrelativistic model. The field theoretic expressions for such splittings are shown to reduce to kinematic and Breit-Fermi terms in the nonrelativistic limit. Algebraic results thus obtained are applied to the specific case of the linear-plus-Coulomb potential, with resultant numbers compared to experiment.

A Historical query language

A historical query language, hquel, is designed as a minimal extension to quel, which is the query language of the database management system ingres. In the underlying data model, each attribute value is stored along with the time interval over which the value is valid. hquel includes new range declarations, set theoretic expressions, and conditions. Aggregate functions of quel are also extended for historical data. A new clause, “when”, is added to aggregate function definition to make aggregation over the time dimension easier. Semantics of time is embedded within the quel semantics without any major modifications. hquel also manipulates set-valued attributes in N1NF relations.

Set operations on polyhedra using binary space partitioning trees

We introduce a new representation for polyhedra by showing how Binary Space Partitioning Trees (BSP trees) can be used to represent regular sets. We then show how they may be used in evaluating set operations on polyhedra. The BSP tree is a binary tree representing a recursive partitioning of d-space by (sub-)hyperplanes, for any dimension d. Their previous application to computer graphics has been to organize an arbitrary set of polygons so that a fast solution to the visible surface problem could be obtained. We retain this property (in 3D) and show how BSP trees can also provide an exact representation of arbitrary polyhedra of any dimension. Conversion from a boundary representation (B-reps) of polyhedra to a BSP tree representation is described. This technique leads to a new method for evaluating arbitrary set theoretic (boolean) expressions on B-reps, represented as a CSG tree, producing a BSP tree as the result. Results from our language-driven implmentation of this CSG evaluator are discussed. Finally, we show how to modify a BSP tree to represent the result of a set operation between the BSP tree and a B-rep. We describe the embodiment of this approach in an interactive 3D object design program that allows incremental modification of an object with a tool. Placement of the tool, selection of views, and performance of the set operation are all performed at interactive speeds for modestly complex objects.

Entropy effects in thermal desorption

The entropy of thermal desorption has been calculated for a single adatom on a harmonic linear chain using information theoretic expressions for the entropy. As a transition state for the process, in the context of absolute rate theory, cannot be specified, the entropy has been calculated for a direct transition to an unrelaxed desorbed state. The resultant entropy changes are shown to be dominated by the isothermal term, which is a simple function of the frequency change and the mass ratio of the system. Deviations from isothermal behaviour are caused by local density effects and are strongly a function of the activation energy of the process. Relaxation of the distribution functions then reduces the entropy towards the isothermal value. It is shown that the order of magnitude of the isothermal entropy change in one dimension is between 0 and −4 R, depending on the masses and force constants. Dimensionality arguments suggest that in a real three-dimensional system the isothermal entropy changes will be approximately three times these values (i.e. 0 to −12 R).

Some Observations Concerning Formal Differentiation of Set Theoretic Expressions

Some Observations Concerning Formal Differentiation of Set Theoretic Expressions

Groups with parametric exponents

1. Introduction. Elsewhere(2) we consider the problem of characterizing all the solutions x, in a free group on generators a,, a2, . . *, a., of a given equation w(x, a,, a2, , a.) = 1. The totality of solutions can be described as the set of all values assumed by a certain finite set of group theoretic expressions upon substituting integers for certain parameters appearing in these expressions as exponents. As a trivial example, the solutions of x-lajlxa1= 1 are all values assumed by a' as v runs through the integers. The general result, and our method of obtaining it, has led us to the study of such expressions, or words, that contain certain parameters Pi, P2, * * *, Vd as exponents. These words may be taken in a natural way as representing elements of a group G that admits additional algebraic operations of raising an element g of G to an exponent a, where a is any element of the ring Z[P1, P2, * * *, Pd] of all polynomials in indeterminates in Pi, P2, * * *, Pv with integer coefficients. More generally, if X is any associative ring with 1, we call a group G an X-group if it is equipped with additional operations g-_g for each a in X, subject to the following axioms: g' = g, g (a+:) = gag 3, g (a0) = (g a) a g(hg) a = (gh) ag. We hasten to note that if n is an integer, the axioms imply g n = gn, so that we may omit all dots. Like the power maps, g y+gn, these operations are not required to define endomorphisms: we do not require that (gh)a=gah/a. The last axiom requires that, like the power maps, these operations commute with all inner automorphisms: (g-'hg) a = g-lhag. The appropriateness of these axioms to our purpose is demonstrated by the fact, proved below, that for X=Z[Pl, V2, P, Pd], a w in the letters a,, a2, * * *, a. containing parameters Pi, P2, * d, assumes the value 1 in the free group on a1, a2, * * *, ar under all substitutions for the parameters if and only if it reduces to the empty word 1 by virtue of the given axioms. The main result of this paper is the solution of an extended problem for free X-groups, X=Z[Pl, P2, * * *, Pd]. An effective process is exhibited whereby, given a w, as above, an element a in X is determined such that, under any substitution of integers for the vi, co assumes the value 1 if and only if a assumes the value 0.