Studying the effect and treatment of misspelled queries in Cross-Language Information Retrieval

In contrast with their monolingual counterparts, little attention has been paid to the effects that misspelled queries have on the performance of Cross-Language Information Retrieval (CLIR) systems. The present work makes a first attempt to fill this gap by extending our previous work on monolingual retrieval in order to study the impact that the progressive addition of misspellings to input queries has, this time, on the output of CLIR systems. Two approaches for dealing with this problem are analyzed in this paper. Firstly, the use of automatic spelling correction techniques for which, in turn, we consider two algorithms: the first one for the correction of isolated words and the second one for a correction based on the linguistic context of the misspelled word. The second approach to be studied is the use of character n-grams both as index terms and translation units, seeking to take advantage of their inherent robustness and language-independence. All these approaches have been tested on a from-Spanish-to-English CLIR system, that is, Spanish queries on English documents. Real, user-generated spelling errors have been used under a methodology that allows us to study the effectiveness of the different approaches to be tested and their behavior when confronted with different error rates. The results obtained show the great sensitiveness of classic word-based approaches to misspelled queries, although spelling correction techniques can mitigate such negative effects. On the other hand, the use of character n-grams provides great robustness against misspellings.     

The representation of radiation reaction in wave mechanics

It is well known that the wave mechanical ψ equation leads to the conclusion that the centroid of the wave mechanical electron should move according to the classical electrodynamic equation of motion in which, however, the terms representing what is commonly called radiation reaction are absent. If v is the velocity of the electron, the classical rate of change of momentum is $\text{md}\text{dt}\text{{}\text{v}\text{(}\text{I}\text{?}\text{v}{}^2\text{c}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{}}$. The equation of motion including radiation reaction terms may be regarded as obtainable by replacing this quantity by one obtained by operating upon it with the operator P^?1

$\text{P={I?}\text{α}{}_1\text{kd}\text{dt}\text{+}\text{α}{}_2\text{d}\text{dt}\text{(}\text{kd}\text{dt}\text{)?·}}{}^{\mathrm{?}}$

where α₁, α₂, etc., are constants and $\text{k = (}\text{I}\text{?}\text{v}{}^2\text{c}{}^2\text{)}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$. The main purpose of the paper is to show that if there be any relativistically invariant ψ equation which leads to the classical equation of motion without radiation reaction terms, then by replacing the vector and scalar potentials U and ? in that equation by P(U) and P(?), a relativistically invariant equation of motion will be obtained including the radiation reaction terms, provided that the $\text{d}\text{dt}$ in P be now regarded as $\text{?}\text{?t}$ + u · grad, where u is the velocity of the wave mechanical density distribution at a point. The purpose is to use the power to produce the equation of motion as a criterion for suggesting the proper modification of the ψ equation to apply in those cases where, on the classical theory, the electron would suffer great acceleration, as in ionization by rapidly moving corpuscles.     

Semiautomatic determination of citation relevancy: A preliminary report

Technology transfer, research and development and engineering projects frequently require in-depth literature reviews. These reviews are carried out using computerized, bibliographic data bases. The review and/or searching process involves keywords selected from data base thesauri. The search strategy is formulated to provide both breadth and depth of coverage and yields both relevant and nonrelevant citations. Experience indicates that about 10–20% of the citations are relevant. As a consequence, significant amounts of time are required to eliminate the nonrelevant citations. This paper describes statistically based, lexical association methods which can be employed to determine citation relevance. In particular, the searcher selects relevant terms from citation-derived indexes and this information along with lexical statistics is used to determine citation relevance. Preliminary results are encouraging with the techniques providing an effective concentration of relevant citations.     

Stabilization of carrier-frequency servomechanisms. III. Methods of obtaining required carrier phase-shift

In a servomechanism using a two-phase alternating current control motor, a 90° difference is required in the phases of the carrier-frequency voltages applied to the fixed and control windings. This part describes and compares various methods of obtaining the phase difference.The question of the possibility of a phase-shifting proportional-derivative parallel “T” is answered in the negative, by the result that in any parallel “T” transfer characteristic, if the quadratic factor in the numerator is of the proportional-derivative form at the correct resonant frequency, the amount of phase shift which may be obtained from the remaining portion of the transfer characteristic is less than are tan $\text{(}\text{2}\text{n}\text{)}$, where n is twice the carrier frequency divided by notch width. Thus for values of n high enough to have an appreciable stabilizing effect, the maximum obtainable intrinsic phase shift is negligible.In order to obtain a large phase shift it is necessary to add either a series input or a load impedance to the parallel “T,” or to use a phase-shifting network preceding or following the parallel “T.” Formulae and design charts are given for determination of the values of the components of phase lag networks.The method of calculation of tolerance requirements on the components, in terms of allowable deviation from the correct phase, is illustrated by an example of a phase lag network used in conjunction with a bridge “T” proportional-derivative network.     

Stabilization of carrier-frequency servomechanisms. II. Design formulae for proportional-derivative networks

In an alternating current servomechanism, the error is proportional to the modulation envelope of a modulated-carrier error signal. It is shown in part I that for stability and fidelity of the servo, it is highly desirable that the effect of the controller includes a proportional-derivative action on the modulation envelope. This action may be obtained with various forms of RC networks, including the parallel “T,” bridge “T,” and Wien Bridge forms.This part contains detailed design procedures and tables of values for the various types of proportional-derivative networks. Several forms of parallel “T” networks arise from the fact that there are five independent time constants in the network, while in order to realize the desired transfer characteristic it is necessary to impose only four conditions. It is indicated how the remaining degree of freedom may be used to obtain the most suitable input and output impedances for the source and load impedances with which the parallel “T” is to be used. The derivations for the parallel “T” formulae are given in an Appendix.Tolerance requirements on the components of parallel “T” and bridge “T” networks are derived. If ±1 per cent components are used at 60 cycles, the resonant frequency will lie between 56.4 and 63.6 cycles, and the notch width (rejection band width) will be within ±0.99 cps. of the correct value. In order to guarantee that the phase shift at 60 cycles is within ±10°, the percentage deviation of each part must be less than ($\text{9.0}\text{T}{}_{\mathrm{d}}\text{ω}{}_0$), where ω₀ is the carrier angular frequency, T_d the derivative time constant.     

Residue matrices and related properties in two-variable reactance functions

In this paper, the characterization of a two-variable reactance polynomial φ(λ,μ) is given in terms of the residue matrices of a single variable reactance matrix, Y(λ). Specificially, if Y(λ) is expressed in terms of its partial fraction as Y(λ)=λH_∞+Σ$\text{H}{}_{\mathrm{i}}\text{+jβ}{}_{\mathrm{i}}\text{λ+jω}{}_{\mathrm{i}}$+G where the residue matrices in general are p.s.d. Hermitian, then the ranks of these residue matrices are fixed in relation to the construction of φ(λ,μ) as the determinant of the two-variable reactance matrix μ1+Y(λ). Three theorems concerning these ranks—one each corresponding to the finite poles, poles at ∞ and the behaviour at λ=0 of Y(λ) are stated and proved. Several properties following from these theorems are studied. Also, implications of these theorems from a network theoretic point of view, like the minimum number of gyrators required to synthesize Y(λ) to yield the specific type of φ(λ,μ) etc., are studied. In the sequel, the concept of “generalized compact pole conditions” is introduced. Finally, these results are applied for the generation of two-variable reactance functions and matrices.     

Air flow separation at high speed

The resistance coefficient of a body moving in a fluid depends on Reynolds Number R, Mach Number M and the parameter $\text{gL}\text{U}{}^2$, which is customarily neglected in view of small weight of the air. Here L denotes a characteristic length; U denotes the body's speed of translation. The author points that dimensional deduction of this parameter does not limit it to the acceleration of gravity, and that the resistance coefficient is affected by the general acceleration to which the air is subjected. Evaluation of the acceleration of the air flowing about spheres puts this parameter in the form $\text{L}\text{R}$, where the characteristic length L is interpreted as the mean free molecular path. Large and small spheres were found to have widely different values of the pressure coefficient $\text{Δp}\text{q}$ for the same Reynolds Number or Mach Number. Here Δp denotes the difference in pressure between front stagnation point and the rear portion of the sphere, and q denotes the dynamic pressure. The plot of $\text{Δp}\text{q}$ against the parameter $\text{L}\text{R}$ removes this confusion. The low values of $\text{Δp}\text{q}$ are found to be associated with $\text{L}\text{R}$ below a certain critical value, and high values of $\text{Δp}\text{q}$ with $\text{L}\text{R}$ above the critical value, which apparently indicates the condition under which the flow separation takes place. Attention is called to the effect of air pressure on the separation as shown by the parameter $\text{L}\text{R}$, and its possible bearing on the drag in high altitude flying.     

Correspondence of document file structures to discipline structures

Online data bases might be more valuable to users if their structures more closely matched those of the disciplines represented by the data bases. To explore this concept, a structure for the field of tropical medicine was derived from the interrelationships of signs and symptoms of 37 tropical diseases. A similar structure was derived for the interrelationships of sign and symptom index terms applied to articles on these topical diseases in the MEDLINE data base. The poor correlation of the two structures led to the suggestion that rigorous indexing of articles with sign and symptom index terms or check tags would enhance the usefulness of the data base. Similar studies could be envisioned for other disciplines and data bases.     

Report on the work of the Bartol Research Foundation, 1933–1934

Using the velocity analyzer of Zartman with improved technique the combined velocity spectrum of Bi atoms and Bi₂ molecules was obtained at 827°, 851°, 875°, 899°, 922°, 947° C. From the spectral distribution curves the relative abundance of Bi atoms and Bi₂ molecules in the beams at the above temperatures could be determined to 1 per cent. The vapor pressure curve of Bi was obtained experimentally by the method of effusion and the values so obtained were combined with the degree of dissociation of the vapor as computed from the beams to give the heat of dissociation. The heat of dissociation was computed from the data, assuming the pressure to be given by the temperature of the crucible T_c. In calculating the heat of dissociation, the equilibrium temperature was taken as that of the slit chamber T_s which was 24° above T_c. The results of these calculations plotted with log₁₀K_p as ordinates against $\text{1}\text{T}{}_{\mathrm{s}}$ give a straight line whose slope yields the value of the heat of dissociation as 77,100±1200 calories. The curves for the distribution of velocities observed and computed on the assumption of a given ratio of Bi atoms to Bi₂ molecules in the beam were compared in an attempt to test the law of distribution of velocities. On the high velocity side agreement in two curves was obtained within the limits of experimental accuracy. On the low velocity side important deviations were noted of such a sort that the observed curves below a velocity $\text{α}\text{2}$, (α is the most probable velocity) gave more molecules than the theory demanded. Other deviations were observed on some of the runs taken with a fourth slit in which a deficiency of molecules was observed between velocities of .75α and $\text{α}\text{2}$. This deviation was probably due to a warping of the fourth slit carriage due to heat. The nature of the variation at velocities less than $\text{α}\text{2}$ indicated the presence of molecules of greater mass than Bi₂ in the beam and at the lower temperatures a distinct peak corresponding to Bi₈ molecules was observed which were present to less than 2 per cent. The vapor pressure curve for Bi was determined by least square reduction of the observed points to be given by $\text{log}{}_{10}\text{P = ? 52.23 ×}\text{195.26}\text{T}\text{+ 8.56}$ between 1100° and 1220° abs. It lies very close to the extrapolated curve given in the International Critical Tables.     

Accurate approximate solutions to oscillatory problems with perturbing singular damping

In this paper we attempt to obtain approximate solutions of improved accuracy for a class of differential equations of the form

$\text{d}{}^2\text{y}\text{d}\text{x}{}^2\text{+εμ(x)}\text{d}\text{y}\text{d}\text{x}\text{+ω}{}^2{}_{\mathrm{c}}\text{y = 0}$

, where ε is a real parameter less than unity, ω_c is a positive real constant of order unity and μ(x) is a singular function of x in the region of interest. It does not appear to be possible to find a general analytic expression for the error estimate of the approximate solution. For the case μ(x) = x^?2, however, it is shown that the approximate solution is accurate to 0(ε²), as x → 0^? from negative values, by comparing it with the numerically integrated solution. For the same case, the approximate solution is orders of magnitude more accurate than Poincaré's first-order perturbation solution, which is accurate to $\text{0(}\text{ε}{}^2\text{ln}\text{|x|}\text{|x|}\text{)}$ as x → 0^?. This work arose in search of analytic solutions to a linearized form of the restricted three-body problem.     

Relationship between index term specificity and relevance judgment

Concurrent concepts of specificity are discussed and differentiated from each other to investigate the relationship between index term specificity and users’ relevance judgments. The identified concepts are term-document specificity, hierarchical specificity, statement specificity, and posting specificity. Among them, term-document specificity, which is a relationship between an index term and the document indexed with the term, is regarded as a fruitful research area. In an experiment involving three searches with 175 retrieved documents from 356 matched index terms, the impact of specificity on relevance judgments is analyzed and found to be statistically significant. Implications for index practice and for future research are discussed.     

An experimental investigation of forced vibrations

The solution of the differential equation y″ + 2Ry′ + n²y = E cos pt is written in a new form which clearly exhibits many important facts thus far overlooked by theoretical and experimental investigators. Writing s = n ? p, and Δn = n ? √n² ? R², it is found: (a) When s ≠ Δn, there are “beats,” and the first “beat” maximum is greater than any later maximum while the first “beat” minimum is less than any later “beat” minimum. The “beat” frequency is $\text{(s ?}\text{Δ}\text{n)}\text{2π}$. (b) When n² ? p² = R², there are no “beats,” and the resultant amplitude grows monotonically from zero to the amplitude of the forced vibration, (c) At resonance, when n = p, we still have maxima which occur with a frequency $\text{Δ}\text{n}\text{2π}$ in a damped system. (d) The absence of “beats” is neither a sufficient nor a necessary condition for resonance in a damped system.In the experimental investigation the upper extremity of a simple pendulum was moved in simple harmonic motion and photographic records obtained of the motion of the pendulum bob. Different degrees of damping were used, ranging from very small to critical.The experimental results are in excellent agreement with theory.     

Perturbation solutions of the Carson–Cambi equation

The periodic differential equation (1+ε cos t)y&#x030B; + py = 0, hereby termed the Carson–Cambi equation, is the simplest second-order differential equation having a periodic coefficient associated with the second derivative. Provided |ε|<1, which is the case we examine, then the differential equation is a Hill's equation and thus possesses regions of stability and instability in the p–ε plane. Ordinary perturbation theory is employed to obtain the stable (periodic) solutions to ε³. Two-timing theory is employed to obtain solutions for values of k near the critical points k = ±$\text{1}\text{2}$, ±$\text{3}\text{2}$, ±$\text{5}\text{2}$. Three-timing is employed to extend the solution near k = ±$\text{1}\text{2}$. The solutions of the Carson–Cambi equation are compared with the solutions of the corresponding Mathieu equation.     

On the compression of search trees

Let X=_x1,_x2,…,_xn$X=x_1\text{,}{x}_2\text{,}\dots \text{,}{x}_n$ be a sequence of non-decreasing integer values. Storing a compressed representation of X that supports access and search is a problem that occurs in many domains. The most common solution to this problem uses a linear list and encodes the differences between consecutive values with encodings that favor small numbers. This solution includes additional information (i.e. samples) to support efficient searching on the encoded values. We introduce a completely different alternative that achieves compression by encoding the differences in a search tree. Our proposal has many applications, such as the representation of posting lists, geographic data, sparse bitmaps, and compressed suffix arrays, to name just a few. The structure is practical and we provide an experimental evaluation to show that it is competitive with the existing techniques.     

End effects on the flow of heat,mass or electrical energy through a cylindrical rod

End effects on the flow of heat, mass or electrical energy through a cylindrical rod were investigated analytically. Three of the eight analytical solutions were evaluated on a $\text{360}\text{91}$ computer and compared with the results of a numerical analysis package dubbed “Heating III” to show that both compared favorably.Platinum and Hastelloy X rods were subjected to an electrical current applied via two electrodes, one covering one end and the application of the other being thesubject of this investigation. End effects based on voltage deviations of one part in a thousand or more were found to extend for a length to diameter ratio ranging from 0·6 to 1·9 depending upon whether the small electrode position being investigated was at the center of the end or on the periphery of the end. Calculated results from Heating III showed excellent agreement with the experimental results.In addition to their reported applications, the analytical solutions represent a contribution to a neglected area of applied mathematical physics and as such should prove equally useful in other areas that are dynamically analogous. Also the discontinuous infinite integral technique of solution has proven to be a very powerful one.     

Angular region: a measure of underdamped behavior

The natural modes of an underdamped dynamical system are given by the characteristic numbers of the quadratic operator pencil

$\text{P(s)=s}{}^2\text{I+sB+A,}$

where the operator A depends on the dissipative and reactive elements of the system, while B depends solely on the reactive elements. The operator P(s) for every applied stimulus vector signal x must satisfy:

$\text{(Bx,x)}{}^2\text{<4(Ax,x).}$

A measure of underdamped behaviour is suggested by predetermining an angular region |φ| containing all natural modes of the system,

$\text{|}\text{tan}\text{φ|?}\text{[4(Ax,x)?(Bx,x)}{}^2\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(Bx,x)}\text{.}$

When a comparison between positive operators A and B is available, say B²=KA, then

$\text{|}\text{tan}\text{φ|?}\text{√(4?K}{}^2\text{)}\text{K}\text{.}$

The paper is motivated by Duffin-Krein-Gohberg's earlier mathematical contributions.     

The reflection of hydrogen atoms from lithium fluoride

The paper describes the phenomena associated with the reflection of a sharply defined beam of hydrogen atoms from a crystal of LiF. Of primary interest is the fact that the atoms show interference effects in agreement with the wave mechanics theory and plane grating diffraction patterns are photographed. Evidence of the thermal agitation of the surface ions is obtained from the diffuse reflection with surrounds the specular beam.The Schrödinger wave equation for the motion of a free particle of mass m is

$\text{▽}{}^2\text{ψ ?}\text{4πmi}\text{h}\text{?ψ}\text{?t}\text{= 0}\text{(I)}$

. The solution of this equation corresponding to the kinetic energy $\text{mv}{}^2\text{2}$ is

where

$\text{v }\text{mv}{}^2\text{2}\text{and}\text{σ}\text{mv}\text{h}$

. The motion of such a particle should have the characteristics of a plane wave of frequency ν and wave-length $\text{λ =}\text{1}\text{σ}$. The experiments of various investigators¹ have shown the validity of the wave theory of the motion of the free electron and have given values of the wave-length in agreement with the theory.The free motion of atoms, ions and molecules should likewise have wave characteristics. In the case of the hydrogen atom, as the simplest example, the complete wave equation may be written in the form

$\text{I}\text{m}\text{▽}{}^2\text{x,y,zψ +}\text{I}\text{μ}\text{▽}{}^2\text{η,μζψ ?}\text{8π}{}^2\text{μ?ψ}\text{mh}{}^2\text{η}{}^2\text{+ μ}{}^2\text{+ ζ}{}^2$

$\text{?}\text{4πi}\text{h}\text{?ψ}\text{?t}\text{= 0,}\text{(3)}$

where x, y, z, are the coördinates of the center of mass of the atom and ξ, η, ζ the coördinates of the electron with respect to the center of mass. If m_? and m₊ are the masses of electron and proton, m and μ have the significance

$\text{m = m}{}_{\mathrm{?}}\text{+ m}{}_{\mathrm{+}}\text{and}\text{I}\text{μ}\text{=}\text{I}\text{m}{}_{\mathrm{?}}\text{+}\text{I}\text{m}{}_{\mathrm{+}}$

. Equation (3) is solved by

$\text{ψ = U}{}_1\text{(x,y,z) U}{}_2\text{(η, ν ζ) ?}{}^{\mathrm{<mtext>2\pi iEt</mtext><mtext>h</mtext>}}$

, where E may have a continuous set of values and represents the total energy. U₁ and U₂ must satisfy the equations

$\text{▽}{}_1{}^2\text{U}{}_1\text{+}\text{8π}{}^2\text{mβU}{}_1\text{h}{}^2\text{= 0,}\text{(4)}$

and

$\text{▽}{}_2{}^2\text{U}{}_2\text{+}\text{8π}{}^2\text{μ}\text{h}{}^2\text{(α ?}\text{μ?}\text{m}\text{η}{}^2\text{+ ν}{}^2\text{+ ζ}{}^2\text{)}\text{U}{}_2\text{= 0}\text{(5)}$

, where

$\text{α + β + E}$

.